 SATELLITE SCHEDULING METHOD AND PROCESSING SYSTEM FOR EARTH OBSERVATION SYSTEMS, INCLUDING ONE OR MO
专利摘要:
refers to a satellite scheduling method (1) including: (a) producing scheduling plans (105), based on task-related input requests to be performed within a given period by one or more remote sensing satellites wherein, for each of said initial scheduling plans, respective tasks are scheduled, which do not conflict with each other in the time and use of satellite resources from the remote sensing satellite (s), with each of the tasks to be performed being scheduled in at least one of the initial scheduling plans; (b) apply genetic algorithm-based processing (108) to initial scheduling plans, producing an optimized genetic algorithm-based plan, and comply with certain satellite resource constraints, tasks to be performed, and determined period of time; and (c) applying simulated annealing-based processing (109) to the genetic algorithm-based scheduling plan, producing a simulated annealing-based scheduling plan that conforms to the constraints, and where a greater number of tasks are scheduled than in the scheduling plan based on genetic algorithms. 公开号:BR102018010426A2 申请号:R102018010426-8 申请日:2018-05-23 公开日:2019-03-26 发明作者:Federico BUNKHEILA；Christian Circi 申请人:Telespazio S.P.A.； IPC主号:
专利说明:
INNOVATIVE METHOD FOR SATELLITE SCHEDULING BASED ON GENETIC ALGORITHMS AND SIMULATED RINGING, AND RELATED MISSION PLANNER PRIORITY CLAIM [001] This application claims the priority of Italian patent application No. 102017000056428 filed on May 24, 2017, the content of which is incorporated herein by reference. TECHNICAL FIELD OF THE INVENTION [002] The present invention relates to Earth Observation (EO - Earth Observatiorí) based on satellite remote sensing systems. In particular, the present invention provides an optimized solution for the so-called Satellite Scheduling Problem (SSP - Satellite Schedu / ing Prob / em), which derives from the classic Resource Constrained Project Scheduling Problem (RCPSP) Prob / em). STATE OF THE ART [003] As is known, satellite remote sensing is based mainly on the use of two types of sensors: - passive sensors, such as optical and infrared sensors, that generally detect electromagnetic radiation emitted and reflected by the Earth's surface (in particular, reflected solar electromagnetic radiation); and - active sensors, such as Synthetic Aperture Rada rs (SARs) and Light Detection And Ranging (LiDAR) sensors, which generally illuminate the Earth's surface by emitting predefined electromagnetic radiation, and then detect backscattered electromagnetic radiation. [004] In this regard, it is worth noting that, below, for the sake of descriptive simplicity, the generic terminologies acquiring an image, acquisition task, and even acquisition (and related synonyms, such as scanning), will be used to denote the satellite activities necessary to obtain an image of the Earth's surface (for example, pointing and acquisition maneuvers to scan a given area of the Earth's surface), based on the use of a Petition 870180071811, of 16/08/2018, p. 112/186 2/56 active or passive board (such as a SAR or an optical sensor). [005] Currently, the design of terrestrial segments for EO satellites is carried out looking for an automation of the processes, in order to make them more efficient and accessible, and with a high performance. In particular, an automatic scheduling of satellite resources to satisfy the requested acquisition tasks would allow to fulfill the objectives of the fundamental mission. In this context, the main requirements relate to the satisfaction of operational performance, together with the continuity of the chronology of operations. For this reason, the way in which automation can be satisfactory is an exciting task, which is currently being deeply investigated in the aerospace sector. [006] In the past, remote sensing missions based on satellites having a fixed attitude were generally designed to explore repeated strips of land, characterized by certain revisit times (typically equal to a predefined number of nodal Earth days). To reduce this limit, the so-called agile satellites, which are characterized by high maneuverability and precise aiming, are currently employed to provide better results in missions that require rapid image retrieval. In fact, with each orbit pass, agile satellites potentially have the ability to acquire images over a wider area of the Earth's surface than traditional satellites. On the other hand, the advantages are offset by an increase in the complexity of managing acquisition tasks, and by the need to introduce optimization processes to satisfy mission objectives and avoid latencies and losses. All of these aspects must be taken into account in the design of the modern Mission Planners (MPs - Mission P / anners) of Terrestrial Segments for new generation satellites. [007] As is known, the SSP (which, as explained above, derives from the classic RCPSP) requires an appropriate search for the best solutions in planning the tasks necessary for the acquisition activities, resulting from the combination of difficult combinatorial optimization problems. [008] With reference to the computational complexity theory, the RCPSP is a generalization of some difficult polynomial problems strongly non-deterministic Petition 870180071811, of 16/08/2018, p. 113/186 3/56 (NP-Hard) well known. This implies that: - an efficient (ie, polynomial) algorithm is not likely to exist for the optimal resolution of the RCPSP; and - general purpose solvers, which do not exploit the particular combinatorial structure of the RCPSP and do not take into account its complexity within their resolution strategies, cannot deal with large instances. [009] For a detailed description of the state of the art related to the SSP and RCPSP, reference will be made below to: - C.S. Sharma, Review: Practical Handbook of Genetic Algorithms by Lance Chambers (Review: Lance Chambers Practical Handbook of Genetic Algorithms), The Mathematical Gazette, vol. 81, No. 491, p. 346 to 348, July 1997, d.o.i .: 10.2307 / 3619253 (referred to below as Refl); - A. Sadegheih, Scheduling problem using genetic aigorithm, Simu / atedAnneaiing and the effects of parameter vaiues on GA performance (Scheduling problems using genetic algorithm, Simulated Ringing and the effects of parameter values on the performance of Genetic Algorithms, Appiied Mathematical Modeiiing ( Applied Mathematical Modeling), Vol. 30, No. 2, pp. 147 to 154, February 2006, doi: 10.1016 / j.apm.2005.03.017 (referred to below as Ref2); - MB Wall, A Genetic Aigorithm for Resource Constrained Scheduling, a doctoral thesis for a graduate degree in Doctor of Philosophy in Mechanical Engineering, at the Massachusetts Institute of Technology (MIT - Massachusetts Institute of Technoiogy), 1996 (referred to below as Ref3); - G. Syswerda, A Study of Reproduction in Generational and Steady State Genetic Algorithms, Foundations of Genetic Algorithms, p. 94 to 101, 1991, d.o.i .: 10.1016 / b978-0-08-050684-5.50009-4 (referred to below as Ref4); - IN. Goldberg, Making Genetic Algorithms Fy (The Making of Innovation), The Design of Innovation, Vol. 7 of the Genetic series Petition 870180071811, of 16/08/2018, p. 114/186 4/56 A / gorithms and Evolutionary Computation (^ 'Genetic Algorithms and Evolutionary Computation), p. 11 to 24, 2002 d.o.i .: 10.1007 / 978-1-4757-3643-4_2 (referred to below as Ref5); - RJ. Mitchell, B. Chambers, A.P. Anderson, Arraypattern synthesís in the compíexplane optimized by a genetic a / gorthm ('Synthesis of arrangement pattern in the complex plane optimized by a genetic algorithm), Eíectronics Letters, Vol. 32, No. 20, p. 1843 to 1845, 1996, d.o.i .: 10.1049 / el: 19961255 (referred to below as Ref6); - J.H. Holland, Genetic Aígorithms (Genetic Algorithms), Scientific American (Scientific American), Vol. 267, n ° 1, pgs. 66 to 72, 1992, d.o.i .: 10.1038 / scientificamerican0792-66 (referred to below as Ref7); - DE de Jong, A. Bucci, DECA: Dimension Extracting Coevoíutionary Aígorithm (Algorithm Co-evolutionary dimension extraction), Proceedings of the 8th Annual Conference on Evolutionary Computation and Genetics - GECCO'06, pp. 313 to 320, Seattle, Washington, USA, July 8-12, 2006, doi: 10.1145 / 1143997.1144056 (referred to below as Ref8); - T. Murata, H. Ishibuchi, H. Tanaka, Genetic aigorithms for fiowshop scheduiing probiems (Genetic algorithms for flow scheduling problems), Computers & Industrial Engineering, vol. 30, No. 4, pgs. 1061 to 1071, 1996, d.o.i .: 10.1016 / 0360-8352 (96) 00053-8 (referred to below as Ref9); - J.F. Gonçalves, J.J. de Magalhães Mendes, M.G.C. Resende, A hybridgenetic aigorithm for the job shop scheduiing probiem (A hybrid genetic algorithm for the discontinuous production scheduling problem), European Journal of Operationai Research, vol. 167, No. 1, pgs. 77 to 95, 2005, d.o.i .: 10.1016 / j.ejor.2004.03.012 (referred to below as Ref10); - - Globus A., J. Crawford, J. Lohn, A. Pryor, A Comparison of Techniques for observing earth scheduiing sateiiites (A comparison of techniques for scheduling Earth observation satellites), the 16th conference on Innovative Applications Procedures Artificial Intelligence - IAAI'04, p. 836 to 843, San Jose, California, July 25-29 Petition 870180071811, of 16/08/2018, p. 115/186 5/56, 2004 (referred to below as Ref11); - H. Yu, H. Fang, P. Yao, Y. Yuan, A combined genetic algorithm / Simulated Annealing algorithm for large scaie system energy integratiod '(A combined genetic algorithm / Simulated Ringing algorithm for energy integration of large systems ), Computers and Chemical Engineering, vol. 24, No. 8, pgs. 2023 to 2035, 2000, d.o.i .: 10.1016 / s0098-1354 (00) 00601-3 (referred to below as Ref12); - AM Zain, H. Haron, S. Sharif, Integration of SimuiatedAnnealing andgeneticgorithm to estimate optimal soiutions for minimizing surface roughness in end milling Ti-6AL-4V (Integration of Simulated and Genetic Ringing algorithm to estimate optimal solutions to minimize the roughness of surface in Ti-6AL-4V final milling), International Journal of Computer Integrated Manufacturing, vol. 24, No. 6, p. 574 to 592, 2011, d.o.i .: 10.1080 / 0951192x.2011.566629 (referred to below as Ref13); - K. Lian, C. Zhang, X. Li, L. Gao, An Effective Hybrid Genetic Simuiated Annealing Algorithm for Process Pianning Probiem (Fifth Conference Simulated Genetic Ringing Algorithm for the Process Planning Problem), Fifth Conference Procedures International on Natural Computing - ICNC'09, vol. 5, pgs. 367 to 373, August 14 to 16, 2009, d.o.i .: 10.1109 / icnc.2009.689 (referred to below as Ref14); - C. Liu, W. Wan, Y. Wu, Image based reconstruction using hybrid optimization of simuiated annealing and genetic algorithm (Procedures of the hybrid optimization of genetic algorithm and simulated ringing), Procedures of the First ACM Summit / SIGEVO on Evolutionary Computing and Genetics - GEC'09, p. 875 to 878, Shanghai, China, June 12 to 14, 2009, d.o.i .: 10.1145 / 1543834.1543964 (referred to below as Ref15); - A. Tamilarasi, TA Kumar, An enhancedgenetic algorithm with simuiated annealing for job-shop scheduiing, The International Journal of Engineering, Science and Technoiogy (International Journal of Engineering, Science and Technology) Technology), vol. Petition 870180071811, of 16/08/2018, p. 116/186 6/56 2, No. 1, pgs. 144 to 151, 2010, d.o.i .: 10.4314 / ijest.v2i1.59105 (referred to below as Ref16); - RR Thamilselvan, P. Balasubramanie, Integrating Genetic Algorithm, Tabu Search and Simuiated Annealing For Job Shop Scheduling Probiern '. ications (International Journal of Computer Applications), Vol. 48, n ° 5, p. 42 to 54, June 2012, d.o.i .: 10.5120 / 7348-0283 (referred to below as Ref17); and - V. Kolici, X. Herrero, F. Xhafa, L. Barolli, Local Search and Genetic Aigorithms for Sateiiite Scheduling Probiems (Eight International Broadband and Wireless Computing Genetic Algorithms) , Communication and Applications (BWCCA - Broadband and Wireiess Computing, Communication and App / ications), October 28 to 30, 2013, doi: 10.1109 / bwcca.2013.58 (referred to below as Ref18). [010] As is known, many decision-making and RCPSP problems can be formulated as two-level programming models (single-purpose or multi-objective), which are intrinsically non-convex, making it difficult to find the optimal global solution. In comparison with previous heuristic algorithms, Evolutionary Algorithms (EAs - Evoiutionary Aigorithms) are much simpler in principle and more efficient in applications. In fact, many applications involve combining a heuristic algorithm with multi-objective optimization, in order to find a set of optimal solutions (at least one solution). This can be made even simpler by means of EAs than with multi-objective hill climbing strategies, because EAs operate with a population of solutions rather than a single solution. A multi-objective approach returns intrinsically, efficiently and simultaneously a number of solutions that can be attributed to the parallelism and globality of EAs (in this context, reference can be made, for example, to Ref1), and this characteristic is independent of the type approach adopted in the multi-objective cost functions (Pareto efficiency / optimal, or not). Petition 870180071811, of 16/08/2018, p. 117/186 7/56 [011] Recently, EAs have been applied in an attempt to solve scheduling problems, providing conflicting results. For example, in Ref2, the use of Genetic Algorithms (GAs) to optimize production schedules provides a general purpose solution to the scheduling problem, where the peculiarities of any particular scenario are taken into account in a function of without disturbing the logic of the standard optimization routine. [012] However, as stated in Ref3, GA does not perform well on problems where resources are severely restricted. In fact, EAs are not strong enough to meet the requested optimization performances. This is explained by the fact that a smaller population size tends to focus on higher quality solutions, relatively faster in evolution, and so GA tends to suffer from a slight case of premature convergence (here, reference can be made for example to Ref4). Thus, GAs have been considered inadequate to provide a convergence to a satisfactory solution in the SSP, thus resulting in the need for an improvement to compensate for this lack, and the need for an improvement in the global schedule based on different characteristics of probabilistic algorithms. [013] As GAs can converge slowly, combining one GA with other heuristics can improve results; for example, a GA can be combined with other meta-heuristics for a neighborhood survey. To this end, Holland's theoretical work on genetic plans (in this context, reference can be made to Ref7) was seen as an obvious place to look for an explanation for the adaptive capacity of GAs. Holland and his students simplified this work and provided the well-known explanation called the Building Block Hypothesis (BBH - Building B / ock Hypothesís) (in this respect, reference can be made to, for example, Ref5, Ref6 and Ref7). [014] Furthermore, according to Ref8, an image of GA emerged as a robust and adaptive research procedure that was surprisingly effective for global heuristic research. [015] BBH is based on two fundamental assumptions: Petition 870180071811, of 16/08/2018, p. 118/186 8/56 1. When a GA solves a problem, there are some low-order and low-definition length schemes with above-average suitability (so-called Building Blocks); 2. A hypothesis that an improved GA performs adaptation by implicitly and efficiently implementing an internal heuristic method. [016] The hypothesis states that small pieces of a solution that exhibit above average performance can be combined and reassembled to create larger pieces with superior average quality. Through simple GA schemes, the solutions are combined step by step to form bigger and better strings, while using the heuristic approach according to BBH, instead of testing any possible binary configuration, the complexity problem can be effectively reduced. [017] In fact, GAs may tend to converge to optimal locations or even arbitrary points instead of the global optimal of the problem, because nominal genetic techniques do not attempt to recombine blocks to escape the impasse. In addition, GAs do not handle complexity well, and where the number of elements exposed to the mutation is large, there is usually an exponential increase in the size of the research space. Thus, a relationship between the mutation of single elements and the recombination of blocks would overcome the disadvantages, and a heuristic / metaheuristic approach as a support for global optimization is beneficial. [018] In Ref9, the greatest performance of a hybrid approach based on GA, in local research and Simulated Ringing (SA - Simu / atedAnnealirg) is demonstrated by computer simulations, while in Ref10, after a schedule is obtained by through a GA, local research is applied to improve the solution. This kind of improvement is due to the fact that, although EAs predominantly copy the behavior of natural evolution and treat solution candidates as individuals who compete in a virtual environment, meta-heuristics use instead the neighbors of a solution as a way to explore the local solution space. Additionally, although metaheuristics prefer better neighbors, they also accept worse neighbors to avoid getting stuck in great places. As a result, if the Petition 870180071811, of 16/08/2018, p. 119/186 9/56 algorithm is executed for an infinite period of time, the global optimum will be found. [019] The SA metaheuristic, for example, decides which candidate solution to be evaluated next, according to the Boltzmann probability factor of the solidified molten metal atom configurations. In particular, SA benefits from proof of optimum performance, at least for an infinitely slow cooling schedule and better than mountain climbing techniques, and is less vulnerable to local minimums (in this context, reference can be made to Ref11), the depth of which increases along with the increasing complexity of the plane. The SA has been successfully adapted to provide approximate solutions for the SSP, being basically a guided algorithm of random local research that allows movements with negative gain. [020] A combination of GAs with SA has already been discussed in different fields. For example, in Ref12, an improved GA is combined with an SA algorithm to avoid the common defect of initial convergence, to solve energy integration problems of large systems. Numerical calculations have shown that the new algorithm can converge more quickly than the SA or GA algorithms alone, and is much more likely to find a global optimum. [021] In addition, Ref13 teaches an integration of SA and GA for the manufacture of a specific metal alloy, and shows that such integration reduces the number of iterations in the search for the optimal solution, compared to conventional GA and SA, respectively. [022] Likewise, a hybrid genetic SA has been developed to minimize manufacturing costs (reference can be made to Ref14 here), where GA is run as the main methodology, while SA is used as a local research strategy to help GA jump out of the great spot. [023] An additional application of GA and SA is presented in Ref15 for the reconstruction of a statistical image, where both algorithms retrieve solutions through a sequence of iterative states. In particular, Ref15 states that, although GA quickly discovers the research space, but has difficulty finding the ideal solution, SA is able to find good quality solutions in a neighborhood when escaping Petition 870180071811, of 16/08/2018, p. 120/186 10/56 of the great location, as the SA works on a single solution at a time. [024] Again with reference to scheduling problems, in Ref16 the use of a hybrid GA together with SA introduces a reasonable combination of local and global research to solve the problem of scheduling batch production (job shop). [025] Furthermore, in Ref17, SA was advantageously used to accelerate a GA to obtain a solution, applying it to members of the population. [026] Additionally, with respect to SSP, in Ref18 the use of combined heuristic and meta-heuristic methods to solve the SSP provides high quality solutions that meet the expected requirements. [027] In addition, US 5,850,617 A, which refers to a system and method for planning routes under multiple restrictions, discloses a route planning mechanism that receives a set of targets that indicate a set of available targets, a set of target parameter limits to categorize target parameters, a set of mission objectives, and a corresponding set of mission limits to categorize mission parameters. The route planning mechanism, according to U.S. 5,850,617 A, can also receive a set of evasions that denote obstacles to be avoided. The mission objectives define a number of priority ordering of different target parameters, each associated with a respective mission status. The next best successive targets are selected and added to a selected target sequence list, until a mission completion criterion is met. Each best next target is selected by determining a mission condition according to the previously selected targets, and according to the corresponding target parameter priority order. The target parameters of each available target are mapped to the respective categorization values according to their respective target limits, and a cost function value is calculated for each available target. A subset of the available targets having a better cost function value is selected. This subset is reduced successively until the subset contains only one target, and then that target is selected as the best next target. The narrowing of the subset Petition 870180071811, of 16/08/2018, p. 121/186 11/56 is performed using the categorization values of the target parameters, applied in the order of priority of the target parameter, which is based on the current condition of the mission. The resulting sequence of selected targets is then passed to a route utilization system, such as a satellite control system. [028] In addition, US 6,405,186 B1, which refers to a restricted Simulated Ringing (SA) satellite request planning method, reveals an iterative method that allows a request plan to be established for a observation satellite. A plan consists of a succession of requests associated with a plurality of opportunities to satisfy such requests. The plan must also obey a plurality of restrictions. Each iterative k of the iterative method, according to U.S. 6,405,186 B1, consists of the following steps: a new opportunity is selected; a provisional plan is derived from the previous k-1 plane, calculated in the previous k-1 iteration, and from the new opportunity; the provisional plan is checked for compliance with said plurality of restrictions; the quality of the said provisional plan is assessed, and it is determined whether the provisional plan should be confirmed as a k-plan, depending on the quality of the said provisional plan and the quality of the aforementioned k-1 plan. In the method according to the document US 6.405.186 B1, it is decided whether or not to confirm the provisional plan through a probabilistic meta-heuristic of the type of SA, and by the rule to build the provisional plan according to the opportunity just selected. DEFINITIONS [029] The following description of the present invention will refer to various elements of mission planning related to satellite missions. Thus, for the sake of clarity of description, conventional definitions of said mission planning elements are provided below: - a Scheduling Session represents the available time interval explored by a Mission Planner (MP - Mission Pianner) for optimal scheduling of the acquisition and download tasks, according to the existing restrictions; - Mission Horizon (MH - Mission Horizorí) represents the period of interest of the scheduling activity (nominally, 24 or 48 hours); Petition 870180071811, of 16/08/2018, p. 122/186 12/56 - an Operational Window (OW - Operational Window) is a sub-portion of the MH, and is a continuous time interval allocated for the acquisition and / or loading (uplink) and unloading activities; an OW can include a Planning Window (PW - Planning WindoW) for the acquisition of image data, a Loading / Unloading Window (UW - Uplink Window, or DW - Downiink WindoW), or a combination of them; - a Programming Request (PR) represents an input requested by the user, including acquisition parameters in terms of Area of Interest (Aol - Area of Interest and acquisition restrictions (such as optical restrictions) to be satisfied within a specified period of validity; - an Acquisition Request (AR - Acquisiton Request) is a geometric sub-portion of an AoI of PR, properly constructed in order to allow its scanning from the orbital point of view of the satellite; an RA is shaped, dimensioned and oriented according to the satellite's Orientation Profile and its payload characteristics; - the Classification represents the priority of the relative acquisition of an RA in relation to the set of RAs relevant to the MH to be scheduled, according to the needs and importance of the users; this value results from a classification process carried out before a Scheduling Session; - a Data Take Opportunity (DTO) represents a continuous time envelope in which an RA is acquirable during a satellite orbit over its area; - a Mobilization Maneuver Opportunity (RMO - Raiiying Maneuver Oppcrtunity) represents a theoretical time envelope within which it is possible to plan a mobilization maneuver, to scan an RA in relation to a reference attitude (for example, a reference attitude). minimum drag attitude) and return at the end; - a Data Take Acquisition (DTA) represents the sub-portion of a DTO effectively used for an AR acquisition; - a Mobilization Maneuver Activity (RMA - Raiiying Maneuver Activity represents the amount of time needed to reach the satellite attitude at the beginning of a DTA; Petition 870180071811, of 16/08/2018, p. 123/186 13/56 - a Download Activity (DLA - DownLoad Activity) represents the amount of time required to download an AR image to the available mission ground stations; - A Task is generally defined as the set of activities necessary to perform a scan or to unload an RA. OBJECTIVES AND SUMMARY OF THE INVENTION [030] In heuristic problems, the search for a robust and consistent set of solutions often occupies a significant part of the design of algorithms. The optimization problem depends on the time period available for the solution to converge, and on Time Complexity, which expresses, for each possible length of data input, the greatest amount of time necessary for the algorithm to solve a problem instance of such size. [031] Considering the scope of SSP optimization, here applied only to the subset of acquisition tasks, Time Complexity is associated with Plan Complexity, which identifies the maximum number of conflicts in the scans to be resolved between executable tasks in the same mission plan. The Complexity of Plan is not easy to estimate a priori, because it depends on the complete exploitation of the entire set of resources of the satellite, according to the objectives of the mission. However, assumptions about the potential amount of conflicts expected during the optimization process can be obtained based on combinatorial theory. [032] An assessment of the number of conflicts is certainly crucial to obtain the potential combinatorics of obtaining satisfactory solutions after the problematic research space is identified. As stated by the theory, an unconfined research tree could be explored from N! different ways, but a number of restrictions generally limit the search to a more limited number of solutions, although strongly dependent on the number of tasks (N) related to the same research space. For the specific SSP, under the hypothesis of a well-designed satellite in terms of resource adequacy, a PW can represent the entire research space in which an acquisition task can potentially be accomplished by consuming a certain amount of satellite resources. Petition 870180071811, of 16/08/2018, p. 124/186 14/56 [033] Therefore, considering N scanning tasks relevant to the same PW, the maximum number of solutions resulting from a theoretically greater number of conflicts (C) is equal to: C max (N -1) 2 [034] Where n SOL = C max !, While the maximum number of iterative steps is obtained by adding all the hypothetical steps necessary for a tree level, which can be limited to infinity as : n = fi | i | 1 | 1 | | 1 V ΐ '^ ΓΤ Cmax steps =) +1 + 2! + 3! + + (N -) ' m ' aX i = 0 £ i = 6 ' C max ! (1) [035] This result attests that Plan Complexity is dramatically dominated by the number of tasks involved in conflicts. Through calculation, the maximum number of iterations can be related to the number of conflicting tasks through the relationship: n steps = (n -1) Π (i |) f (i) (2) i = 2 [036] Where f (i) (with i = 2, ..., N) is the number of events related to a number of i conflicting tasks, respectively. [037] More practically, a set of conflicting ARs can be sequentially scanned in a number of different ways equal to the number of permutations allowed for the conflict. The set of complete solutions to be explored for a given time domain depends on the number of RA tasks (nCi) involved in each of the (i = 1, ..., C) resulting conflicts between relevant DTOs, such as: C n SOL = Π n Ci ! (3) i = 1 [038] An example of multiple conflicts between DTOs is shown in figure 1, where 72 Petition 870180071811, of 16/08/2018, p. 125/186 15/56 different solutions have to be explored for an example of 3 conflicts. [039] As stated earlier, the complexity to be managed by scheduling depends strictly on the combinatorial possibilities given by the maximum number of potential conflicts in a plan that, in the worst case, must be managed within the same PW. According to these assumptions, the SSP's Plan Complexity depends statistically on the number of combinations (cpw) resulting between the number of conflicting tasks within a PW: Cp x Cp W = Π (n!) ^ () (4) n = 1 [040] Where f (n) is the frequency of conflicts between n tasks, with n ç N. [041] According to the combinatorial basics, the permutations from the conflicts of n tasks (n!) Can be easily represented as a set of permutations of tasks taken 2 to 2 at a time; thus, this results in: n! 2 (n - 2)! (5) [042] Thanks to these assumptions, it is possible to bring back each multiple conflict as singular conflicts f (2) between two tasks. [043] Assuming standard ranges typically imposed on DTOs and PW intervals, the frequency distribution of single conflicts for a set of N randomly distributed tasks is illustrated in figure 2. In particular, figure 2 shows the frequency probability distribution of conflicts f (2) between 20 <n <50 DTOs (each lasting, on average, 100 s) in an average PW of (1,200 s) - 105 iterations each. [044] According to the results illustrated in figure 2, a Gaussian distribution of conflicts shows that the function relevant to the frequency of single conflicts is dispersed in a higher average value as the number of tasks increases. [045] Applying equation (4) to the mean f (2), the analysis identifies a minimum of cn = 292 combinations for 20 tasks, up to about cn «10 15 combinations for 50 tasks. O Petition 870180071811, of 16/08/2018, p. 126/186 16/56 The resulting number of conflicts theoretically covers the entire research space that must be investigated using an exact algorithm to guarantee an exact optimal solution. [046] It is clear that a deterministic analysis, which needs to explore at least a relevant portion of the branches of conflict, is not feasible, if applied for a high number of tasks in the nominal period of a Scheduling Session, also for the most efficient exact algorithms of O (2 n ). This means that, for large research spaces and for NP-Hard problems, such as SSPs, it is drastically difficult to obtain an exact solution to the problem. [047] Furthermore, although the analysis of Plan Complexity is an important point in the analysis of an SSP, it is not easy to identify all the critical aspects that could influence the search for optimal solutions. [048] Thus, a general objective of the present invention is to alleviate, at least in part, the technical drawbacks of the methodologies currently used to solve Satellite Scheduling Problems (SSPs). [049] In particular, a first specific objective of the present invention is to provide a methodology for resolving SSPs within satisfactory time intervals. [050] Additionally, a second specific objective of the present invention is to provide a methodology to avoid a persistent permanence in the optimum location, by frequently expanding the investigation in the solution research space, identifying a set of initial solutions having a great internal diversity that allows you to cover a wide area of the research space. [051] These and other objectives are achieved by the present invention, which refers to a method for scheduling satellites, as defined in the attached claims. [052] In particular, the method for scheduling satellites according to the present invention includes: a) Produce initial scheduling plans, based on incoming requests related to tasks to be performed within a certain period of time by one or more remote sensing satellites, where in each of the aforementioned initial scheduling plans the respective tasks are scheduled, that do not conflict with each other over time or in the use of Petition 870180071811, of 16/08/2018, p. 127/186 17/56 satellite resources of the remote sensing satellite (s), with each of the tasks to be performed being scheduled in at least one of the initial scheduling plans; b) Apply processing based on genetic algorithms in the initial scheduling plans, to produce a scheduling plan based on genetic algorithms that: - is globally optimized in relation to the mission objectives; and - complies with certain restrictions related to satellite resources, the tasks to be performed, and the specified period of time; and c) Apply processing based on simulated ringing, starting from the scheduling plan based on genetic algorithms, to produce a scheduling plan based on simulated ringing: - that meets the specific objectives of the mission; - which complies with certain restrictions; and - in which a greater number of tasks are scheduled than in scheduling based on genetic algorithms. [053] In particular, step (b) includes performing an iterative procedure based on genetic algorithms comprising: - in a first iteration based on genetic algorithms: - select a subset of the initial scheduling plans based on the stated mission objectives; and - apply crossing, mutation and elitism techniques, based on respective predefined genetic evolution factors, to the selected subset of the initial scheduling plans to produce evolved scheduling plans that meet the given restrictions; - for each iteration based on a genetic algorithm, after the first iteration: - select, based on the determined mission objectives, a subset of the evolved scheduling plans produced in the previous iteration based on genetic algorithms; and - apply the techniques of crossing, mutation and elitism to the selected subset of Petition 870180071811, of 16/08/2018, p. 128/186 18/56 evolved scheduling plans, produced in the previous iteration based on genetic algorithms, to produce new evolved scheduling plans that meet the given restrictions. [054] In addition, said step (b) also includes: - interrupt the execution of the iterative procedure based on a genetic algorithm, when stopping criteria related to the genetic algorithm are satisfied; and - automatically select, among the evolved scheduling plans produced in the last iteration based on genetic algorithms performed, the one that best fits the determined mission objectives. [055] In addition, the satellite scheduling method includes: - compute an intersection matrix representing conflicts over time and in the use of satellite resources of the tasks to be performed, within the given period of time; - calculate the Complexity of Plan based on the intersection matrix; and - compute the stopping criteria provided, related to the genetic algorithm, based on the intersection matrix, in which the initial scheduling plans are produced based on the said intersection matrix. [056] Preferably, step (c) includes performing an iterative procedure based on simulated ringing, comprising: - in a first iteration based on simulated annealing: - select, according to one or more predefined probability functions, an unscheduled task in the scheduling plan based on genetic algorithms; - identify a neighborhood of the selected task, in which the identified neighborhood includes a set of conflicting tasks not scheduled in the scheduling plan based on genetic algorithms; - perform permutations of conflicting tasks in the identified neighborhood; - apply a simulated ringing technique to the results of the permutations carried out, to find tasks that: - are not scheduled in the scheduling plan based on genetic algorithms; - are schedulable together with the tasks already scheduled in that plan Petition 870180071811, of 16/08/2018, p. 129/186 19/56 scheduling based on genetic algorithms; - adjust to the stated mission objectives; and - comply with the restrictions given; - produce a scheduling plan including the tasks found; - in each iteration based on simulated ringing, after the first iteration: - select, according to the predefined probability function (s), another unscheduled task in the scheduling plan produced in the previous iteration based on simulated ringing; - identify a neighborhood of the selected additional task, in which the identified neighborhood includes a set of conflicting tasks not scheduled in the scheduling plan produced in the previous iteration based on simulated ringing; - perform permutations of conflicting tasks in the identified neighborhood; - apply the simulated ringing technique to the results of the permutations carried out, to find tasks that: - are not scheduled in the scheduling plan produced in the previous iteration based on simulated ringing; - they are scheduled together with the tasks already scheduled in the referred scheduling plan produced in the previous iteration based on simulated ringing; - fit the mission objectives determined; and - comply with the restrictions given; - produce a new scheduling plan, including the tasks found. [057] In addition, said step (c) preferably includes interrupting the execution of the iterative procedure based on simulated ringing, when the stop criteria related to the simulated ringing are satisfied, in which the ringing-based scheduling plan simulated is the scheduling plan produced in the last iteration based on simulated annealing performed. [058] Conveniently, the satellite scheduling method also includes the calculation of the stopping criteria related to the simulated annealing, based on the intersection matrix. [059] Additionally, the present invention also relates to a system of Petition 870180071811, of 16/08/2018, p. 130/186 20/56 processing for Earth Observation (EO) systems, including one or more remote sensing satellites, such processing system being programmed to carry out the satellite scheduling method in accordance with the present invention, thus resulting in said monitoring system processing being configured to operate as a Mission Planner (PM) for said EO systems. BRIEF DESCRIPTION OF THE DRAWINGS [060] For a better understanding of the present invention, the preferred embodiments will now be described purely by means of non-limiting examples, with reference to the accompanying drawings (all out of scale), in which: - Figure 1 schematically illustrates an example of multiple conflicts between DTOs; - Figure 2 shows the frequency distribution of single conflicts for a set of N tasks randomly distributed; Figure 3 schematically illustrates a method of scheduling satellites according to a preferred embodiment of the present invention; - Figure 4 schematically illustrates a Mission Planner according to a preferred embodiment of the present invention; - Figure 5 schematically illustrates an example of a scheme to initialize an Intersection Matrix for a case with five tasks; - Figure 6 schematically illustrates an example of conflicts between DTOs in a case with five tasks; - Figure 7 schematically illustrates an example of so-called conflict-free solutions, computed for a case with five tasks; - Figure 8 schematically illustrates the so-called Extensive Initiation of conflict-free solutions, as a function of the number of input tasks (in particular, from 10 to 50 for a 900 s PW); - Figure 9 schematically illustrates an example of a solution for a PW collecting five viable DTAs; Figure 10 schematically illustrates a GA-based processing step of the satellite scheduling method of figure 3, according to a preferred embodiment of the present invention; Petition 870180071811, of 16/08/2018, p. 131/186 21/56 Figure 11 schematically illustrates an SA-based processing step of the satellite scheduling method of figure 3, according to a preferred embodiment of the present invention; - Figure 12 shows the trend of Plan Complexity as a function of the number of tasks; - Figure 13 shows the evolution of the adequacy according to the probability of accepting the solution; - Figure 14 shows a comparison between the applications of a deterministic algorithm of Search for Depth and Width (BDS - Breadth Depth Search), of a pure simulated annealing, and of the present invention, for a real test scenario; - Figure 15 shows a further comparison between the applications of a pure simulated annealing and the present invention, for said real test scenario; - Figure 16 shows a comparison between the standard deviation and the average value of the number of tasks planned by means of the present invention, in the referred real test scenario; and - Figure 17 shows the average number and the minimum / maximum difference in the number of tasks planned by means of the present invention, in the real test scenario. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION [061] The following discussion is presented to allow an expert in the art to make and use the invention. Various modifications to the forms of incorporation will be readily apparent to those skilled in the art, without departing from the scope of the present invention as claimed. Thus, the present invention is not intended to be limited to the forms of incorporation shown and described, having a broader scope consistent with the principles and characteristics described herein and defined in the appended claims. [062] In general, the present invention relates to an innovative application of heuristic algorithms to satisfactorily solve the Satellite Programming Problem (SSP), according to the specific requirements of the mission. [063] In particular, the present invention relates to a hybrid strategy appropriately combining Genetic Algorithm and Simulated Ringing (GASA - Genetic Algorithm and Simuiated Annealing), in order to optimize the scheduling of a given Petition 870180071811, of 16/08/2018, p. 132/186 22/56 set of Programming Requests (PRs) to be acquired, each duly dimensioned in Acquisition Requests (ARs) according to the satellite acquisition characteristics, within pre-computed acquisition opportunities, called DTOs, in a predefined set Satellite Planning Windows (PWs), which are, as previously defined, sub-portions of the Mission Horizon (MH) for which the SSP is resolved. [064] In particular, the Genetic Algorithm (GA) guarantees qualitative convergence on a large scale and allows the planning of a primary set of scans in the neighborhoods, according to the basic restrictions provided by a Satellite Model (SM - Satellite Modef) customized, relevant to the specific satellite. GA explores the entire domain of MH and globally analyzes the combination of opportunities for the tasks to be planned, converging on an excellent solution in terms of cost function. All ARs, which can be scheduled without significant acquisition effort, are defined according to the results of the adequacy functions. For this purpose, with adequate precision, the best GA solutions are obtained after a limited number of iterations. On the other hand, due to the characteristics of the algorithm, Simulated Ringing (SA) is successively involved in the local optimization steps, in order to adequately resolve the scanning conflicts for the remaining RA tasks. The best stress solutions are obtained within a predicted time interval, thanks to the convergence properties of annealing. [065] Therefore, in accordance with the present invention, to take advantage of both the highlighted optimization features, an integrated heuristic strategy that consecutively exploits GA and SA (GASA) was developed by the Applicant, and applied to the global scheduling. The heuristic process is based on the sequential use of GA and SA adequately adapted to exploit the respective forces. GASA allows to obtain an improvement in the quality of the solutions and a reduction in the execution times, in comparison with the results obtained by the application of a deterministic method suitable to real mission scenarios having different complexities. [066] The following is a preferred embodiment of the present invention specifically related to optical satellites (ie satellites equipped with Petition 870180071811, of 16/08/2018, p. 133/186 23/56 optical sensors) will be described in detail, by way of non-limiting example, it should be understood that the present invention can also be advantageously applied, without any substantial modification, to satellites provided with other types of sensors, such as LiDAR sensors. and with SAR. [067] Figure 3 schematically illustrates, by means of a flowchart, a method of scheduling satellites (indicated as a whole by numeral 1) according to a preferred embodiment of the present invention, in which said method of scheduling satellites is conveniently used (as explained above, as a non-limiting example) to schedule acquisitions made by an optical satellite. For the sake of generality, a generic OW is considered here as the scheduling interval under investigation. [068] In particular, the global scheduling strategy of satellite scheduling method 1 is based on available orbit data sets, since the Sun's local positions for the period of interest are known and are applied to each OW of the MH of interest. An efficient procedure is carried out to identify the start and stop times of the best DTAs relevant to the best set of RAs, according to the mission objectives. This procedure allows the minimization of the number of consultations to the Satellite Model (SM) (indicated by the numeral 21 in figure 3) that are necessary to validate each planned sweep and mobilization maneuver, and, finally, the final plan. [069] In detail, for each MH under investigation, the satellite scheduling method 1 includes: - define the next OW in the list (block 101 in figure 3), and initialize the plan (block 102 in figure 3) based on the condition (status) of the satellite resources resulting from scheduling the previous OW; - compute the OW Plan Complexity (block 103 in figure 3) to define the parameter data (block 104) relevant to the next processing steps, in which said parameter data preferably includes the number of iterations and the limits of time (timeouts), heuristic seeds, genetic factors and ringing factors; in particular, processing step 103 of the scheduling method Petition 870180071811, of 16/08/2018, p. 134/186 24/56 satellites 1 is performed by computing and analyzing an Intersection Matrix properly defined between the acquisition tasks; for more details related to processing step 103 of satellite scheduling method 1, reference can now be made to paragraph 2: - build an initial set of conflict-free solutions (block 105 in figure 3), for which all viable RAs were planned at least in one solution; in particular, the processing step 105 of the satellite scheduling method 1 is performed based on the SM 21 and the orbit data (block 106 in figure 3) related to the optical satellite (specifically, its position and speed), which are obtained from a respective short-term orbit data set (block 107 in figure 3), resulting, in turn, from satellite ephemeris (block 22 in figure 3); for more details related to processing step 105 of the satellite scheduling method 1, reference can now be made to paragraph 3; - perform a processing based on genetic algorithm (GA) (block 108 in figure 3) from the initial set of conflict-free solutions; in particular, as described in paragraph 4 below, in the GA-based processing step 108 of the satellite scheduling method 1, according to relevant probability factors, the solutions evolve through the manipulation of appropriate crossing, mutation and elitism according to SM 21, and are compared and selected to meet the Mission Objectives (for more details related to the Mission Objectives, reference can now be made to paragraph 1); - perform simulated ringing (SA) processing (block 109 in figure 3) from the best solution in terms of Mission Objectives; in particular, as described in paragraph 5 below, in processing step 109 based on SA of the satellite scheduling method 1, the solution evolves following specific methods of selection and exchange of tasks, according to the restrictions given by the rules of maneuver of the SM, and each solution is finally evaluated to be accepted for the next iteration with respect to the typical SA criteria, according to the Mission Objectives (again, for more details related to the Mission Objectives, reference can now be made to the paragraph 1); Petition 870180071811, of 16/08/2018, p. 135/186 25/56 - refine the acquisition reference times, to improve the quality of the planned images to be downloaded (down / oaded) successively within the predefined DWs, if any, and validate the final solution according to the SM validation rules (block 110 in figure 3); and - produce and store (block 111 in figure 3) the best schedule in a Plan Database (indicated by the numeral 23 in figure 3) and then return to step 101 of the method for the next OW. [070] Another aspect of the present invention concerns a Mission Planner (PM) for Terrestrial Segments of EO satellite systems, such MP being designed to execute the satellite scheduling method 1. [071] Preferably, the MP is based on a JAVA architecture with OSGI (Open Service Gateway Initiative), thus being a modular system and a service platform that implements a complete and dynamic component model, operating in a Client / Server context, in which the different scheduling services are executed, on demand, by specific modules (also known as packages), whose life cycles are independent of each other. [072] In this context, figure 4 shows a block diagram representing a functional architecture of a PM (indicated as a whole by the numeral 4) according to a preferred embodiment of the present invention. In particular, MP 4 includes: - a plan initialization module (or package) (in figure 4 called Plan Initiator, indicated by the numeral 401), operable to execute the processing steps 102, 103 and 105 of the satellite scheduling method 1, that is, operable to perform the plan initialization, compute and analyze the plan complexity plan and the Intersection Matrix, and build (that is, compute) the initial set of conflict-free solutions; - a GA processing module (or package) (in figure 4 called GA Executor, indicated by the numeral 402), operable to perform the GA 108-based processing step of the satellite programming method 1; - an SA processing module (or package) (in figure 4 called Petition 870180071811, of 16/08/2018, p. 136/186 26/56 SA, indicated by the numeral 403), operable to perform the processing step based on SA 109 of the satellite scheduling method 1; - a computing module (or package) (in figure 4 called Basic Function Calculator, indicated by the numeral 404), operable to provide basic computing resources for the GA 402 Executor and SA 403 Executor; - a plan validation module (or package) (in figure 4 called Plan Validator, indicated by the numeral 405), operable to perform processing step 110 of satellite scheduling method 1, that is, operable to perform validation the final plan; - an orbit data manipulation module (or package) (in figure 4 called Orbit data manipulator, indicated by the numeral 406), operable to provide ephemeris and data from satellite OWs, from a dynamic database 407 connected to a Flight Dynamics System (FDS - Flight Dynamics System); - a static database 408, which stores satellite parameters and Earth and Sun data; - a module (or package) to collect the Programming Requests (PRs) (in figure 4 called PR List Collector, indicated by the number 409) received from a Request Manager (RM - Request Manager) 52; and - a master package (in figure 4 called Mission Planning Manipulator, indicated by the numeral 410), operable to control and coordinate the activation and completion of the other packages. [073] In detail, once invoked by RM 52, MP 4 collects (through the PR List Collector 409) the list of PRs, orbit data and OWs (through the dynamic database 407) relevant to the MH under investigation, and activates the global scheduling strategy (ie, satellite scheduling method 1) for the subset of PRs to be scheduled. Mission Planning Manipulator 410 is responsible for synchronizing activities, invoking the beginning and ending of specific services according to internal time limits (Timer 411, shown in figure 4). [074] Thanks to the modularity and independence of Mission Planner 4 with respect to the specific mission, it is possible to minimize customization for different applications. For Petition 870180071811, of 16/08/2018, p. 137/186 27/56 For this purpose, the Satellite Model (SM) 21 represents an external element that is invoked from the modules, when necessary. Interactions with the SM 21 are preferably carried out by adopting an SM Packer (SMW - SM Wrappetj specific (in figure 4, indicated by the numeral 53), which handles the different queries according to the specific characteristics of the model. [075] Based on the hardware environment and the performance of the Satellite Model 21, an adjustment of the algorithmic parameters can be conveniently performed to optimize the robustness and precision of the application. In this regard, reference may now be made to paragraph 6. [076] The different aspects of the satellite scheduling method 1 implemented by MP 4 will be described in detail below. 1. MISSION OBJECTIVES [077] In SSP optimization, the heuristic process is guided by the multiple objectives to be accomplished, which are modeled by a weighted multi-objective function, where an objective function f: XY is a mathematical function subject to optimization. The Y domain of an objective function, as well as its range, is a subset of the real numbers (Y ç R), while the X domain is called the SSP research space. [078] Scheduling optimization comprises all the techniques that can be used to find the best elements x * in X with respect to such objective criteria f and F. Thus, the objective of optimization is to find the best strategy x * for assigning the resources to tasks in order to satisfy constraints, optimizing objectives in a predefined scheduling period. [079] For a complex multi-purpose SSP, there may not be a single solution that simultaneously optimizes each objective. In this case, the objective functions are considered to be conflicting, resulting in a multiple number of optimal Pareto solutions. A solution is called non-dominated, Pareto optimal, Pareto efficiency, or not inferior, if none of the objective functions can be improved in value without degrading some of the other objective values. Without additional subjective preference information, all Pareto optimal solutions are considered equally good. For this reason, the Petition 870180071811, of 16/08/2018, p. 138/186 28/56 definition of the best solution, due to the intrinsic character of the Pareto approach, is not applicable. [080] Thus, for the SSP under investigation, it is necessary to recover methods that convert the original problem with multiple objectives into a single objective optimization problem. This is known as a scalar problem. If scaling is done carefully, Pareto optimization of the obtained solutions can be guaranteed [in this context, reference to Y.R. Lee, A. Stam, PL Yu, Dominance Concepts in Random Outcomes, Chapter 2 (pp. 23 to 43), or to P. Serafini, Mathematics of Muiti Objective Optimizatiod ' -objective), Vol. 289 of the series Intemationai Center for Mechanical Sciences (international Center for Mechanical Sciences), doi: 10.1007 / 978-3-70912822-0_2]. [081] The simplest and most effective method to define a single objective is to calculate a linear scalarization F (x) as the sum of all functions fi (x) and F. Each objective fi is multiplied by a weight Wi that represents its value relative in the set of NObj objectives. The use of marked weights also allows you to minimize one objective and maximize another. In any case, the multi-objective problem is reduced to a single objective: ^ Obj F ( x) = w „fn (χ „ ) (6) n = 1 [082] Where the optimal value of F, called the matching function, results in the best value of x * and X * that allows minimization of F (x *) <F (x) with Vx and X. [083] For the purpose of scheduling optimization, the cost function is modeled according to the mission requirement (s) and taking into account all the satellite's general resources. In particular, the fi (x) and F, called Mission Cost Functions (MCFs) are modeled and adjusted according to the restricted renewable and non-renewable resources, which are generally in conflict with each other, at least in terms of: - task priority (pt), which is defined through a priority classification Petition 870180071811, of 16/08/2018, p. 139/186 29/56 relative in the schedulable PW and is imposed a priori (typically by a classifier from the Request Manager 52 subsystem) for the set of Nt planned tasks, where a lower index indicates higher precedence; this means that, in case of conflict and under the same condition, MP 4 gives priority to scheduling priority tasks, according to a specific MCF; - consumption of maneuver time (tM), proportional to the maneuver time tMij between tasks i and j; this MCF gives greater relevance to the faster RMAs than the slowest to acquire an RA; - switching energy consumption (Wm), proportional to switching energy Wmu between tasks i and j; this MCF tends to minimize the energy effort in the RMAs to fulfill an acquisition; - onboard record storage (Sobr), proportional to the onboard instant storage Sobr; this MCF tends to limit the size of the images stored in the On Board Registry (OBR - On BoardRecord); - image quality in terms of average acquisition of Ground Sampling Distance (GSD - Ground Sampling Distance); this MCF tends to give greater relevance to images acquired with greater geometric quality. [084] The reference values of the resource parameters are imposed for the normalization of the relevant MCFs 0 <fi (x) <1. In particular: • NTTot is the total number of tasks to be processed within a PW; • tMMax = L / VMMin is the maximum maneuver time adopting a minimum VMMin maneuver speed, necessary for maneuvering between two task points on the ground having a distance L, which is given by SM 21; • SoBRMax = Sobr x fSOrb, where fSOrb <1 is the maximum fraction of the size of the OBR designed to be allocated to an orbit pass; • WMMax = WMOrb, where WMOrb is the energy provision assigned for 1 orbit pass, which is provided by SM 21; • GSDMin = GSDN / cos («Max) is the worst GSD available for acquiring an AR at the maximum aMax acquisition angle, which is provided by SM 21. [085] In this way, a weighted local cost function, called Petition 870180071811, of 16/08/2018, p. 140/186 30/56 Task Ft (x), can be associated with each scheduled task (Ti), according to the Nobj objectives of the mission (equation 7): N Obj F T (x) = £ r; (T ) = wn = 1 N TTOT -Pt, t Mj + w 2 —— t MMax s ‘OBR + w. 3 S ^ OBRMax + W + GSDj + w 4 ----— h w. W MMax 5 GSD Min [086] Where, for weighted factors, there are results £ w n = 1. n = 1 [087] At this moment, the main criterion leading to scheduling is a global cost function, called Fs (x) Solution Suitability, which links MCFs to the set of Ti and NTAgend tasks scheduled within a PW, which is calculated as (equation 8): N Obj F S (x) = n w n f nn = 1 N 'l'Agend £ T m m = 1 k 7 N 'l'Agend z Σ j = 1 W1k 2 N TT oT -P Tj tMi + w2 - h W3 'MMAX SoBRj WMj 5 GSDj ---- - + W4 ----— + w ---— S OBRMAX W MMAX GSI > kliii N TAgend [088] Where variable x now corresponds to the global set of tasks £ T m already m = 1 planned. [089] However, modeling the MCFs is not enough to guide optimization towards a satisfactory solution. In opposition to the SSP's optimization wishes, minimizing Fs would lead to finding the best solutions with empty plans without scheduled tasks. [090] Therefore, it is important to impose the so-called Penalty Cost Functions (PCFs Pena / ty Cost Functiond), proportional to the set of unscheduled tasks. This is important for maximizing the number of tasks to be scheduled. The goal is to ensure that each task completed under the worst acquisition conditions would cost less than if it were not scheduled. Thus, a PCF having a value equal to Nobj is replaced by a j-th task that is not scheduled in each optimization step. [091] The combination of resulting MCFs and PCFs, for the entire set of RAs involved, defines the final multi-objective suitability function, to be minimized during the optimization process. Therefore, the objective of the optimization associated with each PW to be scheduled results Petition 870180071811, of 16/08/2018, p. 141/186 31/56 in equation 9 below. N Obj 'Nt Ίmin [FQ. (x)] = min Σ w n f n Σ T m + (N TTot - N TAgend ) (9)n = 1 m = 1 ) 2. COMPLEXITY ANALYSIS [092] As explained earlier, processing step 103 of satellite scheduling method 1 includes calculating and analyzing the Plan Complexity using an Intersection Matrix. [093] In particular, a DTO represents the entire interval in which the start of the DTA is feasible. An efficient initialization process provides for the construction of an Intersection Matrix (Matmt) that involves the DTO intervals for the MH under investigation. An Intersection Matrix results from the analysis of (V) χ (V - 1) of the binary intersections between V DTOs of the RA tasks. [094] Specifically, the elements mj (i to j) of Matmt are filled with: -1, if DTOi completely precedes DTOj; +1, if DTOi completely succeeds DTOj; 0, if DTOi intersects DTOj. [095] This type of initialization allows to obtain the number of intersections between the conflicting RAs and then the complexity of the plan. [096] An example of a startup plan is shown in figure 5, for scheduling 5 tasks in a reference MH of 1 PW. In this scenario, RA tasks are classified by priority (p #). The conflict dependency between DTO tasks is shown in figure 6 by means of a graph composed of arcs between each pair of tasks, having a single arrow (if there is no conflict) or a double arrow (if a conflict is generated), according to information from Matmt. [097] The intersection matrix defined above allows the modeling of a Plan Complexity function (Cp), which is associated with conflicts between DTOs within the given MH PW. It is thus related to the sum of the zeros generated from Matmt's mj coefficients: Petition 870180071811, of 16/08/2018, p. 142/186 32/56 N N Cp = ΣΣί. + k) (io) i = 0 j = i + 1 [098] Where k = 1 if (mj to 1), ek = -1 if (mj to 1). [099] Further improvements could be obtained from the preliminary verification of conflicts. In particular, according to the Intersection Matrix, when there is no chance of combining the DTAs of two subsequent conflicting DTOs, it is possible to simplify the graph's complexity. However, in order to obtain this advantage, a certain amount of initial calculations (N - 1) 2 is required , in terms of consultations with SM 21. A minimum overlap is considered according to the satellite's agility characteristics. In particular, if the time of intersection between a pair of DTOs is less than a certain threshold (ie 10 s), the conflict can be neglected. [0100] In this document, the Neighborhood (TaskViz) of a scan task is defined as the time portion of the relevant DTO interval that does not conflict with other DTOs in a given set of tasks. In other words, it represents the interval over which the influence of a scan can be univocal. [0101] It is a fact that the planned DTAs are feasible only if the maneuvers regarding the predefined attitudes relevant to the acquisition of the preceding and successive DTAs are properly valid. Thus, a broader TaskViz means statistically greater probabilities for relevant DTAs to be planned. As a limit, the conflict-free solution represents the locus where each TaskTime corresponds to the complete DTO interval. [0102] In this way, lower density solutions with extended TarefaViz intervals are built, and less effort is required in scheduling due to the limited number of DTO conflicts to be analyzed. This characteristic allows a quick initial design of a useful set of solutions to be improved in the successive stages of optimization. 3. INITIALIZATION OF SOLUTIONS [0103] The initialization of the plan is a necessary process for the instance of the various conditions (status) of the set of satellite resources available at the beginning of the activities Petition 870180071811, of 16/08/2018, p. 143/186 33/56 scheduling, according to the specific mission restrictions. [0104] In particular, a requirement is that, for the Mission Horizon (MH) of interest, the condition of the satellite is compatible with all Mission Rules applicable to the plan, in order to avoid Mission Failures a priori. [0105] Initialization is carried out according to the specific Satellite Model (SM) 21, and to perform this task it is necessary to evaluate: - the set of available OWs; - the energy level on board; - the memory available on board; - the set of stored images to be downloaded (down / oaded) from the previous schedule. [0106] In order to comply with the intended performance, it is necessary to load the set of satellite ephemeris (block 22 in figure 3, and block 407 in figure 4) newly forecast by the Flight Dynamics System 51 for the short interest period (block 107 in figure 3), in order to ensure the minimization of errors in satellite positioning. The ephemeris of the Sun and the compensation of UTC / TAI (Coordinated Universal Time / Internationai Atomic Time - Coordinated Universal Time - International Atomic Time) are conveniently explored for the conversions between the reference frames and the calculation of the angle restrictions of the Sun. [0107] All data sets are stored and accessible whenever the SM 21 is consulted for the execution of a certain task. In order to satisfy the mission requirements, which demand to ensure that each relevant RA for a PW is analyzed, a conflict-free solution is built (block 105 in figure 3) through the exploitation of the SM 21. [0108] In particular, processing step 105 of satellite scheduling method 1 conveniently includes, for each PW: 1. Select a DTO from the set of Task that first conflicts with respect to time, according to the Intersection Matrix (that is, DTOs from zeros in Matint); 2. Randomly select a DTO from the conflicting set, and find a DTA Petition 870180071811, of 16/08/2018, p. 144/186 34/56 relevant that starts from the DTO start time, using a Sweep Maneuver interface (block 112a in figure 3) of SM 21; 3. Proceed chronologically and identify a next set of conflicting DTOs; 4. Randomly select a DTO in the conflicting set, and find a relevant DTA that starts from the start time of the DTO, using the Sweep Maneuver interface (block 112a in figure 3) of SM 21; 5. Validate the RMA between the first and second DTAs, using a Mobilization Maneuver interface (block 112b in figure 3) of the SM 21; if the RMA is not valid, the second DTA is postponed until the RMA is viable; 6. Place the selected DTAs into the solution; 7. Repeat sub-steps 3, 4 and 5 above until the end date of the PW is reached; 8. Build a conflict-free solution, associating it with a Solution Adequacy, according to equation (8). [0109] This process allows the minimization of checks to be performed, in terms of the number of consultations with SM 21 for the validation of the solution. In this regard, figure 7 shows schematically solutions calculated through the implementation of processing step 105 above, for the example of 5 tasks in figure 6, where a minimum overlap between tasks was considered. [0110] Several solutions are reached until certain criteria are reached. Due to the need to maximize the diversity of the solution set to spread germs in the solution research space, it is usually necessary to include each task in at least one solution. This condition is called Extensive Startup. In practice, this means that each viable task is scheduled at least once in the set of conflict-free solutions provided by the initialization process. [0111] A statistical simulation, illustrated in figure 8, shows that the number of solutions requested to meet the scope of the Extensive Startup, with a good approximation, increases linearly according to the number of input tasks. [0112] Conveniently, adjusting the number of conflict-free solutions also considers: - the GA requirements in terms of the population of Spop solutions needed for their Petition 870180071811, of 16/08/2018, p. 145/186 35/56 evolution; - the final time limit for the Scheduling Session. [0113] Thus, a relationship is required, which considers the restrictions defined through combined criteria. [0114] In the end, based on computational assumptions, the initialization timeout to achieve a timely set of initial solutions is considered taking into account a 95% probability of obtaining an Extensive Initialization of the scans, for a number of N tasks per PW. This condition depends marginally on the acquisition performance of the satellite and the extension of the PW period; in fact, random analyzes have shown that similar computational times are required to build a small set having longer solutions (occupied with scans) than a larger set but with shorter solutions, for a fixed number of input tasks. In other words, the computation effort is considered as a function of the number of input tasks, under the condition of equivalent performance of the Satellite Model (SM) 21. 4. GENETIC ALGORITHMS [0115] As is well known, in the field of computer science and artificial intelligence, the Genetic Algorithms (GAs) of the EA family are heuristic searches that mimic the natural selection process, based on Darwin's theory of survival , for the most appropriate solutions. GAs have been investigated for a long time in connection with scheduling optimization problems, for example, by H. Bremermann [see as an example “A method of unconstrained global optimization, Mathematical Biosciences ), Vol. 9, p. 1 to 15, 1970, d.o.i .: 10.1016 / 0025-5564 (70) 90087-8], whose research also included the elements of modern genetic processes. [0116] In addition, RM Friedberg [see, for example, RM Friedberg, B. Dunham, JH North., 'A Learning Machine: Part II, IBM Journal of Research and Development (Journal Research and Development), Vol. 3, No. 3, p. 282 to 287, 1959, d.o.i .: 10.1147 / r.33.0282] and I. Rechenberg [see, for example, The Evolution Strategy - A Mathematical Model of Darwinian Evolution (A Petition 870180071811, of 16/08/2018, p. 146/186 36/56 Evolution Strategy - A Mathematical Model of Darwinian Evolution), in Synergetics - From Microscopic to Macroscopic Order (Synergetics - From Microscopic to Macroscopic Order ”), Springer Series in Synergetics (Synergetics”), Vol. 22, pg. 122 to 132, 1984, doi: 10.1007 / 978-3-642-69540-7_13] were notable pioneers, who provided the basic ideas of analysis and design based on the concepts of biological evolution, and also JH Holland [see for example the Ref7, and also Genetic Aigorithms and Adaptation (Adaptive Control of IH-Defined Systems), pg. 317 to 333, 1984, d.o.i .: 10.1007 / 978-1-4684-8941-5_21] and D.E. Goldberg [see for example Ref5, as well as Genetic Aigorithms and Innovation (Genetic Algorithms and Innovation ”), The Design of Innovation (Vol. 7), Vol. 7 of the GeneticAigorithms and Evolutionary Computation series (Genetic Algorithms and Evolutionary Computing”) , p. 1 to 9, 2002, d.o.i .: 10.10 07 / 978-1-4757-3643-4_1]. [0117] GAs simulate the survival of the fittest among individuals over consecutive generations, to solve an optimization problem where each generation consists of a population of strings analogous to the DNA chromosome. To continue the genetic analogy, a variable on each chromosome is equivalent to a gene whose character is called an allele. Traditionally, gene alleles are represented as binary characters (0/1), but other encodings are also possible. The locus represents the position of the gene in the chromosome chain, while the phenotype represents the properties of the gene determined by its genotype. [0118] Genetic evolution from a state (s) usually begins from a population of randomly generated individuals, and proceeds through an iterative process, where the population computed in each iteration is called a generation. In each generation, the suitability of each individual in the population is assessed. The most suitable individuals are selected stochastically from the current population, so the genome of each individual is modified (recombined and possibly randomly mutated) to form a new generation. The new generation of candidate solutions in the state (s + 1) is then used in the next iteration of the algorithm. Thus, a typical GA requires: - a genetic representation of the domain of solutions and variables; Petition 870180071811, of 16/08/2018, p. 147/186 37/56 - a suitability function to assess the domain of solutions. [0119] Once the genetic representation and the Solution Suitability are applied, GA proceeds by initializing a population of solutions and then improving them through evolutionary techniques. A population of solutions is maintained within the research space, and is then forced to evolve to the next iteration based on the adequacy of the assigned task, according to the adequacy function for the optimization problem to be solved. The goal of GA is to statistically produce offspring having qualities superior to those of the parents, combining alleles of the relevant genes with a set of chromosomes selected within the Solution Set, through appropriate evolutionary techniques. [0120] The following traditional GA techniques are adopted in the present invention: - crossing (single / multi-points); recombining parts of two solutions cut at defined points; in this model, each crossing point corresponds to a random time instant within the solution's time interval; the cutoff points for the crossing are randomly calculated within specific time intervals in which the Task Neighborhoods of the cross solutions do not intersect; - mutation; replacing a scan with a conflicting scan over time, if any; - elitism - the reproduction of a set of iterations of more valuable solutions through iteration. [0121] Commonly, the algorithm ends when a maximum number of generations is produced, a satisfactory level of adequacy is reached, or when there is no more significant progress. [0122] In conclusion, the following statements refer to all GA-based algorithms: - chromosomes in a population compete for resources and partners; - individuals most valued in terms of adequacy produce more offspring than others, in order to reproduce the best qualities of a population; - genes for chromosome candidates for reproduction are combined and propagated by Petition 870180071811, of 16/08/2018, p. 148/186 38/56 the entire population; - each successive generation will become more appropriate to its environment. [0123] The steps statistically allow an improvement in the average adequacy among the population of successive generations, until the convergence towards an adequacy value is reached and no significant improvement in the offspring is noticed. [0124] An efficient representation of each candidate solution in an SSP is given through a standard bit array [0/1], ordered according to a specific variable. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossing operations. However, variable-sized representations can also be used, but the implementation of intersections becomes more complex, like a tree-like evolution. In the application to the resolution of the SSP, the genetic elements are associated with the scanning activities, and each one can be linked to a specific characteristic, as reported in Table 1 below: TABLE 1: GENETIC APPLICATION TO THE SSP Genetic Term Genetic Representation SSP application Chromosome Jail Solution as a sequence of scanning opportunities (DTOs) Gene Character Scanning Opportunity (DTO) Allele Value Scan feasibility (Yes or No) Locus Matrix Index Scan priority (Classification) Phenotype Attribute Sweeping maneuver (DTA) Genotype Attribute Mobilization maneuver (RMA) [0125] Each plan solution (chromosome) that includes a set of AR DTOs (genes) represents a possible schedule in the solution domain, for a PW having a certain set of tasks to be planned. [0126] By definition, the gene allele is equal to 1 if the acquisition of RA is viable through a valid DTA (with which a valid RMA is always associated) within the relevant DTO, otherwise it is defined as 0. Petition 870180071811, of 16/08/2018, p. 149/186 39/56 [0127] According to theory, when applying to the SSP, the gene arrays are ordered chronologically with respect to the start time of the DTOs for each task. In this way, a solution corresponds to a sequence of 0 (that is, zeros) and 1 (that is, ones), according to the viable and non-viable DTAs (phenotypes) for the set of tasks, as shown in figure 9 (which schematically illustrates an example of a solution for a PW that collects 5 viable DTAs for a set of 8 tasks). [0128] Finally, the genotype is linked here to the RMA needed to perform a viable DTA. [0129] In the context of the SSP, the idea is to identify and reproduce a population of valid solutions, increasing their suitability values with each generation, where each solution includes a series of non-conflicting DTAs. Solutions are calculated according to the associated Multi-objective Solution Suitability, and can be classified, ordered and selected according to the relevant suitability. [0130] Each evolution technique is related to a specific genetic factor (gfc for crossing, gfm for mutation, and gfe for elitism), identifying the relevant probability of application during an iteration of GA. The intervals are identified according to the standards adopted in the state of the art. [0131] Genetic factors are appropriately adjusted according to the specific problem and treated as constant. However, the gfm mutation factor can conveniently vary depending on population diversity. If it is not satisfactory, the crossing factor gfc can be increased as in Adaptive GAs, in order to differentiate mainly the input solutions. [0132] In Table 2 below, probability ranges for the genetic factors conveniently explored by the present invention are reported: TABLE 2: PROBABILITY INTERVALS OF GENETIC EVOLUTION FACTORS Genetic Factor description Probability gfc Crossover factor 0.5 to 0.95 gfcm Multiple crossing factor 0.25 to 0.5 gfm Mutation factor 0.01 ~ 0.1 gfe Elitism factor 0.05 ~ 0.2 Petition 870180071811, of 16/08/2018, p. 150/186 40/56 [0133] Figure 10 schematically illustrates, by means of a flowchart, the processing step 108 of the satellite scheduling method 1 according to a preferred embodiment of the present invention. [0134] In particular, based on the initialization of solutions (that is, the processing step indicated by 105 in figure 3, and described in detail in paragraph 3), since the parameters of GA in terms of maximum number of iterations , process time limit, heuristic seeds and genetic factors are defined (block 104a in figure 10), the GA-based procedure of step 108 allows to calculate multiple solutions through the following sub-steps: - initialize the GA for a given PW (block 201 in figure 10), with a population of N conflict-free solutions recovered through the plan initialization process (ie, said processing step 105); - select the best candidate solutions in the state (s) for reproduction through an appropriate selection method, called Competition selection (block 202 in figure 10); - order the solutions according to their Solution Suitability values (block 203 in figure 10), storing them within a Solution Set; - compute and prove candidate solutions to evolve to the state (s + 1) (block 204 in figure 10), according to single and multiple crossing techniques (block 205 in figure 10), mutation (block 206 in figure 10) , and elitism (block 207 in figure 10), based on the Satellite Model (SM) 21, where the Sweep and Mobilization Maneuvers interfaces are used (blocks 112a and 112b in figure 3, corresponding to block 112 in figure 10); genetic techniques are applied according to heuristic seeds and genetic factors (block 104a in figure 10); - the GA ends (block 208 in figure 10) according to the stopping criteria (that is, the maximum number of iterations and process time limits in block 104a in figure 10 in this context, reference can now be made to paragraph 6 ); - if the process is completed (block 209 in figure 10), the resulting Best Solution is validated (block 210 in figure 10) through the Plan Validation interface (blocks 113 Petition 870180071811, of 16/08/2018, p. 151/186 41/56 in figures 3 and 10) of the Satellite Model (SM) 21; otherwise, the N descending solutions are established to be the population for the next generation, and the GA 108-based processing step is iterated again starting from the Competition 202 selection sub-step. 5. SIMULATED RINGING [0135] The first Simulated Ringing (SA) was developed by S. Kirkpatrick [see, for example, S. Kirkpatrick, CD Jr. Gelatt, MP Vecchi, Optimization by Simu / ated Annealing (Simulated Ringing Optimization) , Science, Vol. 220, No. 4598, pgs. 671 to 680, 1983, d.o.i .: 10.1126 / science.220.4598.671], for global optimization in the early 1980s, and performed for various combinatorial optimization problems. Simulated Ringing (SA) is an optimization method that can be applied to research spaces for arbitrary problems. Like simple mountain climbing algorithms, SA needs only a single initial individual as a starting point and a unary search operation. It is inspired by the annealing process in metallurgy and materials science, as for example in the heat treatment of materials in order to change their properties, such as hardness. When annealing, or annealing, a metal, the initial temperature should not be too low and the cooling should be done slowly enough, to prevent the system from being trapped in a non-crystalline metastable state, representing a local minimum of energy. [0136] In physics, each set of positions of all atoms in a system configuration is weighted by its Boltzmann probability factor fs = e (-k B E (s) / T) , where E (s) is the current state energy (s), T is the cooling temperature measured in ° K (that is, degrees Kelvin), and kB = 1.380650524 χ 10 -23 J / K is the Boltzmann constant. [0137] In previous studies by Metropolis et al. [see, for example, N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, AH Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, Vol. 21, n ° 6, pgs. 1087 to 1090, 1953, d.o.i .: 10.1063 / 1.1699114], the Monte Carlo method was developed to calculate the properties of any substance that can be considered composed of individual interactive molecules. This procedure is Petition 870180071811, of 16/08/2018, p. 152/186 42/56 applied with the purpose of simulating a collection of atoms in thermodynamic equilibrium at a certain temperature. [0138] A new geometry close to the state (s + 1) is generated as a random displacement of the current displacement (s) of an atom in each iteration. The energy of the resulting new geometry is calculated, and the Energy Difference (ÁE) between the current geometry and the new geometry ΔΕ = E (s + 1) - E (s) is determined. The probability that this new geometry will be accepted, P (ÁE), is defined as: Ρ (ΔΕ) = ΔΕ> 0 ΔΕ <0 (11) [0139] As a consequence, if the new nearby geometry has a lower energy level, the transition is accepted, otherwise a uniformly distributed random number r (0, 1) is extracted and the step will only be accepted in the simulation if it is less than or equal to the Boltzmann probability factor, r <P (EA), also leading to chances of worsening the solutions to be selected. [0140] In SA, the evolution schedule is typically modeled by reducing the cooling temperature. The rate of decrease in temperature must be precisely adjusted, according to the complexity of the problem and the available convergence time. At high temperatures, fB is very close to 1, leading to the acceptance of many uphill steps. As the temperature drops, the proportion of accepted steps, which would increase the energy level, decreases. On the other hand, when the time spent (ts) expires, this results in T (ts = tmax) = 0, which cancels P (ÁE). Now the system will no longer escape from local regions and will rest at a local minimum. [0141] Subsequent studies have proven that SA algorithms with appropriate cooling strategies converge asymptotically to the global optimum. For example, P.J. van Laarhoven, E.H L. Aarts, Simulated Annealing: Theory and AppUcations', Mathematics and Its AppUcations, vol. 37, 1987, d.o.i .: 10.1007 / 978-94-015-7744-1, and A. Nolte, R. Schrader, A Note on the Finite Time Behavior of Simulated Anneaiing (Uma Petition 870180071811, of 16/08/2018, p. 153/186 43/56 Note on the Finite Time Behavior of Simulated Ringing), Operations Research Proceedings, 1996, p. 175 to 180, 1997, doi: 10.1007 / 978-3-642-60744-8_32, provide lists of the most important works showing that Simulated Ringing will converge to the global optimum if t ™ iterations are performed, including the studies by B. Hajek [see, for example, the tutoring / survey of theory and appiications of Simuiated Anneaiing (research tutorial theory and applications of Simulated annealing), Proceedings of the 24th IEEE Conference on Decision and Control, Vol. 24, p. 755 to 760, December 11 to 13, 1985, doi: 10.1109 / cdc.1985.268599]. The temperature schedule defines how the SA converges to the final solution, and has a major influence on whether the SA algorithm will succeed and how long it will take to find the global optimum. [0142] SA has the advantage of leaving a local minimum, but the disadvantage is that it is possible to return to the solutions already visited. Therefore, oscillations around local minimums are possible, and this can lead to a situation where a lot of computational time is spent on a small part of the solution set. A simple way to avoid this problem is to store all visited solutions in an ordered list, and only accept solutions that are not in the list. However, storing all the visited solutions and testing whether a candidate solution belongs to the list is usually very exhausting, both in terms of memory and computational time [here, for example, reference can be made to P. Brucker, Scheduiing Aigorithms (Scheduling Algorithms), 1995, doi: 10.1007 / 978-3-662-03088-2]. [0143] In the current SA application, the best plan solution from GA-based processing represents the initial schedule, to be updated with the set of tasks not yet planned in the PW search space. Similar to GA-based processing, a solution corresponds to a sequence of 0 (that is, zeros) and 1 (that is, ones), according to the viable and non-viable DTAs for the set of tasks. [0144] In the context of the SSP, the idea is to improve a solution by increasing its Solution Suitability, through an optimal verification and resolution of conflicts between previously planned DTAs and rejected DTAs in each iteration. Petition 870180071811, of 16/08/2018, p. 154/186 44/56 [0145] In Table 3 below, the concepts of SA applied to the SSP are reported: TABLE 3: SIMULATED SEALING APPLICATION TO THE SSP Ringing term Representation of annealing SSP application Energy Double Solution Suitability Cooling temperature Double Evolution Time and Acceptance Threshold [0146] Figure 11 schematically illustrates, by means of a flowchart, the processing step based on SA 109 of the satellite scheduling method 1 according to a preferred embodiment of the invention. [0147] In particular, based on the GA output solution provided by the GA 108-based processing step (shown in figure 10 and described in detail in paragraph 4) for a PW, once the SA parameters are defined ( block 104b in figure 11), the processing step based on SA 109 allows to calculate a single solution through the following sub-steps: - for a given PW, initialize the SA (block 301 in figure 11) with the best valid solution provided by the processing step based on GA 108; - select a new task to be planned according to predefined specific Gaussian and Poisson probability functions (block 302 in figure 11); - identify the scanning task neighborhood according to the influence of the relevant DTO within the intersection matrix (block 303 in figure 11); - compute the permutations of the conflicting tasks, ordered according to the chronology of their task neighborhoods, which promise a greater probability of success for the first tests (block 304 in figure 11); - find and prove the best combination of the exchanged DTAs (block 306 in figure 11), according to the SA acceptance criteria (block 307 in figure 11) and based on SM 21, where the Sweep Maneuver interfaces are used and Mobilization (blocks 112a and 112b in figures 3, corresponding to block 122 in figure 11); - the solution evolves (block 305 in figure 11) based on heuristic seeds, ringing factors (block 104b in figure 11), and the reduction in SA temperature (block 308 in figure 11); Petition 870180071811, of 16/08/2018, p. 155/186 45/56 - terminate the SA (block 309 in figure 11) according to the stopping criteria (that is, the maximum number of iterations and process time limits in block 104b in figure 11 - here, reference can now be made to the paragraph 6). [0148] According to this: - if the process is not completed (block 310 in figure 11) and the resulting Best Solution is valid (block 311 in figure 11) through the Plan Validation interface (blocks 113 in figures 3 and 11) of the Satellite Model (SM ) 21, the solution represents the initial entry for the next iteration of task selection sub-step 302; - if the process is completed and the Best Solution is valid, an optimal PW schedule is produced (blocks 111 in figures 3 and 11). 6. SCHEDULING SETTINGS [0149] While the total time interval available to process the scheduling of an entire Mission Horizon (MH) is considered as a project parameter dependent on the mission's Earth Segment chronology, the internal settings are conveniently adjusted according to the relative properties of the PWs and the algorithmic characteristics. [0150] The main role is played by the Complexity of Plan, which allows an estimate of the size of the research space to be analyzed according to the number of tasks involved to be scanned in a PW. As stated, greater complexity means statistically a greater number of combinations to be resolved and, therefore, a conflict resolution having costly verification. Thus, longer time frames are conveniently allocated to the most complex PWs. [0151] The trend of Plan Complexity as a function of the number of tasks follows a quadratic statistical trend, based on simulations, as shown in figure 12. • Ts as the period available for an MH Scheduling Session having a certain number of (p = 1, P) PWs; • Np as the set of tasks associated with the p-th PW; and • Cp as the Plan Complexity of the p-th PW, calculated according to the equation Petition 870180071811, of 16/08/2018, p. 156/186 46/56 (10). [0152] An a priori assessment of the relative scheduling period for each of the PWs is assumed: NC tt pp T p- 1s p (12) Σ N p C p p = 1 P [0153] From which it follows that Σ T p = T s P = 1 [0154] With reference to the global scheduling procedure (ie, satellite scheduling method 1), the time limits of the three base processes are conveniently adapted based on the characteristics of the Planning Window (PW) to be scheduled. The three basic processes mentioned are: 1. Processing steps 102, 103 and 105 (that is, Extensive Initialization, Plan Complexity, computation and analysis of the Intersection Matrix, and initial calculation of conflict-free solutions); 2. The processing step based on GA 108; and 3. SA-based processing, step 109. [0155] In particular: 1. Adequate time should be left for scheduling initialization (processing steps 102, 103 and 105) in order to calculate, as discussed in paragraph 3, a sufficient number of conflict-free solutions with a maximum rate of diversity; the trend of computational effort with respect to the population of initial solutions is approximately proportional; therefore, an available startup time of: hp = kT p + 2σ (13) Where k is the factor and σ is the standard deviation adapted from the statistical simulations, which allows obtaining the average number of solutions (according to figure 8) to satisfy the Extensive Startup at least 95% of times; Once the satellite model's average mission performance has been fixed for an average start-up, its Petition 870180071811, of 16/08/2018, p. 157/186 47/56 time must not nominally exceed Tp / 3; 2. GA parameters are defined according to GA characteristics, as shown in Table 4 below, where tGA and IterGA identify the stopping criteria; once one of the parameters is exceeded, processing based on GA 108 ends (block 209 in figure 10); GA stopping criteria are defined according to GA characteristics. By means of simulations, it must nominally result that: Tp / 5 <tGA <Tp / 3 and 50 <IterGA <100. TABLE 4: GENETIC ALGORITHM CONFIGURATIONS GA parameter Definition Interval Value tGA Algorithm time limit Between 1/5 and 1/3 Tp IterGA Maximum number of iterations Between 50 and 100 3. The SA parameters are defined according to the available scheduling time and HW performance, as shown in Table 5 below; in particular, tSA and IterSA identify the stopping criteria; once one of the parameters is exceeded, the SA 109-based processing step ends (block 310 in figure 11); through simulations, it nominally results that tSA> Tp / 3 and IterSA = 100, at least; Additional parameters are: • T0, which identifies the initial state temperature; • NpMax, as the maximum number of tasks to be exchanged at the same time; and • sfAcc, as the factor needed to calculate the acceptance limit for solutions. TABLE 5: SIMULATED RING SETTINGS SA parameter Definition Interval Value tSA Algorithm time limit At least 1/3 d Tp IterSA Maximum number of iterations At least 100 T0 Initial cooling Temperature Due to tSA NpMax Maximum number of tasks that can be switched at each iteration Between 9 and 10, according to the calculating performance of the HW and tSA machine Petition 870180071811, of 16/08/2018, p. 158/186 48/56 SA parameter Definition Interval Value sfAcc The solution acceptance function factor > 1 7. GENETIC FACTORS [0156] The genetic factors are basically adjusted according to the maximum values in their probability ranges reported in Table 2, due to the reduced available time for GA processing. [0157] In particular, a maximum crossing rate (gfc = 0.95) is suggested to increase the number of combinations of the solutions designated by the Competition Selection, for which an equal single point and multiple point crossing rate ( gfcm = 0.5) is expected. [0158] However, while elitism can be left as a constant value (gfe = 0.2), considering a population of fixed solutions (almost 2 children from 2 parents) along the iterations, an adaptive mutation it allows an increase in the probability of expanding the exploration of the research space, if there are no improvements for consecutive iterations. In this way, considering an initial mutation (gm0 = 0.1), a surplus (gm + = 0.1) is added if there is no benefit in terms of the adequacy result in the next generation's best solution, while a defect ( gm- = -0.1) is imposed if the benefit occurs. The restriction 0 <gm <1 must not be exceeded when, for the limit case of gm = 1, each solution is subjected to mutation. 8. TEMPERATURE REDUCTION [0159] The cooling rate (β) of the temperature that guides the evolution of SA is conveniently defined according to the tolerance that would be imposed on solutions that are worse than the best. A high cooling rate minimizes the approval of these solutions; on the other hand, slow cooling increases the possibilities for a worse choice, expanding SA research in the solutions domain. [0160] The values of T0 and β are conveniently defined according to the time limit imposed on the SA, and the condition that the temperature T tends to zero in its final condition from equation (14) defined below. Petition 870180071811, of 16/08/2018, p. 159/186 49/56 [0161] Through simulations, an average cooling imposed by conditions 3 <β <5 and T0 = 1 represents a good relationship to be pursued. According to these assumptions, it results easily, in time (ti): T (i,) = e t ~ Í 0 ISA ~ Í 0 (14) [0162] Where t0 and tSA represent the start and end times of the SA 109-based processing step, between sub-steps 301 and 311, respectively. ENERGY ALLOCATION [0163] Energia (E) de SA is conveniently configured according to the suitability of the solution at a given stage. This condition is balanced by the need to achieve an adequate energy difference between the solutions, in order to guarantee a reasonable acceptance probability for the worst solutions. [0164] Energy E is then associated with the Solution Suitability defined in equation (8), resulting in: N Obj fg = Σ i = 1 w i f i z NyAgend '' Σ1 j = 1 (15) [0165] To ensure a satisfactory acceptance limit, the configuration of the weights for the relevant objectives is conveniently defined according to the scope of the mission. 10. ACCEPTANCE FUNCTION [0166] The adjustment between T and E influences the solution's convergence during the evolution of SA in relation to the acceptance probability function, given by the equation: ΔΕ ΔΕ> 0 ΔΕ <0 (16) [0167] Where sfAcc is the solution acceptance factor (see Table 5 for reference), and ÁE = E (s + 1) - E (s) is the energy difference between the states close to the solution . [0168] As shown in figure 13 (which shows the evolution of the Petition 870180071811, of 16/08/2018, p. 160/186 50/56 according to the GASA acceptance probability), even if starting from a lower adequacy value, a very high acceptance function (bad acceptance line) can lead to small improvements or no improvement in convergence, for the best GASA solution. This is due to the fact that a high divergence in relation to the optimal locations does not allow the fixation of sub-optimal neighborhoods within the solutions evolved during the iterations. On the other hand, an appropriate acceptance (good acceptance line) can allow limited but substantial benefits, taking the GASA solution to a final schedule through satisfactory escapes from great locations, as it also potentially accepts solutions for which EA <0 results. This condition could not be achieved if no acceptance threshold is foreseen. 11. Probability Distributions [0169] The relevant distribution widths for the known Gaussian and Poisson probability functions, respectively, are chosen according to the prominence to be given to the priority of the scheduled tasks, respectively as: F p <, lm . <ΡΊ = e (17) F o . „„ (P) = e - x <” | 2 (18) [0170] Where p denotes the Relative Priority Classification between N tasks, defined as an integer ranging from 1 to N, where a lower Classification means a higher priority. [0171] To highlight the selection of priority tasks during the evolution of SA, the relevant variance factor for both distribution widths depends on the relative weight value (w1) of the priority tasks. Resulting in: x = K, ' 1 N ObJ Σ W n = 1 (19) [0172] Where 0 <Ki <1 is an additional adjustment factor that can vary, during annealing iterations, according to the evolution trend. By default, K = 1 can Petition 870180071811, of 16/08/2018, p. 161/186 51/56 be constantly assumed to be a first guess value. 12. TEST APPLICATION OF THE INVENTION [0173] The present invention (GASA) was applied by the Applicant to a challenging test scenario after the careful adjustment discussed in the previous paragraphs. Comparisons of GASA's performance against a deterministic strategy, properly guided to limit the exploration of non-optimal paths, are detailed below. [0174] Under identical conditions and with exploration of the Satellite Model (SM), according to the selected test scenario, a number of 50 iterations were performed for the execution of the present heuristic strategy in each stage of the problem, where a maximum of Tc = 100 s was established as the threshold for algorithmic convergence. [0175] A deterministic comparison algorithm of Depth and Width Survey (BDS) was performed once for each problem. He progressively tried to schedule an RA at each stage until the maximum time limit was reached, while significant computational effort was required to resolve the conflicts as the number of tasks involved increased. To limit the analysis of the search domain, each optimal scan in terms of the Task Suitability function was stored and repeated for the next iterations; in addition, all unviable branches were discarded a priori through an analysis of the previous solutions. [0176] Despite the assumptions made, while for some tasks the BDS-type algorithm takes a short period of time (about 50 s for 10 tasks), for the optimization of 50 tasks it took about 30 hours (108,000 s) . 12.1 PERFORMANCE [0177] The performance of GASA in resolving verification conflicts, between multiple requests, was tested with a real optical satellite mission. The optimization performance related to a strategy based on pure Simulated Ringing (SA) was originally considered as a term for evaluating improvements due to the application of Genetic Algorithms, while the results of the BDS-type algorithm were taken as a common term of comparison. [0178] As shown in figure 14 (which shows a comparison, in terms of the number of planned tasks, between the applications of the BDS type algorithm, a pure SA, Petition 870180071811, of 16/08/2018, p. 162/186 52/56 and a GASA), an average of 1.5 tasks are additionally planned using the GASA technique over pure SA. In particular, from figure 14, it can be seen that GASA maintains performance better when the complexity of the problem increases (greater number of tasks). [0179] Furthermore, as seen in figure 15 (which shows a comparison, in terms of the difference in the planned tasks, between applications of pure SA and GASA), a percentage of about 58% of the solutions coming from GASA maintains on average the error below 1 planned task, against the lower 35% resulting from pure SA. 12.2 GASA CHARACTERISTICS [0180] According to the Plan Complexity trend shown in figure 12, the GASA strategy was analyzed with respect to a set of specific characteristics including robustness, convergence precision and computational effort. a) The guarantee of robustness of an algorithm is given by the ability to converge to a satisfactory solution also when a bad set of inputs is assumed. This characteristic in GASA is achieved through the application of practices that allow an expansion of the research to portions of the solution domain that were not initially taken into account. The adaptive mutation applied during genetic evolution and the acceptance probability imposed in the annealing process are techniques that allow the extension of the research to new solution paths, increasing the possibilities of convergence for optimal results. However, increasing robustness can be achieved through an appropriate adjustment of techniques according to the specific scope of the mission. b) The accuracy of the convergence was analyzed based on the standard deviation associated with the number of tasks planned for the set of iterations. In figure 16 (which shows a comparison between the standard deviation and the average value of the number of tasks planned using the GASA technique) it is shown that the standard deviation (σ) does not increase with the Complexity of Plan and, in most cases, is limited to a fraction of a task, with an average value σ ^ ι = 0.75. This result reveals an adequate repeatability of the results for equivalent scenarios, and a good precision of the proposed algorithm. c) The computational effort was estimated by imposing a convergence time Tc Petition 870180071811, of 16/08/2018, p. 163/186 53/56 = 100 s for algorithmic processing only. Assuming this forced time and according to an interval surplus given by the performance of the SM in Validation, an average total convergence time Twc = 140 s was estimated. [0181] The performance requirement relevant to the optical satellite mission selected to test the present invention requires the execution of the SSP of a minimum number of tasks Ntmh = 100 within a given Scheduling Session Tss = 600 s. [0182] According to the results obtained, an average number of 25 tasks are planned using the GASA strategy for a relevant number of incoming tasks (50 tasks at the beginning), within a 900 s PW. This means that, for an average of 4 planning windows (PWs) of 900 s each (3600 s), a number of 100 tasks must be practically planned. Computational performance is also in line with the requirement; in fact, a maximum time of 4 x 140 s = 560 s <600 s is required for global scheduling. [0183] In addition, as shown in figure 17 (which shows the average number and the minimum / maximum difference in the number of tasks planned using the GASA technique), the GASA strategy managed to recover at least one optimal solution for 40% cases, also for some cases of significant complexity. This means that a parallelization of the strategy theoretically would allow to increase efficiently the probabilities of arriving at optimal solutions for a consistent number of cases with the same computational time effort. 12.3 GASA BENEFITS [0184] The good performance presented together with the speed of convergence (100 s as a standard for the scenarios of interest) make the GASA technique a good method to achieve satisfactory solutions for the SSPs relevant to the mission under investigation. In fact, the growth of the Complexity of Plan did not cause failures in the computed solutions, since, as described, GASA managed to approach, and achieve, optimal solutions. These circumstances occurred in an average time interval up to 700 times shorter than necessary for the convergence of the BDS strategy (140 s versus 108,000 s) in a 50 task test scenario. [0185] The benefits hypothesized from the combination of the different algorithms Petition 870180071811, of 16/08/2018, p. 164/186 54/56 heuristics, during the investigation of the global strategy for multi-objective optimization, proved to be real when applied to the optical satellite mission selected to test the present invention. In fact, the GASA technique is able to satisfy the scheduling requirements necessary for that specific mission. 13. ADVANTAGES OF THE INVENTION [0186] From the foregoing description, the technical advantages of the present invention are immediately clear. [0187] In this regard, it is important to note that the present invention allows the fulfillment of all stages of the mission chain in the Terrestrial Segment of an EO satellite in a multi-mission environment. The present invention allows to maximize the possibilities of acquisition of requests according to specific mission restrictions, minimizing, or rather, resolving, mutual conflicts between acquisition tasks within a predefined Scheduling Session. [0188] In particular, the present invention explores an innovative hybrid strategy for the optimization of the Satellite Scheduling Problem (SSP), such an innovative hybrid strategy (called GASA) being based on Genetic Algorithms (GAs) to find first optimal solutions and in Simulated Ringing (SA) for local research within the vicinity of the solutions recovered by GAs (to try to plan tasks initially rejected according to a best effort approach), thus allowing to extend the search for new solutions and increasing the possibilities of converging for optimal results. [0189] Furthermore, the combined GASA heuristic strategy, as demonstrated earlier by the results of applying the invention to a real optical satellite, offers: - high robustness, when converging to a satisfactory solution also with bad sets of inputs, thanks to the adaptive mutation during the genetic evolution and the adequate design of the acceptance function in the annealing process; - a good repeatability of the results for equivalent scenarios and, therefore, a good precision and quality of the results; and also - predictable time performances. Petition 870180071811, of 16/08/2018, p. 165/186 55/56 [0190] Additionally, it is also worth noting that the Mission Planner (MP) according to the present invention is applicable to a generic EO satellite, as it exploits reusable software elements and, to adapt and interact with different missions, it only requires the configuration of the parameters and the integration of an external Satellite Model (SM), thus allowing also to reduce the number of test and development activities. [0191] In particular, the MP's multi-mission architecture according to the present invention offers several advantages, particularly: - the reduction of effort in the development, testing and integration of the necessary components within the architecture and Terrestrial Segment of the EO systems; and - the application of fully reusable software modules, Graphical User Interfaces (GUIs) and algorithms for extended space programs. [0192] In addition, the Mission-dependent Satellite Model (SM), integrated with the Mission Planner (MP), ensures strict compliance of maneuvers with the satellite mission rules. [0193] Finally, it is important to emphasize that the present invention, although described above with reference to an optical satellite (ie, a remote sensing satellite equipped with an optical sensor), can be applied with advantages in scheduling: - a single remote sensing satellite equipped with a sensor of a different type (such as a SAR or an infrared sensor), or even equipped with several sensors of different types (such as a SAR together with an optical sensor); and also - a constellation of satellites equipped with sensors of the same or different types. [0194] In addition, the present invention can be used with advantages for the optimization of scheduling, not only of the Planning Windows (PWs) for image acquisition, but also: - Loading (Uplink) and Unloading (Downiink) Windows (UWs, DWs); and - more generally, even from generic satellite resources (such as memory resources, energy resources, etc.) from a single EO satellite (in simple and Petition 870180071811, of 16/08/2018, p. 166/186 56/56 multi-spectral) or EO satellite constellations. Petition 870180071811, of 16/08/2018, p. 167/186
权利要求:
Claims (6) [1] Claims 1. Satellite scheduling method (1), characterized by comprising: a) Produce initial scheduling plans (105), based on input requests related to tasks to be performed within a certain period of time by one or more remote sensing satellites, in which, for each of the said scheduling plans respective tasks are scheduled, which do not conflict with each other in time and in the use of satellite resources from the remote sensing satellite (s), with each of the tasks to be performed being scheduled at least at least one of the initial scheduling plans; b) Apply processing based on genetic algorithms (108) to the initial scheduling plans, to produce a scheduling plan based on genetic algorithms that: - is optimized in relation to the mission objectives; and - complies with certain restrictions related to satellite resources, the tasks to be performed, and the specified period of time; c) Apply processing based on simulated ringing (109) to the scheduling plan based on genetic algorithms, to produce a scheduling plan based on simulated ringing: - that meets the stated mission objectives; - which complies with the given restrictions; and - in which a greater number of tasks are scheduled than in the scheduling plan based on genetic algorithms; where, in step (b), an iterative procedure based on genetic algorithms is included, comprising: - in a first iteration based on genetic algorithms: - select a subset of the initial scheduling plans based on the mission objectives (202, 203); and - apply crossing (205), mutation (206), and elitism (207) techniques, based on the respective predefined genetic evolution factors for the selected subset of the initial scheduling plans, to produce scheduling plans Petition 870180071811, of 16/08/2018, p. 168/186 [2] 2/4 evolved that meet the given restrictions; - in each iteration based on genetic algorithms, after the first iteration: - select, based on the determined mission objectives, a subset of the evolved scheduling plans produced in the previous iteration based on genetic algorithms (202, 203); and - apply the techniques of crossing (205), mutation (206) and elitism (207) to the selected subset of the evolved scheduling plans produced in the iteration based on previous genetic algorithms, to produce new evolved scheduling plans that meet the given restrictions; with the mentioned step (b) also including: - stop performing the iterative procedure based on genetic algorithms, when certain stop criteria related to genetic algorithms are met (208, 209); and - automatically select, among the evolved scheduling plans produced in the last iteration based on genetic algorithms performed, the one that best fits the determined mission objectives; with the satellite scheduling method (1) also including: - compute an intersection matrix (103) representing conflicts over time and in the use of satellite resources for tasks to be performed within the given period of time; - compute the Complexity of Plan (103) based on the intersection matrix; and - compute certain stopping criteria related to genetic algorithms, based on the intersection matrix (104, 104a); and with the initial scheduling plans being produced based on the intersection matrix (105). 2. Method of scheduling satellites according to claim 1, characterized in that step (c) includes performing an iterative procedure based on simulated ringing comprising: - in a first iteration based on simulated annealing: - select, according to one or more predefined probability functions, Petition 870180071811, of 16/08/2018, p. 169/186 [3] 3/4 an unscheduled task in the scheduling plan based on genetic algorithms (302); - identify a neighborhood of the selected task (303), with the neighborhood identified including a set of conflicting tasks not scheduled in the scheduling plan based on genetic algorithms; - perform permutations of conflicting tasks in the identified neighborhood (304); - apply a simulated ringing technique (305, 306, 307, 308) to the results of the permutations performed, to find tasks that: - are not scheduled in the scheduling plan based on genetic algorithms; - are schedulable together with the tasks already scheduled in that scheduling plan based on genetic algorithms; - are suited to the mission objectives determined; and - comply with the restrictions given; - produce a scheduling plan including the tasks found; - in each iteration based on simulated ringing, after the first iteration: - select, according to the predefined probability function (s), another unscheduled task in the scheduling plan produced in the previous iteration based on simulated ringing (302); - identify a neighborhood of the selected additional task (303), in which the identified neighborhood includes a set of conflicting tasks not scheduled in the scheduling plan produced in the previous iteration based on simulated ringing; - perform permutations of conflicting tasks in the identified neighborhood (304); - apply the simulated ringing technique (305, 306, 307, 308) to the results of the permutations carried out, to find tasks that: - are not scheduled in the scheduling plan produced in the previous iteration based on simulated ringing; - they are scheduled together with the tasks already scheduled in the referred scheduling plan produced in the previous iteration based on simulated ringing; - fit the mission objectives determined; and Petition 870180071811, of 16/08/2018, p. 170/186 [4] 4/4 - comply with the restrictions given; - produce a new scheduling plan, including the tasks found; with step (c) also including the interruption of the execution of the iterative procedure based on simulated ringing, when certain stopping criteria related to the simulated ringing are met (309,310); and with the scheduling plan based on simulated annealing being the scheduling plan produced in the last iteration based on simulated annealing performed. 3. Method of scheduling satellites, according to claim 2, characterized by also including the computation of certain stopping criteria related to the simulated ringing, based on the intersection matrix (104, 104b). 4. Method of scheduling satellites, according to any of the preceding claims, characterized in that the mission objectives determined are mathematically represented by a global cost function calculated based on several local cost functions based on the given restrictions. [5] 5. A processing system (4) for Earth Observation systems, including one or more remote sensing satellites, characterized in that said processing system (4) is programmed to execute the satellite scheduling method (1) as claimed in any of the preceding claims. [6] 6. Software program product, characterized by comprising one or more portions of software code that are executable by a processing system, so that, when executed, said processing system executes the satellite scheduling method (1) as claimed in any of claims 1 to 4.
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公开号 | 公开日 EP3406531B1|2020-10-28| US20180341894A1|2018-11-29| EP3406531A1|2018-11-28| ES2842591T3|2021-07-14| AR111895A1|2019-08-28| US10726368B2|2020-07-28| CN108960483A|2018-12-07| RU2018118555A|2019-11-21| IT201700056428A1|2018-11-24|
引用文献:
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法律状态:
2019-03-26| B03A| Publication of a patent application or of a certificate of addition of invention [chapter 3.1 patent gazette]|
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