Optimized deployment method and system for low-orbit large-scale satellite constellation

Abstract

The invention relates to the technical field of satellites, and particularly discloses an optimized deployment method and system for a low-orbit large-scale satellite constellation, and the method comprises the steps: S1, constructing a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and vehicle parameters; s2, establishing a multivariable mixed integer optimization objective function according to information contained in nodes and edges in the constellation deployment network model; s3, determining a limited main problem RMP and a sub-problem of the target function, and solving the RMP through a column generation algorithm to obtain a target value and a dual variable; s4, when any sub-problem has a new column, and the new column is added into the RMP to reduce the target value, adding the new column into the RMP to update the target value and the dual variable; and S5, directly outputting a satellite launching deployment scheme or outputting the satellite launching deployment scheme after solving the target value of an integer according to a branch and bound method when all the sub-problems do not have new columns or all the new columns are added into the RMP so that the target value cannot be reduced.

Description

Technical Field

[0001] The present invention relates to the field of satellite technology, and in particular to a method for optimizing the deployment of a large-scale low-orbit satellite constellation. Background Art

[0002] Traditional optimization methods, such as the simplex method and heuristic algorithms, have many deficiencies when dealing with large-scale mixed integer optimization problems. When faced with large-scale time-layer related variables to be optimized and multiple coupled complex equality / inequality constraints, these methods often show problems such as large optimal solution search space dimensions, low computational efficiency, and algorithm parameter settings relying on experience. These deficiencies make it difficult for traditional methods to effectively solve complex optimization problems in the deployment of large-scale low-orbit constellation launches. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a method and system for optimizing the deployment of a large-scale low-orbit satellite constellation, which converts complex solution constraints into multiple simple sub-problems, effectively reducing the search space for the optimal solution and improving computational efficiency.

[0004] The present invention provides a method for optimizing deployment of a large-scale low-orbit satellite constellation, comprising:

[0005] Step S1, obtaining a low-orbit large-scale constellation, satellite parameters and carrier parameters, and constructing a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and carrier parameters;

[0006] Step S2, establishing a multivariable mixed integer optimization objective function according to information contained in nodes and edges in the constellation deployment network model;

[0007] Step S3, determining the restricted main problem RMP and subproblems of the objective function, and solving the RMP by a column generation algorithm to obtain the objective value and dual variables;

[0008] Step S4, when any sub-problem has a new column, and the addition of the new column to the RMP makes the target value smaller, the new column is added to the RMP to update the target value and the dual variable;

[0009] Step S5, when there are no new columns in all sub-problems, or when all new columns added to the RMP cannot make the target value smaller, directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving the integer target value according to the branch and bound method; the satellite launch deployment plan includes at least: launch time, launch path and launch cost.

[0010] In a possible implementation, the S2 includes:

[0011] The objective function J is as follows:

[0012]

[0013]

[0014] Among them, J1 is the first objective function, J2 is the second objective function, x is the number of satellites carried by each carrier, y is the decision variable, d is the demand for satellites at node i, v and V are carrier indexes, l and N are orbital indexes, is the launch cost of launching vehicle v into orbit l, is the decision variable for launching the vehicle v to the target orbit l at time k, The manufacturing cost of each satellite is is the number of satellites launched by vehicle v into orbit l, represents the satellite storage cost per unit time, is the time difference between time node i and time node j, U k Constellation performance evaluation at time k, Δt k is the time difference between time node k and time node k+1, and k and K are time series indexes.

[0015] In a possible implementation, the constraints of the objective function include flow constraints, edge capacity constraints, carrier availability constraints, and dual variable constraints; S2 includes:

[0016] The flow constraints are as follows:

[0017]

[0018] The capacity constraints on each edge are as follows:

[0019]

[0020] The vehicle availability constraints are as follows:

[0021]

[0022] The dual variable constraints are as follows:

[0023]

[0024] Among them, i is the node name, V is the node set, k and K are time series indexes, is the flow from node i to node j at time k, is the flow from node j to node i at time k, is the demand for satellites by node i at time k, j is the node name, N + (i)is the set of nodes that have inflow effects on node i, N - (i) is the set of nodes that have outflow effects on node i, κ ij is the maximum flow allowed by the edge formed by nodes i and j, is the decision variable for launching vehicle v to target orbit l at time k, l and N are orbit indices, and A is the set of orbit edges.

[0025] In a possible implementation, S3 includes:

[0026] Get the new column;

[0027] When the new column exists, adding the new column to the RMP;

[0028] The RMP is solved by a column generation algorithm to obtain the target value and the dual variable.

[0029] In a possible implementation, S3 further includes:

[0030] The new column is added to the RMP according to the following formula:

[0031]

[0032] X p ≤κ

[0033] BX p =d p

[0034] X p ≥0

[0035] Where c is the construction cost and time cost information of each arc in the constellation deployment network model, ω * is the dual variable of the capacity constraint, is the dual variable of the flow constraint, X p is the satellite traffic represented by the satellite p to be solved, matrix B is the vertex-edge association matrix, κ is the edge capacity information, d p For the requirements related to satellite p.

[0036] In a possible implementation, S3 further includes:

[0037] Setting all decision variables in the RMP to binary variables and setting parameters of the mixed integer programming MIPGap;

[0038] The objective value and dual variables in integer form are obtained through mixed integer programming.

[0039] In a possible implementation, S3 further includes:

[0040] Dummy variables and dummy costs are set in the RMP.

[0041] In a possible implementation, S3 further includes:

[0042] The dummy variables and dummy costs are set in the RMP according to the following formula:

[0043] J1=c T Yλ+c init λ

[0044] J2=-U(Yλ)Δt k

[0045] Yλ≤κ

[0046] Λλ=1 |p|

[0047] 0≤λ[i],i∈[1,...|P|]

[0048] Among them, λ is the selection of each satellite path, U is the constellation performance evaluation, Δt k is the time difference between time node k and time node k+1, c init is the initial penalty variable, the matrix Y represents all possible paths of satellite p, N represents the number of possible paths, P represents the number of nodes, and Y v represents the vth path of Y, c is the deployment cost and time cost of each arc segment, c T is the inversion of c, κ is the capacity information of the edge, and i is a positive integer.

[0049] In a possible implementation, the S4 includes:

[0050] The sub-problems are screened by using the dual variables of the capacity constraint of the objective function to obtain a sub-problem set without repeated sub-problems;

[0051] The subproblem set is solved by Dijkstra algorithm or A* algorithm to obtain a new column, and the target value and dual variable are updated according to the new column.

[0052] The present invention also provides a low-orbit large-scale satellite constellation optimization deployment system, which is applied to any of the above-mentioned optimization deployment methods, including:

[0053] A model building module, used to obtain a low-orbit large-scale constellation, satellite parameters and carrier parameters, and build a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and carrier parameters;

[0054] A function building module, used to build a multivariable mixed integer optimization objective function based on the information contained in the nodes and edges in the constellation deployment network model;

[0055] A first solving module, used for determining the restricted main problem RMP and subproblems of the objective function, and solving the RMP by a column generation algorithm to obtain the objective value and the dual variable;

[0056] A second solving module is configured to add a new column to the RMP to update the target value and the dual variable when a new column exists in any subproblem and the new column is added to the RMP so as to reduce the target value;

[0057] The output module is used to directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving the integer target value according to the branch and bound method when there are no new columns in all sub-problems or all new columns added to the RMP cannot make the target value smaller; the satellite launch deployment plan at least includes: launch time, launch path and launch cost.

[0058] The optimization deployment method and system of a large-scale low-orbit satellite constellation provided by the present invention is based on a multivariable mixed integer optimization mathematical equation generated by a partial time expansion dynamic network model of space logistics, and adopts the Danzig-Wolf decomposition idea to convert complex solution constraints into multiple simple sub-problems. By setting a sub-problem filter, the dual variables of the capacity constraint are judged to be positive or negative, and the saturated path is screened to avoid repeated calculations. The sub-problem solution is converted into a minimum path problem, and a minimum path solution method such as Dijkstra and A* algorithm is adopted, thereby effectively reducing the optimal solution search space and improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A schematic diagram of a flow chart of an optimized deployment method provided by an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of constructing a constellation deployment network model provided by an embodiment of the present invention;

[0061] Figure 3 A schematic diagram of sub-problems and solution times of different algorithms provided by an embodiment of the present invention;

[0062] Figure 4 A schematic diagram of launch deployment windows for satellites provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following detailed description of the embodiments of the present invention is further described in detail in conjunction with the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to exemplarily illustrate the principles of the present invention, but cannot be used to limit the scope of the present invention, that is, the present invention is not limited to the preferred embodiments described, and the scope of the present invention is defined by the claims.

[0064] In the description of the present invention, it should be noted that, unless otherwise specified, “plurality” means two or more than two; the terms “first”, “second”, etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; for ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0065] Figure 1 A schematic diagram of a flow chart of an optimized deployment method provided by an embodiment of the present invention, such as Figure 1 As shown, the present invention provides a method for optimizing deployment of a large-scale low-orbit satellite constellation, comprising:

[0066] Step S1, obtaining a low-orbit large-scale constellation, satellite parameters and carrier parameters, and building a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and carrier parameters;

[0067] Figure 2 The corresponding relationship between each node and arc type in the constellation deployment network model and the significance of each decision node in the specific launch mission is demonstrated.

[0068] Step S2, establishing a multivariable mixed integer optimization objective function based on the information contained in the nodes and edges in the constellation deployment network model;

[0069] Step S3, determining the restricted main problem RMP and subproblems of the objective function, and solving the RMP by a column generation algorithm to obtain the objective value and dual variables;

[0070] In a possible implementation, S3 further includes: setting all decision variables in the RMP as binary variables and setting parameters of the mixed integer programming MIPGap; and obtaining the target value and dual variable in integer form by solving the mixed integer programming.

[0071] In a possible implementation, S3 further includes: setting virtual variables and virtual costs in the RMP.

[0072] Step S4, when there is a new column in any sub-problem, and the addition of the new column to the RMP makes the target value smaller, the new column is added to the RMP to update the target value and the dual variable;

[0073] In a possible implementation, S4 includes: screening subproblems by dual variables constrained by the capacity of the objective function to obtain a subproblem set with duplicate subproblems removed; solving the subproblem set by Dijkstra algorithm or A* algorithm to obtain a new column, and updating the objective value and dual variables according to the new column.

[0074] Step S5, when there are no new columns in all sub-problems, or when all new columns added to RMP cannot make the target value smaller, directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving the integer target value according to the branch and bound method; the satellite launch deployment plan includes at least: launch time, launch path and launch cost.

[0075] The optimization deployment method of the present invention is described below in conjunction with the formula.

[0076] According to the information contained in the nodes and edges in the constellation deployment network model, it is converted into a multivariable mixed integer optimization mathematical equation.

[0077] The objective function J is as follows:

[0078]

[0079] Among them, J1 is the first objective function, J2 is the second objective function, x is the number of satellites carried by each carrier, y is the decision variable, d is the demand for satellites at node i, v and V are carrier indexes, l and N are orbital indexes, is the launch cost of launching vehicle v into orbit l, is the decision variable for launching the vehicle v to the target orbit l at time k, The manufacturing cost of each satellite is is the number of satellites launched by vehicle v into orbit l, represents the satellite storage cost per unit time, is the time difference between time node i and time node j, U k Constellation performance evaluation at time k, Δt k is the time difference between time node k and time node k+1, and k and K are time series indexes.

[0080] In a possible implementation, the constraints of the objective function include flow constraints, edge capacity constraints, carrier availability constraints, and dual variable constraints;

[0081] The flow constraints are as follows:

[0082]

[0083] The capacity constraints on each edge are as follows:

[0084]

[0085] The vehicle availability constraints are as follows:

[0086]

[0087] The dual variable constraints are as follows:

[0088]

[0089] Among them, i is the node name, V is the node set, k and K are time series indexes, is the flow from node i to node j at time k, is the flow from node j to node i at time k, is the demand for satellites by node i at time k, j is the node name, N + (i) is the set of nodes that have an inflow effect on node i, N - (i) is the set of nodes that have outflow effects on node i, κ ij is the maximum flow allowed by the edge formed by nodes i and j, is the decision variable for launching vehicle v to target orbit l at time k, l and N are orbit indices, and A is the set of orbit edges.

[0090] The original integer programming problem is reformulated as a set covering problem, that is, the problem of solving the optimization variables of the carrier transit time waiting time is transformed into a satellite launch path selection problem to adapt to the column generation method.

[0091] Minimize λ

[0092]

[0093] J1=c T Yλ (2-2)

[0094] J2=-U(λ)Δt k (2-3)

[0095] subject to

[0096] Yλ≤κ (2-4)

[0097] Λλ=1 |p| (2-5)

[0098] λ∈{0,1} x (2-6)

[0099] Among them, J1 is the first objective function, J2 is the second objective function, and c Tis the inversion of c, where c is the deployment cost and time cost of each arc segment, λ is the selection of each satellite's path, matrix Y represents all possible paths of satellite p, U is the constellation performance evaluation, Δt k is the time difference between time node k and time node k+1, κ is the time cost, and n is the number of nodes.

[0100] In a possible implementation, S3 includes: obtaining a new column; when the new column exists, adding the new column to the RMP; solving the RMP through a column generation algorithm to obtain a target value and a dual variable.

[0101] Add a new column to RMP according to the following formula:

[0102]

[0103] X p ≤κ (3-2)

[0104] BX p =d p (3-3)

[0105] X p ≥0 (3-4)

[0106] Among them, c is the construction cost and time cost information of each arc in the constellation deployment network model, ω* is the dual variable of the capacity constraint, is the dual variable of the flow constraint, X p is the satellite traffic represented by the satellite p to be solved, matrix B is the vertex-edge association matrix, κ is the edge capacity information, d p For the requirements related to satellite p.

[0107] The constraints on the optimization variables are relaxed, and the original problem is transformed into a linear programming to construct a restrictive master problem RMP. Virtual variables and virtual costs are set in the RMP, and the column generation method is allowed to be started when the path matrix Y is empty.

[0108] In a possible implementation, S3 further includes:

[0109] The dummy variables and dummy costs are set in RMP according to the following formula:

[0110] J1=c T Yλ+c init λ (4-1)

[0111] J2=-U(Yλ)Δt k (4-2)

[0112] Yλ≤κ (4-3)

[0113] Λλ=1|p| (4-4)

[0114] 0≤λ[i],i∈[1,...|P|] (4-5)

[0115] Among them, λ is the selection of each satellite path, U is the constellation performance evaluation, Δt k is the time difference between time node k and time node k+1, c init is the initial penalty variable, the matrix Y represents all possible paths of satellite p, N represents the number of possible paths, P represents the number of nodes, and Y v represents the vth path of Y, c is the deployment cost and time cost of each arc segment, c T is the inversion of c, κ is the capacity information of the edge, and i is a positive integer.

[0116] The following is a simulation experiment of the optimization deployment method of the present invention, and the experimental process is as follows:

[0117] Step 1: Given a large-scale low-orbit constellation, satellite and carrier-related parameters, set the parking orbit constellation and the target orbit constellation, and build the corresponding constellation deployment network model based on the parameters. The relevant parameters are as follows in Tables 1 and 2:

[0118] Table 1

[0119]

[0120]

[0121] Table 2

[0122]

[0123]

[0124] Based on passenger demand and transportation schedules, a multi-level graph model containing different launch modes (different types of carriers, different orbit entry modes, etc.) is generated. By reading static network files and time-extended network files, a basic network is constructed, and a time-extended network is generated based on the launch time information of the carrier, finally forming a complete constellation deployment network model.

[0125] The constellation deployment network model includes nodes and arcs, where nodes represent stations of transportation vehicles or departure and destination of passengers, and arcs represent connections between transportation vehicles or walking paths.

[0126] Step 2: Use the column generation algorithm to solve the continuous relaxation problem.

[0127] First, initialize the parameters of the column generation algorithm, including the graph model, satellite mission requirements, source nodes and sink nodes, virtual time cost and virtual launch cost. Then, construct the restricted master problem RMP, add virtual variables and capacity constraints, carrier availability constraints in the RMP, and set the objective function. The objective function adopts weighted multi-objective optimization, assigning different weights to time cost and launch cost respectively. By solving the RMP, the initial solution is obtained and its dual variable is calculated.

[0128] Step 3. In each iteration of the column generation algorithm, first solve the RMP and update the objective value and dual variables. Then, solve the subproblem, find new paths, and add them to the RMP. The subproblem can be solved by Dijkstra's algorithm or A* algorithm. For each passenger demand, calculate its shortest path and adjust the path cost according to the dual variables. If a new path is found, add it to the RMP and update the objective value and dual variables of the RMP. Repeat the above process until the stopping condition is met, that is, no new paths are found or the objective value of the RMP no longer changes.

[0129] Step 4: In the last step of the column generation algorithm, an integer solution is obtained through mixed integer programming. All decision variables in RMP are set as binary variables, and the MIPGap parameters are set to control the accuracy of the mixed integer solution. The final integer solution is obtained by solving the mixed integer programming problem. Based on the integer solution, the optimal path for each passenger is determined, and the path type and number are counted.

[0130] Step 5: Use the four algorithm configurations (Filter_on, A*), (Filter_on, Dijstra), (Filter_off, A*), and (Filter, Dijstra) to solve 10 times respectively, and compare the number of sub-problems and the average calculation time, and output the performance comparison results of different algorithms. The output includes instance construction time, solution time, integer solution solution time, optimality gap, and the number of sub-problems solved during the solution process. By counting and drawing the distribution map of path types and numbers, the launch deployment of the constellation is analyzed. The results are as follows: Figure 3 shown.

[0131] The column generation algorithm has high algorithm compatibility. The above verifies the influence of whether to use subproblem filters when selecting subproblems and whether to use A* algorithm and Dijstra algorithm when solving subproblems on the final solution time. Gurobi supports the use of hierarchical and weighted methods to solve multi-objective optimization problems. Since Dijstra and A* algorithms are limited to solving single-objective problems, the weighted method is used to transform multi-objective optimization problems into single-objective optimization problems.

[0132] Subproblem filters are implemented and tested to analyze their impact on the algorithm's performance. The purpose of the subproblem filter is to reduce the number of pricing problems that need to be solved in the column generation algorithm, thereby improving the overall solving efficiency. The filter determines whether a specific satellite task needs to be rerun by checking whether each satellite task uses an arc with a negative capacity dual variable. If the pricing problems of all satellite tasks have been solved in the previous iteration and no new columns have been added to the basis, or the objective value has not changed in the last iteration, then no satellite task will be rerun.

[0133] From the experimental results, when the filter is not used, the Dijkstra algorithm and the A algorithm solve 25920 and 19440 pricing problems, respectively, and the solution time is 140.97 seconds and 131.23 seconds, respectively. After the filter is enabled, the number of pricing problems solved by the two algorithms is reduced to 20880 and 16129, respectively, and the solution time is also reduced to 108.5 seconds and 92.23 seconds, respectively. This shows that the subproblem filter effectively reduces the number of pricing problems that need to be solved, thereby shortening the total solution time of the algorithm. In particular, the performance improvement of the A algorithm after the filter is enabled is more significant, and the solution time is reduced by 15.0% year-on-year, while the solution time of the Dijkstra algorithm is reduced by 15.0% year-on-year. This result emphasizes the importance of subproblem filters in optimization algorithms, especially when dealing with large-scale optimization problems. By effectively reducing unnecessary calculations, subproblem filters not only improve the efficiency of the algorithm, but also help save computing resources, and are an important tool for solving complex optimization problems.

[0134] The algorithm performance of using Dijkstra algorithm and A algorithm to solve subproblems under different configurations was compared. Specifically, the solution time and the number of pricingproblems processed by the two algorithms were examined under the conditions of enabling and disabling the subproblem filter. First, when the subproblem filter was turned off, the model solution time using Dijkstra algorithm was 140.97 seconds, while when using A algorithm, the solution time dropped to 131.23 seconds, a year-on-year decrease of 6.9%. This shows that A algorithm is more efficient than Dijkstra algorithm without using filters. Furthermore, when the subproblem filter was enabled, the solution time of Dijkstra algorithm was 108.5 seconds, while A algorithm was further shortened to 92.23 seconds, a year-on-year decrease of 15.0%. This result emphasizes the significant improvement of the solution efficiency of A algorithm after enabling the filter. In addition, from the perspective of the number of pricingproblems processed, A algorithm processed a smaller number of problems regardless of whether the filter was enabled, which may be due to its higher path search efficiency, thereby reducing unnecessary calculations and iterations.

[0135] In summary, the A* algorithm shows better time efficiency and processing efficiency than the Dijkstra algorithm when solving the sub-problems of the satellite launch deployment optimization problem, regardless of whether the sub-problem filter is applied. This finding provides strong data support for selecting more efficient algorithms in similar optimization problems in the future.

[0136] Step 6: If necessary, set the decision variables of the last column generation iteration to binary to find an integer solution, thereby completing the optimization of the launch deployment strategy of the satellite constellation. Output the satellite launch deployment decision time node to the schedule, so as to realize the formulation of the satellite deployment strategy for the entire constellation. The visualization results are as follows: Figure 4 As shown, the horizontal axis is time, the vertical axis is the satellite launch mission number, the dark color represents the satellite waiting time on the ground, and the light color represents the satellite in-orbit operation time.

[0137] In one example, Figure 4 One of the drawn data is: 3863.7113066666666,[source_1,623,source node,(34.7,-120.6),001,738.4,waiting layer,(34.7,-120.6),001,740.03333333333333,route layer,(7771.0,10.0),T2,740.63333333333333,waitinglayer,(7771.0,10.0),sink_1,713,sink node,(7771,0.0)],416.

[0138] 3863.7113066666666 is the total weighted satellite launch cost and satellite time cost. The information of each node is in brackets. Four nodes form a group, which are node code, time from mission zero, node type or network layer, and geographical location (latitude and longitude for launch site, and orbital altitude and right ascension of orbital node). The number after the brackets is the number of nodes traversed to find the path. Finally, the satellite deployment decision process is obtained, for example, satellites 1, 3, 4, and 7 are used for direct launch, and satellites 2, 5, and 6 are used for indirect launch. The visualization results of multiple plotted data are as follows. Figure 4 Since some processes are too short to be reflected, they are simplified into the launch waiting phase and the on-orbit maneuvering phase.

[0139] The present invention also provides a low-orbit large-scale satellite constellation optimization deployment system, which is applied to any of the above-mentioned optimization deployment methods, including:

[0140] A model building module is used to obtain low-orbit large-scale constellations, satellite parameters and carrier parameters, and build a constellation deployment network model based on the low-orbit large-scale constellations, satellite parameters and carrier parameters;

[0141] A function building module is used to build the objective function of multivariable mixed integer optimization based on the information contained in the nodes and edges in the constellation deployment network model;

[0142] The first solving module is used to determine the restricted main problem RMP and subproblems of the objective function, and solve the RMP through a column generation algorithm to obtain the objective value and dual variables;

[0143] The second solving module is used to add the new column to the RMP to update the target value and the dual variable when there is a new column in any sub-problem and the new column is added to the RMP to make the target value smaller;

[0144] The output module is used to directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving the integer target value according to the branch and bound method when there are no new columns in all sub-problems or all new columns added to the RMP cannot make the target value smaller; the satellite launch deployment plan includes at least: launch time, launch path and launch cost.

[0145] The optimization deployment method and system of a large-scale low-orbit satellite constellation provided by the present invention is based on a multivariable mixed integer optimization mathematical equation generated by a partial time expansion dynamic network model of space logistics, and adopts the Danzig-Wolf decomposition idea to convert complex solution constraints into multiple simple sub-problems. By setting a sub-problem filter, the dual variables of the capacity constraint are judged to be positive or negative, and the saturated path is screened to avoid repeated calculations. The sub-problem solution is converted into a minimum path problem, and a minimum path solution method such as Dijkstra and A* algorithm is adopted, thereby effectively reducing the optimal solution search space and improving the calculation efficiency.

[0146] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for optimizing the deployment of a large-scale low-orbit satellite constellation, characterized in that: include: Step S1, obtaining a low-orbit large-scale constellation, satellite parameters and carrier parameters, and constructing a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and carrier parameters; Step S2, establishing a multivariable mixed integer optimization objective function according to information contained in nodes and edges in the constellation deployment network model; Step S3, determining the restricted main problem RMP and subproblems of the objective function, and solving the RMP by a column generation algorithm to obtain the objective value and dual variables; Step S4, when any sub-problem has a new column, and the addition of the new column to the RMP makes the target value smaller, the new column is added to the RMP to update the target value and the dual variable; Step S5, when all sub-problems do not have new columns, or all new columns added to the RMP cannot make the target value smaller, directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving the integer target value according to the branch and bound method; The satellite launch deployment plan includes at least: launch time, launch path and launch cost.

2. The optimization deployment method according to claim 1, characterized in that: The S2 includes: The objective function J is as follows: Among them, J1 is the first objective function, J2 is the second objective function, x is the number of satellites carried by each carrier, y is the decision variable, d is the demand for satellites at node i, v and V are carrier indexes, l and N are orbital indexes, is the launch cost of launching vehicle v into orbit l, is the decision variable for launching the vehicle v to the target orbit l at time k, The manufacturing cost of each satellite is is the number of satellites launched by vehicle v into orbit l, represents the satellite storage cost per unit time, is the time difference between time node i and time node j, U k Constellation performance evaluation at time k, Δt k is the time difference between time node k and time node k+1, and k and K are time series indexes.

3. The optimization deployment method according to claim 1, characterized in that: The constraints of the objective function include flow constraints, edge capacity constraints, carrier availability constraints and dual variable constraints; S2 includes: The flow constraints are as follows: The capacity constraints on each edge are as follows: The vehicle availability constraints are as follows: The dual variable constraints are as follows: Among them, i is the node name, V is the node set, k and K are time series indexes, is the flow from node i to node j at time k, is the flow from node j to node i at time k, is the demand for satellites by node i at time k, j is the node name, N + (i) is the set of nodes that have an inflow effect on node i, N - (i) is the set of nodes that have outflow effects on node i, κ ij is the maximum flow allowed by the edge formed by nodes i and j, is the decision variable for launching vehicle v to target orbit l at time k, l and N are orbit indices, and A is the set of orbit edges.

4. The optimization deployment method according to claim 1, characterized in that: The S3 includes: Get the new column; When the new column exists, adding the new column to the RMP; The RMP is solved by a column generation algorithm to obtain the target value and the dual variable.

5. The optimization deployment method according to claim 4, characterized in that: The S3 further includes: The new column is added to the RMP according to the following formula: X p ≤K BX p =d p X p ≥0 Where c is the construction cost and time cost information of each arc in the constellation deployment network model, ω * is the dual variable of the capacity constraint, is the dual variable of the flow constraint, X p is the satellite traffic represented by the satellite p to be solved, matrix B is the vertex-edge association matrix, κ is the edge capacity information, d p For the requirements related to satellite p.

6. The optimization deployment method according to claim 1, characterized in that: The S3 further includes: Setting all decision variables in the RMP to binary variables and setting parameters of the mixed integer programming MIPGap; The objective value and dual variables in integer form are obtained through mixed integer programming.

7. The optimization deployment method according to claim 1, characterized in that: The S3 further includes: Dummy variables and dummy costs are set in the RMP.

8. The optimization deployment method according to claim 7, characterized in that: The S3 further includes: The dummy variables and dummy costs are set in the RMP according to the following formula: J1=c T Yλ+c init l J2=-U(Yλ)Δt k Yλ≤κ Ll=1 |p| 0≤λ[i],i∈[1,...|P|] Among them, λ is the selection of each satellite path, U is the constellation performance evaluation, Δt k is the time difference between time node k and time node k+1, c init is the initial penalty variable, the matrix Y represents all possible paths of satellite p, N represents the number of possible paths, P represents the number of nodes, and Y v represents the vth path of Y, c is the deployment cost and time cost of each arc segment, c T is the inversion of c, κ is the capacity information of the edge, and i is a positive integer.

9. The optimization deployment method according to claim 1, characterized in that: The S4 includes: The sub-problems are screened by using the dual variables of the capacity constraint of the objective function to obtain a sub-problem set without repeated sub-problems; The subproblem set is solved by Dijkstra algorithm or A* algorithm to obtain a new column, and the target value and dual variable are updated according to the new column.

10. An optimized deployment system for a large-scale low-orbit satellite constellation, applied to the optimized deployment method according to any one of claims 1 to 9, characterized in that: include: A model building module, used to obtain a low-orbit large-scale constellation, satellite parameters and carrier parameters, and build a constellation deployment network model according to the low-orbit large-scale constellation, satellite parameters and carrier parameters; A function building module, used to build a multivariable mixed integer optimization objective function based on the information contained in the nodes and edges in the constellation deployment network model; A first solving module, used for determining the restricted main problem RMP and subproblems of the objective function, and solving the RMP by a column generation algorithm to obtain the objective value and the dual variable; A second solving module is configured to add a new column to the RMP to update the target value and the dual variable when a new column exists in any subproblem and the new column is added to the RMP so as to reduce the target value; An output module, used for directly outputting the satellite launch deployment plan or outputting the satellite launch deployment plan after solving the target value of an integer according to the branch and bound method when all sub-problems do not have new columns or all new columns added to the RMP cannot make the target value smaller; The satellite launch deployment plan includes at least: launch time, launch path and launch cost.

Images