An Optimization Deployment Method and System for a Low-Earth Orbit Large-Scale Satellite Constellation

Abstract

The present invention relates to the field of satellite technology, and specifically discloses an optimization deployment method and system for a low-earth orbit large-scale satellite constellation. The method includes: S1, constructing a constellation deployment network model according to the low-earth orbit large-scale constellation, satellite parameters and carrier vehicle parameters; S2, establishing an objective function of multivariable mixed-integer optimization based on the information contained in the nodes and edges of the constellation deployment network model; S3, determining the restricted master problem RMP and sub-problems of the objective function, and solving the RMP through the column generation algorithm to obtain the objective value and dual variables; S4, when there is a new column in any sub-problem, and adding the new column to the RMP makes the objective value decrease, adding the new column to the RMP to update the objective value and dual variables; S5, when there are no new columns in all sub-problems, or adding all new columns to the RMP cannot make the objective value decrease, directly outputting the satellite launch deployment plan or outputting the satellite launch deployment plan after solving for the integer objective value according to the branch and bound method.

Description

Technical Field

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

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

[0003] In view of the above problems, the object of the present invention is to provide an optimized deployment method and system for a low-earth orbit large-scale satellite constellation, which transforms complex solution constraints into multiple simple sub-problems, effectively reduces the optimal solution search space, and improves the computational efficiency.

[0004] The present invention provides an optimized deployment method for a low-earth orbit large-scale satellite constellation, including:

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

[0006] Step S2, establishing an objective function for multi-variable mixed integer optimization according to the information contained in the nodes and edges of the constellation deployment network model;

[0007] Step S3, determining the restricted master problem RMP and sub-problems of the objective function, and solving the RMP through a column generation algorithm to obtain an objective value and dual variables;

[0008] Step S4, when there is a new column in any sub-problem, and adding the new column to the RMP makes the objective value decrease, adding the new column to the RMP to update the objective value and the dual variables;

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

[0010] In a possible implementation manner, 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 vehicle, y is the decision variable, d is the demand for satellites at node i, v and V are vehicle indices, l and N are orbit indices, is the launch cost for launching vehicle v into orbit l, is the decision variable for launching vehicle v into the target orbit l at time k, is the manufacturing cost of each satellite, is the number of satellites carried by launching vehicle v into orbit l, represents the storage cost per unit time of the satellite, is the time difference between time node i and time node j, U k Effectiveness evaluation of the constellation at time k, Δt k is the time difference between time node k and time node k + 1, k and K are time series indices.

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

[0016] The flow constraints are as follows:

[0017]

[0018] The edge capacity constraints 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 indices, 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 at 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 with an outflow effect on node i, κ ij is the maximum allowable throughput of the edge formed by nodes i and j, is the decision variable launched by vehicle v into target orbit l at time k, l and N are orbit indices, and A is the set of orbit edges.

[0025] In one possible implementation, S3 includes:

[0026] Obtain the new column;

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

[0028] Solve the RMP through a column generation algorithm to obtain the objective value and dual variables.

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

[0030] Add the new column 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 flow represented by the satellite p to be solved, the matrix B is the vertex-edge incidence matrix, κ is the edge capacity information, d p is the demand related to satellite p.

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

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

[0038] Solve through mixed integer programming to obtain the objective value and dual variables in integer form.

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

[0040] Set dummy variables and dummy costs in the RMP.

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

[0042] Set dummy variables and dummy costs 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] where λ is the selection of the path of each satellite, U is the constellation effectiveness 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, Y v represents the v-th 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 edge capacity information, and i is a positive integer.

[0049] In a possible implementation, S4 includes:

[0050] Screen the sub-problems through the dual variables of the capacity constraint of the objective function to obtain a set of sub-problems that remove duplicate sub-problems;

[0051] Solve the set of sub-problems through the Dijkstra algorithm or A* algorithm to obtain new columns, and update the objective value and dual variables according to the new columns.

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

[0053] A model construction module, configured to obtain a low-earth orbit large-scale constellation, satellite parameters, and carrier parameters, and construct a constellation deployment network model according to the low-earth orbit large-scale constellation, satellite parameters, and carrier parameters;

[0054] A function establishment module, configured to establish an objective function for multi-variable mixed integer optimization according to the information contained in the nodes and edges of the constellation deployment network model;

[0055] A first solving module, configured to determine a restricted master problem (RMP) and a sub-problem of the objective function, and solve the RMP through a column generation algorithm to obtain an objective value and dual variables.

[0056] A second solving module, configured to add the new column to the RMP to update the objective value and the dual variables when there is a new column in any sub-problem and adding the new column to the RMP makes the objective value smaller.

[0057] An output module, configured to directly output a satellite launch deployment plan when there is no new column in all sub-problems or adding all new columns to the RMP cannot make the objective value smaller, or output a satellite launch deployment plan after obtaining an integer objective value by solving according to the branch and bound method; the satellite launch deployment plan at least includes: launch time, launch path, and launch cost.

[0058] The optimization deployment method and system for a low-earth orbit large-scale satellite constellation provided by the present invention are based on a multi-variable mixed integer optimization mathematical equation generated by a space logistics partial time-expanded dynamic network model, and adopt the Danziig-Wolf decomposition idea to transform complex solution constraints into multiple simple sub-problems. By setting a sub-problem filter, positive and negative judgments are made on the dual variables of the capacity constraint to screen saturated paths and avoid repeated calculations. The sub-problem solution is transformed into a minimum path problem, and minimum path solution methods such as the Dijkstra and A* algorithms are used, thereby effectively reducing the optimal solution search space and improving the calculation efficiency. Description of the Drawings

[0059] Figure 1 It is a schematic flow chart of the optimization deployment method provided by the embodiment of the present invention;

[0060] Figure 2 It is a schematic diagram of the construction of the constellation deployment network model provided by the embodiment of the present invention;

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

[0062] Figure 4 It is a schematic diagram of each satellite launch deployment window provided by the embodiment of the present invention. Detailed Embodiments

[0063] The following further describes in detail the embodiments of the present invention in conjunction with the drawings and embodiments. The detailed description and drawings of the following embodiments 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 described preferred embodiments, 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, the meaning of "a plurality of" is two or more; the terms "first", "second", etc. are only used for descriptive purposes and cannot be construed as indicating or implying relative importance; for those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0065] Figure 1 The flowchart of the optimization deployment method provided for the embodiments of the present invention is as Figure 1 shown. The present invention provides an optimization deployment method for a low-earth orbit large-scale satellite constellation, including:

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

[0067] Figure 2 It shows the corresponding relationship between the meaning of each node and arc segment type in the constellation deployment network model and each decision node in the specific launch mission.

[0068] Step S2: Establish an objective function for multi-variable mixed integer optimization according to the information contained in the nodes and edges of the constellation deployment network model;

[0069] Step S3: Determine the restricted master problem RMP and sub-problems of the objective function, and solve the RMP through the column generation algorithm to obtain the objective value and dual variables;

[0070] In a possible implementation manner, S3 further includes: setting all decision variables in the RMP as binary variables and setting the parameters of the mixed integer programming MIPGap; solving through the mixed integer programming to obtain the objective value and dual variables in integer form.

[0071] In a possible implementation manner, 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 adding the new column to the RMP makes the objective value smaller, add the new column to the RMP to update the objective value and dual variables;

[0073] In a possible implementation manner, S4 includes: screening the sub-problems through the dual variables of the capacity constraint of the objective function to obtain a set of sub-problems after removing duplicate sub-problems; solving the set of sub-problems through the 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 for all sub - problems, or when adding all new columns to the RMP does not make the objective value smaller, directly output the satellite launch deployment plan, or output the satellite launch deployment plan after obtaining an integer objective value by solving 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 formulas.

[0076] According to the information contained in the nodes and edges in the constellation deployment network model, it is transformed into a multi - variable 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 vehicle, y is the decision variable, d is the demand for satellites at node i, v and V are vehicle indices, l and N are orbit indices, is the launch cost of vehicle v launched into orbit l, is the decision variable of vehicle v launched into the target orbit l at time k, is the manufacturing cost of each satellite, is the number of satellites carried by vehicle v launched into orbit l, represents the storage cost per unit time of the satellite, is the time difference between time node i and time node j, U k Effectiveness evaluation of the constellation at time k, Δt k is the time difference between time node k and time node k + 1, k and K are time - series indices.

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

[0081] The flow constraints are as follows:

[0082]

[0083] The capacity constraints of 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 indices, 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 of node \(i\) for the satellite at time \(k\), \(j\) is the node name, \(N\) + (i) is the set of nodes with an inflow effect on node \(i\), \(N\) - (i) is the set of nodes with an outflow effect on node \(i\), \(\kappa\) ij is the maximum allowable throughput of the edge formed by nodes \(i\) and \(j\), is the decision variable launched from vehicle \(v\) to target orbit \(l\) at time \(k\), \(l\) and \(N\) are orbit indices, and \(A\) is the orbit edge set.

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

[0091] Minimize \(\lambda\)

[0092]

[0093] \(J1 = c\) T \(Y\lambda (2 - 2)\)

[0094] \(J2=-U(\lambda)\Delta t\) k (2 - 3)

[0095] subject to

[0096] \(Y\lambda\leqslant\kappa (2 - 4)\)

[0097] \(\Lambda\lambda = 1\) |p| (2 - 5)

[0098] \(\lambda\in\{0,1\}\) n (2 - 6)

[0099] Among them, \(J1\) is the first objective function, \(J2\) is the second objective function, \(c\) T is the inversion of \(c\), \(c\) is the deployment cost and time cost of each arc segment, \(\lambda\) is the selection of the path of each satellite, the matrix \(Y\) represents all possible paths of satellite \(p\), \(U\) is the constellation efficiency evaluation, \(\Delta t\) k is the time difference between time node \(k\) and time node \(k + 1\), \(\kappa\) is the time cost, and \(n\) is the number of nodes.

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

[0101] Specifically, the new column is added to the 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] 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 flow represented by the satellite p to be solved, the matrix B is the vertex-edge incidence matrix, κ is the capacity information of the edge, and d p is the demand related to the satellite p.

[0107] Relax the constraints on the variables to be optimized, transform the original problem into a linear programming to construct the restricted master problem RMP, and set virtual variables and virtual costs in the RMP to allow the column generation method to be started when the path matrix Y is empty.

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

[0109] Set virtual variables and virtual costs in the 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] Where λ is the selection situation of the path of each satellite, U is the constellation efficiency evaluation, and Δtk is the time difference between time node k and time node k + 1, c init is the initial penalty variable, matrix Y represents all possible paths of satellite p, N represents the number of possible paths, P represents the number of nodes, Y v represents the v-th 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 optimized deployment method of the present invention. The experimental process is as follows:

[0117] Step 1: Given the relevant parameters of the low-earth orbit large-scale constellation, satellites and launch vehicles, set the parking orbit constellation and the target orbit constellation, and construct the corresponding constellation deployment network model according to the parameters. The relevant parameters are shown in Table 1 and Table 2 below:

[0118] Table 1

[0119]

[0120]

[0121] Based on the passenger demand and the timetable of the transportation vehicle, generate a multi-level graph model including different launch modes (different types of launch vehicles, different orbit injection modes, etc.). By reading the static network file and the time-expanded network file, construct the basic network, and generate the time-expanded network according to the launch time information of the launch vehicle, and finally form a complete constellation deployment network model.

[0122] The constellation deployment network model includes nodes and arcs, where the nodes represent the stations of the transportation vehicle or the departure and destination of the passengers, and the arcs represent the connections between the transportation vehicles or the walking paths.

[0123] Step 2: Use the column generation algorithm to solve the continuous relaxation problem.

[0124] First, initialize the parameters of the column generation algorithm, including the graph model, satellite mission requirements, source node and sink node, virtual time cost and virtual launch cost, etc. Then, construct the restricted master problem RMP, add virtual variables and capacity constraints, launch vehicle availability constraints in RMP, and set the objective function. The objective function adopts weighted multi-objective optimization, and different weights are assigned to the time cost and the launch cost respectively. By solving RMP, obtain the initial solution and calculate its dual variables.

[0125] Step 3: In each iteration of the column generation algorithm, first solve the RMP, update the objective value and dual variables. Then, solve the sub-problem, find a new path, and add it to the RMP. The sub-problem can be solved by the Dijkstra algorithm or the 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 path is found or the objective value of the RMP no longer changes.

[0126] Step 4: In the last step of the column generation algorithm, solve the integer solution through mixed integer programming. Set all decision variables in the RMP as binary variables and set the MIPGap parameter to control the mixed integer solution accuracy. Obtain the final integer solution by solving the mixed integer programming problem. According to the integer solution, determine the optimal path for each passenger and count the path types and quantities.

[0127] Step 5: Use the four algorithm configurations of (Filter_on, A*), (Filter_on, Dijstra), (Filter_off, A*), and (Filter, Dijstra) to perform 10 solutions respectively, compare the number of sub-problems and the average calculation time, and output the comparison results of different algorithm performances. The output includes the instance construction time, solution time, integer solution solving time, optimality gap, and the number of sub-problems solved during the solution process. By statistically analyzing and plotting the distribution map of path types and quantities, analyze the launch and deployment situation of the constellation, and the results are as Figure 3 shown.

[0128] The column generation algorithm has high algorithm compatibility. The above verifies the influence of whether to use a sub-problem filter when selecting sub-problems and using the A* algorithm and the Dijstra algorithm when solving sub-problems on the final solution time. Gurobi supports using two methods, hierarchical type and weighted type, to solve multi-objective optimization problems. Since the Dijstra and A* algorithms are limited to solving single-objective problems, the weighted method is used to transform the multi-objective optimization problem into a single-objective optimization problem.

[0129] Analyze the impact of the subproblem filter on the algorithm performance by implementing and testing it. 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 all pricing problems of the satellite tasks have been solved and no new columns have been added to the basis in the previous iteration, or the objective value has not changed in the last iteration, then no satellite tasks will be rerun.

[0130] From the experimental results, when the filter is not used, the Dijkstra algorithm and the A algorithm solve 25,920 and 19,440 pricing problems respectively, and the solving times are 140.97 seconds and 131.23 seconds respectively. After enabling the filter, the number of pricing problems solved by these two algorithms is reduced to 20,880 and 16,129 respectively, and the solving times are 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 solving time of the algorithm. In particular, the performance improvement of the A algorithm after enabling the filter is more significant, with the solving time reduced by 15.0% year-on-year, while the solving time of the Dijkstra algorithm is reduced by 15.0% year-on-year. This result emphasizes the importance of the subproblem filter in optimizing algorithms, especially when dealing with large-scale optimization problems. By effectively reducing unnecessary calculations, the subproblem filter not only improves the efficiency of the algorithm but also helps to save computing resources, and is an important tool for solving complex optimization problems.

[0131] The algorithm performance of using Dijkstra's algorithm and A* algorithm to solve sub-problems under different configurations was compared. Specifically, the solution time and the number of pricing problems processed by these two algorithms were examined under the conditions of enabling and disabling the sub-problem filter. First, when the sub-problem filter was turned off, the model solution time using Dijkstra's 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 indicates that without using the filter, A* algorithm is more efficient than Dijkstra's algorithm. Further, when the sub-problem filter was enabled, the solution time of Dijkstra's 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 in the solution efficiency of A* algorithm after enabling the filter. In addition, from the perspective of the number of pricing problems processed, whether the filter was enabled or not, A* algorithm processed fewer problems, which may be due to its higher path search efficiency, thus reducing unnecessary calculations and iterations.

[0132] In summary, when solving sub-problems of the satellite launch deployment optimization problem, A* algorithm shows better time efficiency and processing efficiency than Dijkstra's algorithm whether the sub-problem filter is applied or not. This finding provides strong data support for choosing a more efficient algorithm in future similar optimization problems.

[0133] Step 6: When necessary, set the decision variables of the last column generation iteration to binary to find the integer solution, thus completing the optimization of the satellite constellation launch deployment strategy. Output the satellite launch deployment decision time nodes to the schedule, so as to realize the formulation of the satellite deployment strategy for the entire constellation. The visualization result is as Figure 4 shown. The abscissa is time, and the ordinate is the satellite launch mission number. The dark color represents the waiting time of the satellite on the ground, and the light color represents the on-orbit operation time of the satellite.

[0134] In an example, Figure 4 one of the plotted data is: 3863.7113066666666,,[source_1,623,source node,(34.7,-120.6),001,738.4,waiting layer,(34.7,-120.6),001,740.0333333333333,route layer,(7771.0,10.0),T2,740.6333333333333,waitinglayer,(7771.0,10.0),sink_1,713,sink node,(7771,0.0)],416.

[0135] 3863.7113066666666 is the total cost of weighted satellite launch cost and satellite time cost. The information in the brackets behind is for each node, with four in a group, which are the node code, the time from the mission zero point, the node type or the network layer where it is located, and the geographical location (the launch site is the longitude and latitude, and the rest are the orbital altitude and the right ascension of the ascending node of the orbit). The number behind the brackets is the number of nodes traversed to find this path. Finally, a satellite deployment decision-making process such as direct launch for satellites 1, 3, 4, and 7 and indirect launch for 2, 5, and 6 is obtained. The visualization results of multiple drawing data are as follows Figure 4 Since some processes are too short to be reflected, they are simplified to the launch waiting segment and the on-orbit maneuvering segment.

[0136] The present invention also provides an optimized deployment system for a low-earth orbit large-scale satellite constellation, which is applied to any of the above optimized deployment methods, including:

[0137] A model construction module for obtaining a low-earth orbit large-scale constellation, satellite parameters, and carrier parameters, and constructing a constellation deployment network model according to the low-earth orbit large-scale constellation, satellite parameters, and carrier parameters;

[0138] A function establishment module for establishing an objective function of multi-variable mixed integer optimization according to the information contained in the nodes and edges in the constellation deployment network model;

[0139] A first solution module for determining the restricted master problem RMP and sub-problems of the objective function, and solving the RMP by the column generation algorithm to obtain the objective value and dual variables;

[0140] A second solution module for adding a new column to the RMP when there is a new column in any sub-problem and adding the new column to the RMP makes the objective value smaller, so as to update the objective value and dual variables;

[0141] An output module for directly outputting the satellite launch deployment plan when there are no new columns in all sub-problems, or when adding all new columns to the RMP cannot make the objective value smaller, or outputting the satellite launch deployment plan after solving the integer objective value according to the branch and bound method; the satellite launch deployment plan at least includes: launch time, launch path, and launch cost.

[0142] The optimization deployment method and system for a low-orbit large-scale satellite constellation provided by the present invention are based on a multi-variable mixed-integer optimization mathematical equation generated by a space logistics partial-time extended dynamic network model. Using the Danziig-Wolf decomposition idea, complex solution constraints are transformed into multiple simple sub-problems. By setting a sub-problem filter, positive and negative judgments are made on the dual variables of the capacity constraint to screen saturated paths and avoid repeated calculations. The solution of the sub-problem is transformed into a minimum path problem, and minimum path solution methods such as the Dijkstra and A* algorithms are used, thereby effectively reducing the optimal solution search space and improving the calculation efficiency.

[0143] 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 within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. An optimized deployment method for a low-earth orbit large-scale satellite constellation, characterized in that, Including:: Step S1: Obtain the low-Earth orbit large-scale constellation, satellite parameters, and carrier parameters, and construct a constellation deployment network model based on the low-Earth orbit large-scale constellation, satellite parameters, and carrier parameters; Step S2: Establish an objective function for multi-variable mixed-integer optimization based on the information contained in the nodes and edges of the constellation deployment network model; Step S3: Determine the restricted master problem RMP and sub-problems of the objective function, and solve the RMP through the column generation algorithm to obtain the objective value and dual variables; Step S4: When there is a new column in any sub-problem, and adding the new column to the RMP makes the objective value smaller, add the new column to the RMP to update the objective value and the dual variables; Step S5: When there are no new columns in all sub-problems, or adding all new columns to the RMP does not make the objective value smaller, directly output the satellite launch deployment plan or output the satellite launch deployment plan after solving for the integer objective value according to the branch and bound method; The satellite launch deployment plan at least includes: launch time, launch path, and launch cost.

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

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

4. The optimization deployment method according to claim 1, characterized in that The S3 includes: Obtain the new column; When there is the new column, add the new column to the RMP; Solve the RMP through the column generation algorithm to obtain the objective value and dual variables.

5. The optimization deployment method according to claim 4, wherein The S3 also includes: Add the new column to the RMP according to the following formula: X p ≤ κ BX p = d p X p ≥0 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 flow represented by the satellite p to be solved, the matrix B is the vertex-edge incidence matrix, κ is the capacity information of the edge, d p is the demand related to the satellite p.

6. The optimization deployment method according to claim 1, wherein The S3 also includes: Set all decision variables in the RMP to binary variables and set the parameters of the mixed integer programming MIPGap; Solve through the mixed integer programming to obtain the integer form of the objective value and dual variables.

7. The optimization deployment method according to claim 1, wherein The S3 also includes: Set virtual variables and virtual costs in the RMP.

8. The optimization deployment method according to claim 7, wherein The S3 also includes: Set virtual variables and virtual costs in the RMP according to the following formula: J1 = c T Yλ + c init λ J2 = -U(Yλ)Δt k Yλ≤κ Λλ = 1 |p| 0≤λ[i],i∈[1,...|P|] Among them, λ is the selection situation of the path of each satellite, U is the constellation efficiency evaluation, and Δt k is the time difference between time node k and time node k + 1, and 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 v-th path of Y. c is the deployment cost and time cost of each arc, and 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, wherein The S4 includes: Screen the sub-problems through the dual variables of the capacity constraints of the objective function to obtain a set of sub-problems with duplicate sub-problems removed; Solve the set of sub-problems through the Dijkstra algorithm or A* algorithm to obtain a new column, and update the objective value and dual variables according to the new column.

10. An optimized deployment system for a low-earth orbit large-scale satellite constellation, which is applied to the optimized deployment method according to any one of claims 1-9, and is characterized in that, Including: A model construction module for obtaining the low-Earth orbit large-scale constellation, satellite parameters, and carrier parameters, and constructing a constellation deployment network model based on the low-Earth orbit large-scale constellation, satellite parameters, and carrier parameters; A function establishment module for establishing an objective function for multi-variable mixed-integer optimization based on the information contained in the nodes and edges of the constellation deployment network model; A first solving module for determining the restricted master problem RMP and sub-problems of the objective function, and solving the RMP through the column generation algorithm to obtain the objective value and dual variables; A second solution module, configured to add the new column to the RMP to update the objective value and the dual variable when there is a new column in any sub-problem and adding the new column to the RMP makes the objective value smaller; An output module, configured to directly output the satellite launch deployment plan or output the satellite launch deployment plan after obtaining an integer objective value by solving according to the branch and bound method when there is no new column in all sub-problems or adding all new columns to the RMP cannot make the objective value smaller; The satellite launch deployment plan at least includes: launch time, launch path, and launch cost.

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