An inter-group competition optimization method for satellite cluster game quantity programming

Abstract

The application discloses an inter-group competition optimization method for satellite cluster game quantity programming, and specifically comprises the following process: considering two indexes of quantity and game effect, considering two constraints of calling quantity limitation and game potential energy ratio limitation, and constructing a cluster quantity demand programming mathematical model; an inter-group mismatch competition optimization method is designed for solving, first, the particle swarm is randomly divided into a plurality of sub-populations each consisting of six particles, the sub-populations are randomly divided into two groups, and each group is sorted according to the fitness; then, the two groups of particles cross and compete through a mismatch relationship to obtain a failure and a winning particle group; finally, competition is carried out in the winning group according to the fitness. The above process is repeated until a termination condition is met. Since six particles are used as a basic optimization unit, and a mismatch learning and elite learning strategy is proposed, the evolution efficiency is effectively improved, and the satellite cluster game quantity demand programming problem is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of optimization algorithm technology, specifically to an inter-swarm competition optimization method for quantitative programming in satellite swarm games. Background Technology

[0002] Increasingly complex adversarial missions can no longer be accomplished by a single satellite. Satellite constellations, with their advantages of high flexibility, rapid response, collaborative decision-making, and improved survivability, have become one of the most promising platforms for complex space-based game-playing missions. Space-based swarm game-playing can be subdivided into a situational awareness layer, a decision-making and planning layer, and an execution layer. Among these, quantity requirement planning is a crucial part of the decision-making and planning layer. It mainly involves comprehensively analyzing key information from both sides of the game to determine the types and quantities of missions our satellites will participate in. This is the core technology and main challenge of the satellite swarm game-playing mission planning and decision-making layer.

[0003] The quantity requirement planning problem refers to the problem of finding the types and quantities of satellites available to both sides and the number of satellites available to the opponent in a satellite swarm game scenario, in order to save satellite resources while ensuring the effectiveness of the swarm game.

[0004] Due to the numerous decision variables and complex optimization relationships, the quantity requirement planning problem exhibits multiple peaks and extremely high dimensionality. Traditional exact solutions often encounter difficulties in addressing this problem. Metaheuristic algorithms are highly regarded for their parallelism and global search capabilities and have received considerable attention in solving optimization problems. Although metaheuristic algorithms have made significant progress in solution quality, challenges remain. Some studies have shown that combining metaheuristics with heuristic algorithms can effectively enhance the performance of heuristic methods. Therefore, our research focuses on swarm intelligence within the field of metaheuristic algorithms and introduces a novel heuristic approach.

[0005] As one of the most well-known variants of the Particle Swarm Optimization (PSO) algorithm, Competitive Swarm Optimization (CSO) abandons the individual and global optimum of PSO, opting instead to utilize information from high-quality particles to guide low-quality particles. CSO allows almost every particle to influence other particles, significantly enhancing the diversity of the particle swarm. However, CSO has a simple and fixed structure; as the particle swarm size increases, while ensuring population diversity, the convergence efficiency between particles decreases drastically. Existing algorithms typically employ a fixed or hierarchical learning order within the particle swarm. These methods inevitably lose some valuable particle information during the particle sorting process. Therefore, to address these challenges, Inter-Swarm Mismatched Competitive Optimization (IMCSO) is introduced to further alleviate the local convergence problem in quantity requirement planning. Summary of the Invention

[0006] To address the above issues, this invention proposes an inter-swarm mismatch competition optimization method for the satellite swarm game quantity demand planning problem. This method solves the problems of particle swarm structure flexibility and particle swarm diversity encountered by the particle swarm optimization algorithm in solving optimization problems, and achieves an effective solution to the satellite swarm game quantity demand planning problem.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] An inter-swarm competition optimization method for quantitative programming in satellite swarm games includes the following steps:

[0009] Step 1: Construct a mathematical optimization model for satellite cluster game quantity demand planning: Considering two optimization indicators—the number of satellites called up and the cluster game effect—and two constraints—the number of satellites limited and the cluster efficiency ratio limited—the following mathematical optimization model for satellite cluster game quantity demand planning is constructed to optimize the number of our satellites:

[0010]

[0011] Where k1 and k2 are the proportional coefficients of the optimization index. Let q represent the game effect value of our i-th type of satellite against the j-th type of satellite in the target cluster. 1 This is a vector representing the number of our satellites, and its elements are... Let Ψ represent the number of satellites of type i, Φ be the game effect matrix, Φ be the effective game relationship matrix, K be the ratio of satellite cluster potential energy, and LI be the number of satellites of type i. i x is the maximum number of times each type of satellite can be called. ij To assign logical values;

[0012] Step 2: Set the particle swarm size to m, which is divisible by 6. Randomly divide the particle swarm into several subpopulations consisting of six particles each. Then, randomly divide the six particles into two groups. Compare the particles with lower fitness in the two groups. The group with lower fitness is labeled Group1, and the other group is labeled Group2. In each group, the particles are sorted by fitness from smallest to largest. The particle with the lowest fitness is labeled as the winner, the particle with the middle fitness is labeled as the runner, and the particle with the highest fitness is labeled as the loser. That is, they are recorded as winner, runner-up, and loser in that order.

[0013] Step 3: Within the same subpopulation, the two groups of particles compete in a team-by-team manner according to a fixed mismatch crossover relationship, specifically "Group 1 winner - Group 2 runner-up, Group 1 runner-up - Group 2 loser, Group 1 loser - Group 2 winner". Based on this, the groups of particles that lost and won the competition are obtained. This stage is called mismatch learning. Particles from the group that lost the competition are directly retained in the next iteration, and particles from the group that won the competition are recorded as elite particles.

[0014] Elite particles are sorted by fitness from smallest to largest. The runner-up learns from the winner, and the loser learns from the winner and the runner-up. This stage is called elite learning.

[0015] According to the mismatch competition mechanism, the winning particle W in each subpopulation is paired up. M And the failed particle L M L M Retained as elite particles, W M The update process is represented as follows:

[0016]

[0017]

[0018] in, and W corresponds to each of the t iterations. M Position and velocity, and They represent L in iteration t+1 respectively M Position and velocity, and L represents M Position and velocity, R1 represents the average position of the particle swarm, and R2, R3 are three random variables in the range [0,1]. These are control parameters used for control. The impact, use This represents the average position of all particles in t iterations;

[0019] Step 4: Sort the three winning elite particles according to their fitness values, with the particle with the lowest fitness being W. E The particle with the second fitness is R. E The particle with the highest fitness is L. E W E Keep it until the next iteration, R E Particles towards W E and The learning and updating process is represented as:

[0020]

[0021]

[0022] L E Particle towards R E and W E The learning and updating process is represented as follows:

[0023]

[0024]

[0025] In the above process, R E The evolutionary order of particles takes precedence over L. E Particles, making L E Particles towards the updated R E Particle learning;

[0026] Step 5: Repeat steps 1, 2, 3, and 4 until the termination condition is met, and finally output the optimization result.

[0027] The advantages of this invention over the prior art are as follows:

[0028] 1. This invention uses a subpopulation of six particles as the evolution range of the particles and introduces an inter-group mismatch cross-learning strategy, which breaks the rule of competition between particles of the same level in traditional algorithms, allows more particles of different levels to compete, effectively protects the information of inferior particles, and improves the diversity of the particle swarm.

[0029] 2. This invention divides particle swarm evolution into two stages: mismatch learning and elite learning. The first stage mainly targets inferior particles, while the second stage mainly targets superior particles. The two-stage academy ensures that almost all particles in the particle swarm can fully update their own information, thereby improving the convergence of the particle swarm. Attached Figure Description

[0030] Figure 1 This is a flowchart of an inter-swarm competition optimization method for quantity planning in satellite swarm game according to the present invention;

[0031] Figure 2 This is a diagram of the solution algorithm architecture in this invention. Specific implementation methods

[0032] The present invention will now be described in detail. The accompanying drawings are for illustrative purposes only and should not be construed as limiting the invention.

[0033] like Figure 1 As shown, the inter-swarm competition optimization method for quantitative programming in satellite swarm games according to the present invention includes the following steps:

[0034] Step 1: Construct a mathematical optimization model for the quantitative demand programming of satellite cluster game. The specific steps are as follows:

[0035] Considering two optimization metrics, q, the number of satellites and the effect of cluster game theory. 1 This is a vector representing the number of our satellite constellations, and its elements are... This represents the number of satellites of type i, where n is the total number of our satellites. This represents the game effect value of our i-th type of satellite against the j-th type of satellite in the target cluster, where m is the total number of enemy satellites. The calculation formula is:

[0036]

[0037] Where D(·) is the Dirichlet function, its value is 0 when the independent variable is less than 0, and 1 otherwise, L i ,L j These represent the payload capacities of the enemy and our side, respectively, M i M j These refer to the mobility capabilities of both sides.

[0038] The ratio K of the potential energy in the satellite cluster game is expressed as:

[0039]

[0040] Where || represents the 2-norm; Ψ 1 Let R be the game effect matrix of our satellite cluster R against the target cluster B, and let the elements in the matrix be... Φ 1 This is the effective strike relationship matrix of our satellite constellation R against target constellation B, where the elements in the matrix are... This indicates whether our j-th type of satellite has the ability to compete with the opponent's i-th type of satellite, and its calculation formula is:

[0041]

[0042] In the formula, TH is the effective game threshold. When the game effect value of our satellite against the target exceeds TH, it indicates that the satellite has the ability to play the game effectively.

[0043] The target variable is defined based on our variable definition and is marked as "2".

[0044] The potential energy ratio constraint of satellite constellations is expressed as:

[0045]

[0046] The mathematical optimization model for satellite cluster game quantity demand planning, which optimizes the number of our satellites, is as follows:

[0047]

[0048] Where k1 and k2 are the proportional coefficients of the optimization index. q represents the game effect value of our i-th type of satellite against the enemy j-th type of satellite. 1 This is a vector representing the number of our satellites, and its elements are... Let Ψ represent the number of satellites of type i, Φ be the game effect matrix, Φ be the effective game relationship matrix, K be the ratio of satellite cluster potential energy, and LI be the number of satellites of type i.i x is the maximum number of times each type of satellite can be called. ij To assign logical values;

[0049] Step 2: Divide the particle swarm into several subpopulations consisting of six particles each. Divide each subpopulation into two groups, such as... Figure 2 As shown, the specific steps are as follows;

[0050] The learning and evolution process of particles is divided into a cross-learning stage and an elite learning stage, with each stage updating and iterating for different levels of particle groups.

[0051] The initial particle swarm size is set to m, which is divisible by 6.

[0052] The particle swarm is randomly divided into m / 6 subpopulations;

[0053] Each subspecies population is randomly divided into two groups, and each group consists of three randomly assigned particles;

[0054] Compare the fitness of the particle with the lowest fitness in the two groups of particles;

[0055] The group with low fitness was labeled Group1, and the other group was labeled Group2;

[0056] Particles within each group are sorted in ascending order of fitness;

[0057] The particle with the lowest fitness is marked as the winner;

[0058] The particle in the middle of the fitness score is labeled as a runner;

[0059] The particle with the highest fitness is marked as a loser;

[0060] The three particles in Group 1 are represented as w1, r1, and l1, respectively.

[0061] The three particles in Group 2 are represented as w2, r2, and l2, respectively.

[0062] Step 3: The two groups of particles in the subpopulation compete in a crossover relationship according to a fixed mismatch relationship, that is, they compete according to the matching rule of "Group 1 winner - Group 2 runner-up, Group 1 runner-up - Group 2 loser, Group 1 loser - Group 2 winner", specifically:

[0063] w1 from Group 1 competes with r2 from Group 2;

[0064] r1 in Group 1 competes with l2 in Group 2;

[0065] l1 from Group 1 competes with w2 from Group 2;

[0066] The winning particle in each competition is denoted as W. M Failed particles are denoted as L. M ;

[0067] Winning particle W M Retain their key information and move directly to the next stage;

[0068] Failed particle L M Particles are updated according to the mismatch learning update formula;

[0069] The formulas for updating particle position and velocity are as follows:

[0070]

[0071]

[0072] in, and W corresponds to each of the t iterations. M Position and velocity, and They represent L in iteration t+1 respectively M Position and velocity, and L represents M Position and velocity, R1 represents the average position of the particle swarm, and R2, R3 are three random variables in the range [0,1]. These are control parameters used for control. The impact;

[0073] There are two versions:

[0074] This represents the average position of all particles in t iterations;

[0075] This represents the average position of six particles in the subpopulation during t iterations;

[0076] Unless otherwise specified, this invention adopts the default usage.

[0077] Step 4: Sort the winning particles and compete according to their size, including:

[0078] For the three winning particles W M Sorted by fitness value, those with lower fitness are called elite particles;

[0079] The particle with the lowest fitness is denoted as W. E The particle with the second fitness is R. E The particle with the highest fitness is L. E ;

[0080] The lowest fitness particle W E Maintain the existing advantages;

[0081] Particle R with second fitness E From W E and In the learning process, the formulas for updating particle position and velocity are as follows:

[0082]

[0083]

[0084] The particle with the highest fitness, L E From W E and R E Learning in the middle, updating position and velocity can be represented as:

[0085]

[0086]

[0087] In the above process, R E The evolutionary order takes precedence over L. E This makes L E Can be sent to the updated R E study;

[0088] Step 5: Repeat steps 1-4 until the iteration termination condition is met, and output the optimization result of the optimization problem.

[0089] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for inter-swarm competition optimization in satellite swarm game quantitative programming, characterized in that, Includes the following steps: Step 1: Construct a mathematical optimization model for satellite cluster game quantity demand planning: Considering two optimization indicators—the number of satellites called up and the cluster game effect—and two constraints—the number of satellites limited and the cluster efficiency ratio limited—the following mathematical optimization model for satellite cluster game quantity demand planning is constructed to optimize the number of our satellites: Where k1 and k2 are the proportional coefficients of the optimization index. Let q represent the game effect value of our i-th type of satellite against the j-th type of satellite in the target cluster. 1 This is a vector representing the number of our satellites, and its elements are... Let Ψ represent the number of satellites of type i, Φ be the game effect matrix, Φ be the effective game relationship matrix, K be the ratio of satellite cluster potential energy, and LI be the number of satellites of type i. i x is the maximum number of times each type of satellite can be called. ij To assign logical values; Step 2: Set the particle swarm size to m, which is divisible by 6. Randomly divide the particle swarm into several subpopulations consisting of six particles each. Then, randomly divide the six particles into two groups. Compare the particles with lower fitness in the two groups. The group with lower fitness is labeled Group1, and the other group is labeled Group2. In each group, the particles are sorted by fitness from smallest to largest. The particle with the lowest fitness is labeled as the winner, the particle with the middle fitness is labeled as the runner, and the particle with the highest fitness is labeled as the loser. That is, they are recorded as winner, runner-up, and loser in that order. Step 3: Within the same subpopulation, the two groups of particles compete in a team-by-team manner according to a fixed mismatch crossover relationship, specifically "Group 1 winner - Group 2 runner-up, Group 1 runner-up - Group 2 loser, Group 1 loser - Group 2 winner". Based on this, the groups of particles that lost and won the competition are obtained. This stage is called mismatch learning. Particles from the group that lost the competition are directly retained in the next iteration, and particles from the group that won the competition are recorded as elite particles. Elite particles are sorted by fitness from smallest to largest. The runner-up learns from the winner, and the loser learns from the winner and the runner-up. This stage is called elite learning. According to the mismatch competition mechanism, the winning particle W in each subpopulation is paired up. M And the failed particle L M L M Retained as elite particles, W M The update process is represented as follows: in, and W corresponds to each of the t iterations. M Position and velocity, and They represent L in iteration t+1 respectively M Position and velocity, and L represents M Position and velocity, R1 represents the average position of the particle swarm, and R2, R3 are three random variables in the range [0,1]. These are control parameters used for control. The impact, use This represents the average position of all particles in t iterations; Step 4: Sort the three winning elite particles according to their fitness values, with the particle with the lowest fitness being W. E The particle with the second fitness is R. E The particle with the highest fitness is L. E W E Keep it until the next iteration, R E Particles towards W E and The learning and updating process is represented as: L E Particle towards R E and W E The learning and updating process is represented as follows: In the above process, R E The evolutionary order of particles takes precedence over L. E Particles, making L E Particles towards the updated R E Particle learning; Step 5: Repeat steps 1, 2, 3, and 4 until the termination condition is met, and finally output the optimization result.

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