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Research on Force Assignment in Multipoint Sealing and Controlling Action Based on GA-SA
- WANG Shuqin, HUANG Qian
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2024, 33(4):
1-6.
DOI: 10.12005/orms.2024.0104
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Sealing and controlling action is an important military action, is often used in diversified tasks by the PAP, and has a very close relationship with the completion of diversified tasks. The force assignment problem in multipoint sealing and controlling action is how to assign force based on these actual situations, and these actual situations often contain the decentralized troop stations, the different force conditions (like equipment, the number and quality of force, etc.) of each station and the different distances from station to control point, etc. And at the same time, it is best to achieve the goal of minimizing the cost of completing the task and getting the maximum sealing and controlling action probability. Because the problem often contains multiple troop stations and task points, it is always a NP difficult problem when the problem scale is large. Finding the optimal force assignment plan for the problem becomes a thought-provoking question. In literature review, it is found that there are many studies about the force assignment problem of other military operations, but they seldom pay attention to the force assignment problem of multipoint sealing and controlling action of PAP. So, in order to find the optimal plan for the sealing and controlling action force assignment quickly and accurately, and improve the accuracy and scientificity of the sealing and controlling action force assignment further, a force assignment model for multipoint sealing and controlling action is established, this model contains two objective functions, one is maximizing the sealing and controlling action probability of each control point, and the other is minimizing the total moving distance of all groups, the model considers the different sealing and controlling action probabilities and moving distances of each group.
Because the model is a multi-objective mixed integer programming model, and contains maximum-minimum objective function, when the problem scale is large, it will be difficult to obtain its optimal solution by traditional algorithms. So a Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm is proposed. Based on the genetic algorithm, this GA-SA has been improved in the following five aspects. Firstly, the algorithm uses decimal coding, sets the number of genes of the chromosome to n, The numbers on the chromosome are composed of 1 to m(m is the total number of sealing and controlling points), and the number of sealing and controlling groups of station i occupies ni bits of the chromosome(ni is the number of the groups that can be assigned in station i), from $\sum_{j=0}^{i-1}$ni+1 bit to $\sum_{j=0}^{i}$ni bit of the chromosome. Secondly, the fitness function is constructed by the following formula, where the good solutions and bad solutions are well distinguished.
$f_i=\min _{j=1,2, \cdots, m}\left\{w_j^a\left(\frac{d_{\min }}{d_i}\right)^b\right\}$,i=1,2,…,popsize.
Where, wj is the sealing and controlling probability of point j in chromosome i,di is the total distance of chromosome i,dmin is the minimum total distance of all chromosomes, a,b is the weigtht parameter. Thirdly, the algorithm improves the selection, crossover, and mutation operators based on the problem. Fourthly, the ability to find the optimal solution of the algorithm is further enhanced by using simulated annealing operations. Fifthly, the algorithm uses elite strategy, lets the best solution of each generation avoid genetic manipulation and keeps it directly for the next generation, and in this way, the convergence of the algorithm is ensured well. In order to verify the effectiveness and superiority of the GA-SA, this algorithm is implemented using MATLAB language. And the repeated experiments are conducted based on a numerical example with 8 control points and 10 troops stations. At first, the parameters a and b of the fitness function are analyzed in these experiments, and their optimal value is selected. Then, repeated comparative experiments are conducted on the GA-SA, GA and SA by using the same numerical examples under the same conditions. In the experiment, it is found that the running time of GA-SA is slightly longer than the other two algorithms, but its convergence speed is fast, and its optimal solution is better than the other two algorithms, In the 500 iterations, GA-SA get the biggest minimum sealing and controlling probability(0.87595), the maximum fitness function value (0.055888) and the shorter total moving distance(1518.4854),and the optimal force assignment plan is determined by the GA-SA at last. However, due to the randomness of the algorithm, the results are uncertain in each 500 iterations, and because of the many parameters in the algorithm, the coupling design of parameters needs further research.
