Research On Solving Nash Equilibrium Strategies For Region Air-Defense Force Deployment Based On Particle Swarm Optimization

Air-defense force deployment is a very important part of the air-defense combat, the reasonable deployment can give full play to the advantages of all kinds of air-defense force, and provide important guarantee to achieve final victory. According to region air-defense deployment problem, a deployment game model is established by measuring the fighting-effectiveness for military aircraft, the weight of war zone, and the uncertain factors in the war. The particle swarm optimization algorithm(PSO) is applied to the model to solve the Nash equilibrium for obtaining optimal strategies for both sides. By fusion immune thought and adding the extreme variation to improve PSO algorithm, the simulation is demonstrated to show the validity of the improved algorithm.Firstly, a basic region air-defense deployment model is established based on the fighting-effectiveness of both sides and the weight of war zone. And the method of rejecting repeated strictly dominant strategy is applied to the model to solve the pure strategy Nash equilibrium. Among them, the logarithmic method is used to calculate the fighting-effectiveness index, and the fuzzy comprehension evaluation is used to access the weight of war zone.Secondly, by analyzing the characteristics of uncertain factors in the war, a random correction factor obeyed the normal distribution is introduced to improve the basic game model. After proving that the model has mixed strategies, the problem of Nash equilibrium solution is transformed into a single objective optimization problem. By adding the function of particle initialization and correction, PSO can be applied to the optimization.Finally, to overcome the fault that the basic particle swarm optimization(BPSO) is easy to fall into local optimum, two method based on the fusion immune thought and the extreme variation are proposed. By involving the antibody concentration inhibitionmechanism and immune memory function of immune algorithm, the immune particle swarm optimization algorithm(IPSO) maintained the diversity of population and increased the ability of global search. When the population stagnated, the extreme variation particle swarm optimization(EVPSO) varied the global extreme, so that the population can jump out of the local optimum. Experiments show that the improved algorithm on the convergence speed and accuracy are improved.