Research On Intelligent Optimization Algorithm Of Complementarity Problems

Complementarity problems is an important optimization problem in the field of mathematical planning,it is widespread in many practical life such as network equilibrium,engineering mechanics,and so on.Therefore,the research on complementarity problems is highly valued by the majority of scholars.With the advent of intelligent optimization algorithms,such as genetic algorithms,particle swarm optimization,etc.,many related algorithms are widely used in optimization problems.When the intelligent optimization algorithm solves optimization problems,it has unconditional constraints,simple calculation process and high computational efficiency.For the solution of complementarity problems,the basic mathematical method is to give information such as the initial point of the feasible interval,which makes it difficult for the mathematical method to find the optimal value of the complementarity problem within a certain range.In recent years,with the wide application of intelligent optimization algorithms in the field of mathematical optimization and engineering,people began to explore the relationship between intelligent optimization algorithms and the solution of complementarity problems.In this paper,the intelligent optimization algorithm is used to solve the complementarity problem.Through the research of the intelligent optimization algorithm,we have found a general intelligent optimization algorithm for solving complementary problems.This research has important practical significance for the research of complementarity problems.This paper mainly studies the improvement of genetic algorithm and particle swarm optimization and applies the improved intelligent optimization algorithm to solve the complementarity problem.This paper first describes the basic categories of complementarity problems and the mathematical methods for solving complementarity problems,and introduces three intelligent optimization algorithms that are widely used in optimization problems.Based on the detailed description of these algorithms,several methods for improving genetic algorithm and particle swarm optimization are introduced.By introducing the simulated annealing algorithm,the linear decreasing inertia weight and the constriction factor,the genetic algorithm and particle swarm algorithm are improved.A simulated annealing genetic algorithm and an improved particle swarm algorithm were formed.For non-smooth complementarity problems,the complementarity problems can be smoothed first,and then two improved genetic algorithms and particle swarm algorithms are applied to solve multiple complementarity problem instances.By comparing the optimal value,fitness value,mean square error and calculation time obtained by the simulated annealing genetic algorithm and the improved particle swarm algorithm.Selecting an algorithm with high accuracy and fast convergence rate for complementarity problems as a general intelligent optimization algorithm.