Application Research Of Improved Genetic Algorithm On Multi Objective Optimization Problem

Genetic algorithm is a kind of stochastic search algorithm which simulates biological natural selection and natural evolution. It is suitable for solving highly complex nonlinear problems and has been widely used. In solving the optimization problem of complex system with single objective, the advantage of genetic algorithm is fully demonstrated. However, the optimization problem in reality always has multiple targets.These targets can not reach the best at the same time, but inhibit each other. In order to achieve the equilibrium optimization of each objective, the value of the oneof the targetsshould be increased to reduce the value of the other targets.Multi objective genetic algorithm has a good effect on the optimization of multi-objective problems.These typical algorithms mainly include Vector Evaluated Genetic Algorithm, Niched Pareto Genetic Algorithm, Non-dominated Sorting Genetic Algorithm, Pareto Archived Evolution Strategy and so on.Based on the work of the reference [1] and [2],this article designed two kinds of improved genetic algorithm for solving multi-objective problems.The main work and research results are as follows:(1) A multi objective genetic algorithm using external pareto solution set was designed. Multiple objectives genetic algorithm will fall into the local optimal and premature convergence in the process of solving multi-objective problems. The algorithm calculates the convex part of the global optimal solution of the multi-objective problem by assigning weights.Then these solution are selected as a part of the initial population which will be used to selection, crossover and mutation with other random individuals. The excellent random individuals will search the non-convex part of the global optimal solution and the global optimal solution will eliminate the worse random individuals as the iterative process continues. The functions ZDT1,ZDT2,ZDT3,ZDT4,ZDT6 are tested. The experimental results show that the coverage and uniformity of the solution set of the improved algorithm is more advantage than NMOGA algorithm.(2) A multi objective genetic algorithm based on information entropy was designed. This algorithm is improved which based on traditional nsga-2 algorithm. It chooses one object at the start of the genetic operation, and calculates the number of the clusters on this object. Using the number of the clusters can calculate the information entropy of the population. The information entropy is used as a factor to change the crossover probability and mutation probability,which makes the crossover probability and mutation probability control the optimization of the population and the convergence of the population.The functions ZDT1,ZDT2,ZDT3,ZDT4,ZDT6 and a product scheduling problem are tested. The experimental results show that the solution of the improved nsga-2 algorithm which based on the information entropy is more uniform than the solution of the nsga-2 algorithm.