Research Of Multiobjective Programming Algorithm Based On Mind Evolution

Multiobjective programming, which has important functions on solving the modern economic and social problems, is a new active subject of applied mathematics. Although the traditional algorithms for solving multiobjective programming problems have history for several decades, evolutionary algorithms are especially suited for multiobjective programming problems. Multiobjective programming evolutionary algorithms have recently become a popular research realm.Mind Evolutionary Computation is a new kind of evolutionary algorithm which simulates the progress process of human being mind. Replacing crossover and mutation operators by similartaxis and dissimilation operations to overcome the problems of Genetic Algorithm, it has superiorities in some aspects.This paper mainly researches the method of using Mind Evolutionary Computation to sovle multiobjective programming problems. We propose a kind of multiobjective Mind Evolutionary Computation called NSMEA.Multiobjective Mind Evolutionary Computation NSMEA, which calculates the fitness of individuals on the base of improved Pareto fast nondominated sorting, applies Pareto efficiency theories to Mind Evolutionary Computation. The basic principle is: First, a number of individuals are scattered in the whole solution space, and then some better individuals are selected according to the fitness and density information as the initial centers of each group(dissimilation operation I ). Secondly, perform operation similartaxis for each group:.Some individuals are scattered with normal distribution around the group's center. The nondominated solutions of the all individuals in the group are selected as the winners, and then some individuals are scattered around the them. This process is repeated until the group matures. Thirdly, fitness values are assigned to winners of all groups. The nondominated solutions are selected as global optimation solutions. The mature groups are judged to be released or not, and centers of groups which are not mature are adjusted according to the fitness values of individuals (dissimilation operation II ). The nondominated solutions are approaching the Pareto optiimal front through the action of similartaxis and dissimilation operations.This paper analyzes the convergence of NSMEA on the basis of basic probability theories. Probabilistic convergence and almost sure convergence of this algorithm are defined. It is theoretically proved that, under some conditions, the sequence of winners generated through operation similartaxis almost sure converges to local Pareto optimal solution set. The sequence of nondominated solutions generated through operation of similartaxis and dissimilation almost sure converges to global Pareto optimal solution set.In the end, it is shown by experiments that the algorithm is feasible and effective. The classic test problems of converxity, non-converxity, discreteness and non-uniformity are used to test this algorithm. NSMEA is also compared with some excellent algorithms(mainly with NSGA II ). Test result shows that NSMEA performs well on all kinds of promblems. This algorithm has shown very good performance on some problems in comparison to other multiobjective evolutionary algorithms, and is better than PAES, SPEA, and NSGA II. It converges to Pareto front fast, and obtains a large number of solutions. Although NSMEA converges to Pareto front slowly on test problems with high dimension solution space, it can converge to Pareto front finally, and can get more solution points than other algorithms.In a word, NSMEA is a kind of effective multiobjective evolutionary algorithm which can converge to global Pareto optimal solution set.