Research On A Improved Genetic Algorithm For Multi-Objective Optimization Problems

As an important branch in the field of optimization, the purpose of multi-objective optimization problem (MOP) is to optimize multiple numerical goals simultaneously in some sense. Now, MOP has gained more and more attentions from the scholars since that its applications are very wide in the real-world life. For example, the goal of a factory designing one product may involve high yield, good quality, low cost consumption, high profit and so on. It is impossible to optimize all objectives simultaneously considering that the objectives often conflict with each other and improvement of one objective may lead to deterioration of another. Recently, it is noticeable that the traditional optimization methods for MOP begin to become inadequate because many real-world MOPs seem to be more and more comprehensive.With the development of intelligent optimization methods, genetic algorithm (GA) has been applied widely to solve MOPs due to its robust and adaptive capacity in solving many complex optimization problems. In recent years, researchers have proposed many strategies in GA for MOPs where elitist non-dominated sorting GA (NSGA-II) is one of important solution methods. In this paper, we hybridize a local search strategy with NSGA-Ⅱ in order to improve its exploitation capacity and then propose an improved multi-objective GA. The major works can be described as follows.(1) We briefly introduce the background and significance of the research topic in this paper.(2) We review the related works which include of the theories of MOP, the traditional optimization methods for MOP and GA for MOPs. Especially, the basic principle of NSGA-II is introduced particularly and then its strength and weakness is analyzed deeply.(3) We design and propose an improved multi-objective GA. Considering that NSGA-II owns good global exploration capacity, but exhibits poor local exploitation, we design a local search strategy for NSGA-Ⅱ in order to enhance its performance for MOPs. In the proposed local search strategy, two different local search schemes are used for the different individuals that are chosen from the Pareto optimal solution set in the population. If the selected individual is an endpoint in the Pareto optimal solution set, the purpose of executing local search for it is to find a better individual or be able to expand the Pareto front. If the selected one is not an endpoint, the direct replacement and the probable replacement are both in consideration. When achieving a better individual which can dominate the original individual via executing local search, the original individual will be replaced by the dominated one directly. When achieving a non-dominated individual, the following formula will be used to verify the possibility of the new individual replacing the original one. f1-f1’/f1max-f1min+f2-f2’/f2max-f2min where f is the objective function value of the original individual and f’ is the objective function value of the newly-generated individual by local search.If the value of this formula is greater than 0, which shows that the change of individual may be helpful, the new individual will replace the original one with a large probability. If the value is smaller than 0, which means that the change may be not helpful, the new individual will replace the original one with a small probability.(4) We carry out some experiments and analyze the relevant results in order to examine the performance of the proposed algorithm. In the simulation experiments,10 benchmark functions of MOP are used and the performance of our proposed improved multi-objective GA is examined and analyzed through comparing with NSGA-II via the two different measurements of MOP.