The Development Of Multi-objective Evolutionary Algorithm And Its Application

With the development of human society, many decision-making problems are becoming more and more complicated, the mathematical model of single target is not proper to describe all the characters of the problems. Therefore, the mathematical model of practical problems has several objectives, namely the multi-objective problem. It is important that studying the optimal solutions of multi-objective problem has significantly academic meanings and well practical values.In the process of solving multi-objective optimization problems, since the different targets conflict each other, there does not exist a solution called the best solution to make every target get the optimal solution. An optimal solution for one target will also decline other targets’ superiority. The solution for multi-objective is not a single one but a group of Pareto set. How to get the Pareto set which closes to the ideal Pareto frontier and spreads widely, but the distribution of wide range of non-dominated solutions is the key to solving the multi-objective problems. Evolutionary algorithms have the advantages that traditional methods do not have in solving multi-objective problems, so how to solve the multi-objective problem has become a hotspot in the field of evolutionary algorithm.Through reading relevant literatures at home and abroad extensively, studying the theories of multi-objective and evolutionary algorithm carefully and improving evolutionary operators, we propose a fast evolutionary algorithm based on normalized (Normalized Fast Evolutionary Algorithm, NFEA). By verifying on some typical high-dimensional single-objective and multi-objective functions, the results show that the improved algorithm is significantly effective. The paper is organized as follows:Firstly, the paper introduces the relevant concepts of multi-objective optimization and the traditional methods for solving multi-objective problems. Secondly, we analyze the research status of multi-objective evolutionary algorithm at home and abroad. Finally, we give the basic concepts of multi-objective evolutionary algorithm and also analyze the design goals and points.By designing a new comparison method for individuals and improving evolutionary operators, we propose a new algorithm, namely NFEA. Through initializing the solution set which includes feasible and infeasible solutions, the algorithm could research the solution space as far as possible. We get a new method for individual’s comparison by normalizing the function values of each target. We apply the adaptive mutation operator and the elitism strategy so that the algorithm could converge quickly in the early stage of the process and ensure the optimal solution in the later stage. By correcting the degenerated offspring, the algorithm could approach the optimal solution always, prevent repeated individuals’ research effectively and improve the efficiency of the optimization algorithm. The results on typical high-dimensional single-target and multi-objective problems show that the NFEA could not only improve the global search ability and accelerate the convergence, but also improve the quality of the solutions.At last, we summarize the research work and prospect the research directions in the future.