Research On Improved Differential Evolutionary Algorithm For Multi-Objective Optimization

Optimization problems come from the real word problems. In daily life, we can meet many optimization problems. Many of these problems are multi-objective optimization problems. In the multi-objective optimization problems, the objectives are usually conflicting. The number of Pareto optimal solutions is usually infinite. How to find a number of uniformly and widely distributed Pareto optimal solutions for the decision maker is very important.Evolutionary algorithm, as a representative of nature-inspired algorithms, which is a random, simple and adaptive globally search algorithm, has become an important tool of solving multi-objective optimization problems. In this paper, first, the basic concepts, theories and frameworks of the evolutionary algorithm and the multi-objective optimization are introduced. Then the differential evolutionary algorithm is reviewed and an improved multi-objective differential evolution algorithm (LSMODE) is proposed, which uses a new local search strategy in which a new local search operator can automatically adjust the search step length. At the same time the values of factor F and factor CR in DE are adjusted adaptively. And a method to deal with variables being out of bounds during the optimization process is proposed. Experimental results show that LSMODE can find a larger number of uniformly and widely distributed Pareto-optimal solutions than the current classical algorithm NSGA-Ⅱcan.In addition, a new differential evolution algorithm to solve multi-objective TSP problem is given in the paper. The algorithm makes some adjustment to LSMODE such that the resulting algorithm is more suitable to the multi-objective TSP optimization model. In the algorithm, a new formula for mutation and a new local search operator are introduced. And a method to deal with variables being out of bounds is proposed. The experimental results show that the method is effective.