Neighborhood Knowledge-Based Evolutionary Algorithm for Multiobjective Optimization Problems

Although there are a variety of approaches to solve multiobjective optimization problems, few of them makes systematic use of the neighborhood relationship between the candidate solutions observed during the search process to improve the final results. In this paper, a new evolutionary algorithm, referred to as the neighborhood knowledge-based evolutionary algorithm (NKEA), is proposed to solve the multiobjective optimization problem. NKEA not only takes into account the advantages of NSGA-II, and JGGA, such as the fast nondominated sorting algorithm and horizontal transmission of information in a candidate solution, but also exploits systematically the neighborhood knowledge acquired during the search process. Specifically, NKEA consists of three major stages: the direction learning stage, the mutual adaptation stage, and the self adaptation stage. NKEA not only uses the fast nondominated sorting algorithm to find the Pareto optimal solutions, but also adopts the elitist strategy to maintain the best individuals for the next generation based on this strategy. Two adaptive control functions in the mutual adaptation stage and the self adaptation stage are designed to adjust the respective contributions of coarse local search and fine local search, which allows NKEA to perform a more thorough local search. Finally, we introduce a new notion, known as the measure space, which integrates multiple measures, such as the convergence metric and the diversity metric, to evaluate the performance of the algorithm. The results of our experiments show that NKEA not only achieves good performance in a large number of multiobjective optimization problems, but also outperforms most of the state-of-the-art approaches in these problems.