Development of evolutionary multiobjective optimization algorithms that can automatically adjust the balance between diversity and convergence

点击翻译按钮获取中文摘要

In this research, we first examined the number of overlapping solutions during the execution of NSGA-II. Whereas only a few overlapping solutions were included in each population of NSGA-II in computational experiments on multiobjective problems with continuous decision variables, we observed many overlapping solutions in the application of NSGA-II to combinatorial multiobjective problems. Thus we examined the effects of removing overlapping solutions from each population in the decision and objective spaces. The removal of overlapping solutions, however, did not significantly improve the performance of NSGA-II. We only observed a slight increase in the diversity of solutions. Next we combined a scalar fitness function (e.g., weighted sum) into NSGA-II. More specifically, we implemented an idea of probabilistically using a scalar fitness function in NSGA-II for parent selection and generation update. Computational experiments on various multiobjective problems clearly demonstrated that the probabilistic use of a scalar fitness function drastically improved the performance of NSGA-II. Then we proposed an idea of using multiple similar scalar fitness functions in order to concentrate the multiobjective search of NSGA-II on a particular region in the objective space. This idea worked very well in searching for Pareto-optimal solutions in a small region of the objective space. The proposed idea also worked well in the search for optimal solutions of single-objective problems by multiobjective optimization techniques. Finally we tried to improve the performance of existing evolutionary optimization algorithms. We showed that the use of non-geometric crossover and similarity-based parent selection clearly improved the performance of NSGA-II. We also proposed an iterated version of indicator-based evolutionary algorithms in order to improve their scalability to multiobjective problems with many objectives.