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

在本研究中，我们首先考察了NSGA-II执行过程中重叠解的数量。在具有连续决策变量的多目标问题的计算实验中，NSGA-II的每个群体中只包含少数重叠解，而在组合多目标问题的应用中，我们观察到许多重叠解。因此，我们检查了在决策和目标空间中从每个人口中去除重叠解决方案的影响。然而，去除重叠溶液并没有显著改善NSGA-II的性能。我们只观察到解决方案的多样性略有增加。接下来，我们将标量适应度函数（如加权和）合并到NSGA-II中。更具体地说，我们实现了在NSGA-II中概率地使用标量适应度函数进行亲本选择和代更新的想法。各种多目标问题的计算实验清楚地表明，标量适应度函数的概率使用大大提高了NSGA-II的性能。为了使NSGA-II的多目标搜索集中在目标空间的特定区域上，提出了使用多个相似标量适应度函数的思想。在目标空间的小区域内寻找帕累托最优解时，这个想法非常有效。所提出的思想也适用于用多目标优化技术寻找单目标问题的最优解。最后，我们尝试改进现有进化优化算法的性能。结果表明，使用非几何交叉和基于相似性的亲本选择明显提高了NSGA-II的性能。我们还提出了一种迭代版本的基于指标的进化算法，以提高其对具有多目标的多目标问题的可扩展性。

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.