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

在这项研究中，我们首先研究了在执行NSGA-II的重叠解决方案的数量。而只有少数重叠的解决方案，包括在每个人口的NSGA-II在计算实验中的多目标问题与连续的决策变量，我们观察到许多重叠的解决方案，在应用NSGA-II组合多目标问题。因此，我们研究了从决策空间和目标空间中的每个种群中删除重叠解决方案的效果。然而，去除重叠的解决方案，并没有显着提高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，我们结合标量适应度函数（例如，NSGA-II中。更具体地说，我们实现了一个想法的概率使用标量适应度函数在NSGA-II的父选择和世代更新。各种多目标问题的计算实验清楚地表明，概率使用标量适应度函数大大提高了NSGA-II的性能。然后，我们提出了使用多个相似的标量适应度函数的思想，以集中在目标空间中的特定区域的NSGA-II的多目标搜索。这个想法在目标空间的一个小区域中搜索帕累托最优解时非常有效。所提出的想法也很好地在搜索单目标问题的最优解的多目标优化技术。最后，我们试图改善现有的进化优化算法的性能。我们发现，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。我们还提出了一个迭代版本的基于指标的进化算法，以提高其可扩展性，多目标问题与许多目标。

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.