Parameter control has succeeded in accelerating the convergence process of evolutionary algorithms. Empirical and theoretical studies for classic pseudo-Boolean problems, such as OneMax, LeadingOnes, etc., have explained the impact of parameters and helped us understand the behavior of algorithms for single-objective optimization. In this work, by transmitting the techniques of single-objective optimization, we perform an extensive experimental investigation into the behavior of the self-adaptive GSEMO variants. We test three self-adaptive mutation techniques designed for single-objective optimization for the OneMinMax, COCZ, LOTZ, and OneJumpZeroJump problems. While adopting these techniques for the GSEMO algorithm, we consider different performance metrics based on the current non-dominated solution set. These metrics are used to guide the self-adaption process. Our results indicate the benefits of self-adaptation for the tested benchmark problems. We reveal that the choice of metrics significantly affects the performance of the self-adaptive algorithms. The self-adaptation methods based on the progress in one objective can perform better than the methods using multi-objective metrics such as hypervolume, inverted generational distance, and the number of the obtained Pareto solutions. Moreover, we find that the self-adaptive methods benefit from the large population size for OneMinMax and COCZ.

翻译：参数控制成功加速了进化算法的收敛过程。针对OneMax、LeadingOnes等经典伪布尔问题的实证与理论研究解释了参数的影响，并帮助我们理解单目标优化中算法的行为。在本工作中，通过移植单目标优化技术，我们对自适应GSEMO变体的行为进行了广泛的实验研究。我们针对OneMinMax、COCZ、LOTZ和OneJumpZeroJump问题测试了三种为单目标优化设计的自适应变异技术。在将这些技术应用于GSEMO算法时，我们基于当前非支配解集考虑了不同的性能指标。这些指标用于指导自适应过程。我们的结果表明，自适应对所测试的基准问题具有益处。我们揭示，指标的选择显著影响自适应算法的性能。基于单个目标进展的自适应方法，其表现可能优于使用超体积、反转世代距离和获得的Pareto解数量等多目标指标的方法。此外，我们发现对于OneMinMax和COCZ问题，自适应方法受益于较大的种群规模。