Self-adaptive polynomial mutation in NSGA-II

Evolutionary multi-objective optimization is a field that has experienced a rapid growth in the last two decades. Although an important number of new multi-objective evolutionary algorithms have been designed and implemented by the scientific community, the popular Non-Dominated Sorting Genetic Algorithm (NSGA-II) remains as a widely used baseline for algorithm performance comparison purposes and applied to different engineering problems. Since every evolutionary algorithm needs several parameters to be set up in order to operate, parameter control constitutes a crucial task for obtaining an effective and efficient performance in its execution. However, despite the advancements in parameter control for evolutionary algorithms, NSGA-II has been mainly used in the literature with fine-tuned static parameters. This paper introduces a novel and computationally lightweight self-adaptation mechanism for controlling the distribution index parameter of the polynomial mutation operator usually employed by NSGA-II in particular and by multi-objective evolutionary algorithms in general. Additionally, the classical NSGA-II using polynomial mutation with a static distribution index is compared with this new version utilizing a self-adapted parameter. The experiments carried out over twenty-five benchmark problems show that the proposed modified NSGA-II with a self-adaptive mutator outperforms its static counterpart in more than 75% of the problems using three quality metrics (hypervolume, generalized spread, and modified inverted generational distance).