Multi-objective Optimization-based Selection for Quality-Diversity by Non-surrounded-dominated Sorting

Abstract

Quality-Diversity (QD) algorithms, a subset of evolutionary algorithms, maintain an archive (i.e., a set of solutions) and simulate the natural evolution process through iterative selection and reproduction, with the goal of generating a set of high-quality and diverse solutions. Though having found many successful applications in reinforcement learning, QD algorithms often select the parent solutions uniformly at random, which lacks selection pressure and may limit the performance. Recent studies have treated each type of behavior of a solution as an objective, and selected the parent solutions based on Multi-objective Optimization (MO), which is a natural idea, but has not lead to satisfactory performance as expected. This paper gives the reason for the first time, and then proposes a new MO-based selection method by non-surrounded-dominated sorting (NSS), which considers all possible directions of the behaviors, and thus can generate diverse solutions over the whole behavior space. By combining NSS with the most widespread QD algorithm, MAP-Elites, we perform experiments on synthetic functions and several complex tasks (i.e., QDGym, robotic arm, and Mario environment generation), showing that NSS achieves better performance than not only other MO-based selection methods but also state-of-the-art selection methods in QD.