Diversity Assessment in Many-Objective Optimization

Maintaining diversity is one important aim of multiobjective optimization. However, diversity for many-objective optimization problems is less straightforward to define than for multiobjective optimization problems. Inspired by measures for biodiversity, we propose a new diversity metric for many-objective optimization, which is an accumulation of the dissimilarity in the population, where an <inline-formula> <tex-math notation="LaTeX">$ L_{ p}$ </tex-math></inline-formula>-norm-based (<inline-formula> <tex-math notation="LaTeX">$\,{ p}{ <}{ 1}$ </tex-math></inline-formula>) distance is adopted to measure the dissimilarity of solutions. Empirical results demonstrate our proposed metric can more accurately assess the diversity of solutions in various situations. We compare the diversity of the solutions obtained by four popular many-objective evolutionary algorithms using the proposed diversity metric on a large number of benchmark problems with two to ten objectives. The behaviors of different diversity maintenance methodologies in those algorithms are discussed in depth based on the experimental results. Finally, we show that the proposed diversity measure can also be employed for enhancing diversity maintenance or reference set generation in many-objective optimization.