Evolutionary Multi-Objective Diversity Optimization

TL;DR

This paper introduces a bi-objective evolutionary approach to generate diverse high-quality solutions, providing insights into quality-diversity trade-offs across various combinatorial optimization problems.

Contribution

It presents a novel framework for evolving populations of populations to optimize both quality and diversity simultaneously, compatible with existing multi-objective algorithms.

Findings

Non-dominated populations show rich qualitative features.

The approach provides insights into problem-specific quality-diversity trade-offs.

Implemented in NSGA-II and SPEA2, tested on multiple combinatorial problems.

Abstract

Creating diverse sets of high quality solutions has become an important problem in recent years. Previous works on diverse solutions problems consider solutions' objective quality and diversity where one is regarded as the optimization goal and the other as the constraint. In this paper, we treat this problem as a bi-objective optimization problem, which is to obtain a range of quality-diversity trade-offs. To address this problem, we frame the evolutionary process as evolving a population of populations, and present a suitable general implementation scheme that is compatible with existing evolutionary multi-objective search methods. We realize the scheme in NSGA-II and SPEA2, and test the methods on various instances of maximum coverage, maximum cut and minimum vertex cover problems. The resulting non-dominated populations exhibit rich qualitative features, giving insights into the optimization instances and the quality-diversity trade-offs they induce.