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Evolutionary Multi-Objective Diversity Optimization

Anh Viet Do, Mingyu Guo, Aneta Neumann, Frank Neumann

TL;DR

This work reframes diverse high-quality solution sets as a bi-objective optimization problem, seeking a spectrum of quality-diversity trade-offs by evolving a population of populations. It introduces a practical scheme that treats each population as an individual and applies standard evolutionary operators directly to the concatenated solution representations, with careful handling of ordering and recombination. The scheme is instantiated in NSGA-II and SPEA2 and evaluated on maximum cut, maximum coverage, and minimum vertex cover instances, revealing rich, interpretable fronts and informative insights into the interaction between objective quality and diversity. The results demonstrate viability and offer guidance on problem-specific heuristics, signaling that future advances may lie in memetic hybrids to achieve state-of-the-art performance.

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.

Evolutionary Multi-Objective Diversity Optimization

TL;DR

This work reframes diverse high-quality solution sets as a bi-objective optimization problem, seeking a spectrum of quality-diversity trade-offs by evolving a population of populations. It introduces a practical scheme that treats each population as an individual and applies standard evolutionary operators directly to the concatenated solution representations, with careful handling of ordering and recombination. The scheme is instantiated in NSGA-II and SPEA2 and evaluated on maximum cut, maximum coverage, and minimum vertex cover instances, revealing rich, interpretable fronts and informative insights into the interaction between objective quality and diversity. The results demonstrate viability and offer guidance on problem-specific heuristics, signaling that future advances may lie in memetic hybrids to achieve state-of-the-art performance.

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.
Paper Structure (10 sections, 6 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 10 sections, 6 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Evolutionary Multi-Objective Diversity Optimization
  3. Implementing Populations as Individuals
  4. Individual representation
  5. Recombination
  6. Problem Settings and Experiments
  7. Maximum Cut
  8. Maximum Coverage
  9. Minimum Vertex Cover
  10. Conclusions

Figures (3)

  • Figure 1: Unions of final populations across all runs on Max cut instances. For each run, dominated points are excluded.
  • Figure 2: Unions of final populations across all runs on Max coverage instances. For each run, dominated points are excluded.
  • Figure 3: Unions of final populations across all runs on Min vertex cover instances. For each run, dominated points are excluded.