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Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives.

Weijie Zheng1, Benjamin Doerr2

  • 1School of Computer Science and Technology, International Research Institute for Artificial Intelligence, Harbin Institute of Technology, Shenzhen, China zhengweijie@hit.edu.cn.

Evolutionary Computation
|April 6, 2023
PubMed
Summary
This summary is machine-generated.

Multiobjective evolutionary algorithms (MOEAs) struggle with multimodal problems. New strategies like heavy-tailed mutation and stagnation detection significantly speed up convergence on complex bi-objective problems, improving theoretical bounds and practical performance.

Keywords:
Multiobjective evolutionary algorithmsmultimodal problemsruntime analysistheory of computing

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Area of Science:

  • Artificial Intelligence
  • Optimization
  • Computational Intelligence

Background:

  • Multiobjective evolutionary algorithms (MOEAs) excel in practice but lack theoretical understanding, especially for multimodal objectives.
  • Existing theory often focuses on simplified unimodal problems, not reflecting real-world complexities.
  • The OneJumpZeroJump problem is introduced as a benchmark for multimodal bi-objective optimization.

Purpose of the Study:

  • To theoretically analyze the performance of MOEAs on multimodal multiobjective problems.
  • To introduce and evaluate novel techniques for improving MOEA efficiency in challenging optimization landscapes.
  • To bridge the gap between theoretical understanding and practical success of MOEAs.

Main Methods:

  • Theoretical analysis of a simple evolutionary multiobjective optimizer (SEMO) and its global variant (GSEMO) on the OneJumpZeroJump problem.
  • Derivation of runtime bounds for GSEMO, including tight bounds for specific parameter ranges.
  • Integration of heavy-tailed mutation and a stagnation detection strategy into GSEMO, followed by theoretical and experimental evaluation.

Main Results:

  • SEMO fails to find the complete Pareto front for the OneJumpZeroJump problem.
  • GSEMO achieves the full Pareto front with provable expected runtime bounds, including a tight bound of 32enk+1±o(nk+1) for k=o(n).
  • Heavy-tailed mutation and stagnation detection improve GSEMO's expected runtime by a factor of at least kΩ(k), with stagnation detection offering further polynomial speedup.

Conclusions:

  • The OneJumpZeroJump problem serves as a valuable benchmark for multimodal MOEAs.
  • Techniques successful in single-objective optimization, like heavy-tailed mutation and stagnation detection, are effective for multimodal multiobjective problems.
  • This research advances the theoretical understanding of MOEAs and provides practical strategies for improving their performance on complex problems.