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Consensus-based optimization for multi-objective problems: a multi-swarm approach

Author

Listed:
  • Kathrin Klamroth

    (University of Wuppertal)

  • Michael Stiglmayr

    (University of Wuppertal)

  • Claudia Totzeck

    (University of Wuppertal)

Abstract

We propose a multi-swarm approach to approximate the Pareto front of general multi-objective optimization problems that is based on the consensus-based optimization method (CBO). The algorithm is motivated step by step beginning with a simple extension of CBO based on fixed scalarization weights. To overcome the issue of choosing the weights we propose an adaptive weight strategy in the second modeling step. The modeling process is concluded with the incorporation of a penalty strategy that avoids clusters along the Pareto front and a diffusion term that prevents collapsing swarms. Altogether the proposed K-swarm CBO algorithm is tailored for a diverse approximation of the Pareto front and, simultaneously, the efficient set of general non-convex multi-objective problems. The feasibility of the approach is justified by analytic results, including convergence proofs, and a performance comparison to the well-known non-dominated sorting genetic algorithms NSGA2 and NSGA3 as well as the recently proposed one-swarm approach for multi-objective problems involving consensus-based optimization.

Suggested Citation

  • Kathrin Klamroth & Michael Stiglmayr & Claudia Totzeck, 2024. "Consensus-based optimization for multi-objective problems: a multi-swarm approach," Journal of Global Optimization, Springer, vol. 89(3), pages 745-776, July.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-024-01369-1
    DOI: 10.1007/s10898-024-01369-1
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    References listed on IDEAS

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    1. Saul Gass & Thomas Saaty, 1955. "The computational algorithm for the parametric objective function," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 39-45, March.
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