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

• Published in: Journal of global optimization Vol. 89; no. 3; pp. 745 - 776
• Main Authors: Klamroth, Kathrin, Stiglmayr, Michael, Totzeck, Claudia
• Format: Journal Article
• Language: English
• Published: New York, NY Springer US 01.07.2024; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Computer Science; Consensus-based methods; Genetic algorithms; Global optimization; Mathematics; Mathematics and Statistics; Methods; Modelling; Multiobjective optimization; Multiple objective analysis; Operations Research/Decision Theory; Optimization; Pareto optimization; Real Functions; Sorting algorithms; Global optimization; Multiobjective optimization; Consensus-based methods
• ISSN: 1573-2916; 0925-5001; 1573-2916
• DOI: 10.1007/s10898-024-01369-1

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.