The Hybridization of Branch and Bound with Metaheuristics for Nonconvex Multiobjective Optimization

TL;DR

This paper introduces a hybrid framework combining branch and bound with multiobjective evolutionary algorithms to efficiently solve nonconvex multiobjective optimization problems, ensuring global convergence and improved search performance.

Contribution

It proposes a novel hybrid approach that leverages the strengths of both methods, enhancing bounds and convergence in nonconvex multiobjective optimization.

Findings

Hybrid algorithms outperform standalone methods in benchmark tests.

The framework guarantees global convergence.

Numerical experiments show improved efficiency and solution quality.

Abstract

A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization strategies. A multiobjective evolutionary algorithm is intended for inducing tight lower and upper bounds during the branch and bound procedure. Tight bounds such as the ones derived in this way can reduce the number of subproblems that have to be solved. The branch and bound method guarantees the global convergence of the framework and improves the search capability of the multiobjective evolutionary algorithm. An implementation of the hybrid framework considering NSGA-II and MOEA/D-DE as multiobjective evolutionary algorithms is presented. Numerical experiments verify the hybrid algorithms benefit from synergy of the branch and bound method and multiobjective evolutionary algorithms.