A general hybrid framework for many-objective optimization: integrating local search into reference-vector-based evolutionary algorithms

Abstract

We address the problem of achieving convergence and diversity in many-objective problems, focusing on continuous and unconstrained functions. It is known that with increasing numbers of objectives (say from 4 to 20) even modern many-objective Evolutionary Algorithms (EAs) may struggle to converge to, and fully distribute across the Pareto front. This paper presents a general and modular hybrid approach that integrates local search into reference-vector-based Many-Objective Evolutionary Algorithms (MaOEAs), addressing issues such as weakened selection pressure and the increasing complexity of exploring high-dimensional objective spaces. The hybrid approach employs Sequential Quadratic Programming (SQP) guided by achievement scalarizing directions, derived from either the Weighted Achievement Scalarizing Function (W-ASF) or the Penalty-based Boundary Intersection (PBI) schemes, depending on the decomposition strategy of the underlying MaOEA. It is designed to be broadly applicable with limited parameter tuning, facilitating integration with algorithms from the NSGA-III and MOEA-DD families. The effectiveness of the proposed approach is demonstrated through extensive experiments on standard continuous-variable many-objective benchmark problems as well as on representative real-world case studies. Results show that integrating local search significantly enhances performance, while a principled method for setting hybrid parameters ensures robustness and reproducibility. Although limited to an empirical study over a (large) test function suite, these findings highlight the potential of combining mathematical programming techniques with evolutionary algorithms for high-dimensional many-objective optimization problems.