Accelerating Large-scale Multiobjective Optimization via Problem Reformulation

Abstract

Large-scale multiobjective optimization problems with hundreds of decision variables pose significant challenges to existing evolutionary algorithms due to the curse of dimensionality. This work presents LSMOF, a reformulation-based framework that accelerates large-scale multiobjective optimization. The key insight is decision variable analysis: variables are categorized based on their convergence and diversity contributions, then the original high-dimensional problem is reformulated into a low-dimensional weight-vector optimization task. This reformulation dramatically reduces the search space while preserving the problem structure, enabling efficient evolutionary search. Extensive experiments on benchmark problems with up to 1,000 decision variables demonstrate the superiority of LSMOF over state-of-the-art large-scale MOEAs.

Paper figures

Paper figure: Optimization results on large-scale multiobjective benchmark (D = 500), showing Pareto front approximation by LSMOF compared to several state-of-the-art algorithms. The reformulation-based approach achieves significantly better convergence and diversity.

Key contributions

• Decision variable analysis categorizes variables by their contribution to convergence versus diversity, enabling targeted treatment of each group.
• A problem reformulation strategy transforms the original high-dimensional search into low-dimensional weight-vector optimization, reducing the search space while preserving Pareto-front structure.
• Demonstrated on benchmarks with up to 1,000 dimensions, LSMOF significantly outperforms state-of-the-art large-scale MOEAs in both convergence speed and solution quality.

Resources