Decision Variable Analysis-Guided Differentiated Fuzzy Search for Large-Scale Multi-Objective Optimization

2026-07-18

AI Summary

This study addresses the challenge of balancing convergence and diversity in large-scale multi-objective optimization within high-dimensional decision spaces, where existing fuzzy search methods often fall short due to their uniform granularity across all variables. To overcome this limitation, the work explicitly incorporates decision variable roles into the fuzzy search framework by first analyzing variables to identify their functional heterogeneity, then establishing a mapping between variable roles and search granularities to enable a differentiated fuzzy search mechanism. Furthermore, a dual-metric-based phase transition strategy is introduced to dynamically adjust the intensity of fuzzy updates. Evaluated on benchmark test suites such as LSMOP and UF—each featuring 1,000-dimensional decision variables—the proposed approach significantly outperforms state-of-the-art large-scale multi-objective evolutionary algorithms, demonstrating its effectiveness and superiority in high-dimensional optimization scenarios.

Abstract

Large-scale multi-objective optimization problems (LSMOPs) are challenging due to their high-dimensional decision spaces. Fuzzy search is an effective technique for improving search efficiency, while decision variable analysis can reveal the distinct roles of variables in promoting convergence and maintaining diversity. However, existing fuzzy search methods generally employ a uniform search granularity for all variables, overlooking the heterogeneous search requirements implied by variable roles. To address this limitation, this paper proposes a Decision variable analysis-guided Differentiated Fuzzy Search method, termed DDFS. The proposed method establishes an explicit mapping between decision-variable roles and fuzzy search granularities. Decision variable analysis is employed to identify variable roles and search sensitivities, enabling different variable groups to adopt differentiated fuzzy search behaviors during offspring generation. Furthermore, a Dual-Indicator Stage Transition Mechanism is developed to dynamically adjust fuzzy-updating intensity throughout the evolutionary process, balancing early-stage search-space compression and late-stage convergence refinement. Extensive experiments on the LSMOP and UF benchmark suites with up to 1000 decision variables show that DDFS generally achieves competitive performance against several representative large-scale multi-objective evolutionary algorithms. The results suggest that explicitly incorporating decision-variable roles into fuzzy search can help improve optimization performance in high-dimensional decision spaces.

Problem

• large-scale multi-objective optimization
• decision variable analysis
• fuzzy search
• search granularity
• variable roles

Innovation

• Differentiated Fuzzy Search
• Decision Variable Analysis
• Large-Scale Multi-Objective Optimization
• Search Granularity Adaptation
• Dual-Indicator Stage Transition