A Landscape-Aware Differential Evolution for Multimodal Optimization Problems

2024-08-05

arXiv.org

AI Summary

This work addresses multimodal optimization problems (MMOPs), aiming to simultaneously locate multiple global optima while ensuring high convergence accuracy. We propose Landscape-Aware Differential Evolution (LADE), introducing a novel triple landscape-aware mechanism: (1) adaptive peak exploration, (2) a peak-discrimination strategy that applies precision refinement exclusively to globally optimal peaks, and (3) adaptive reinitialization guided by the spatial distribution of already discovered peaks. LADE dynamically models terrain knowledge from historical search trajectories, synergistically preserving population diversity and enhancing peak identification efficiency. Evaluated on 20 standard MMOP benchmarks, LADE consistently outperforms seven state-of-the-art algorithms and four CEC competition winners, achieving new state-of-the-art performance in both the number of successfully identified global peaks and their localization accuracy.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this paper, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual locating a found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or a found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution of the found peaks, which helps explore more peaks. The experiments are conducted on 20 widely-used benchmark MMOPs. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performed algorithms proposed recently and four winner algorithms in the IEEE CEC competitions for multimodal optimization.

Problem

• Locate multiple global peaks in MMOPs
• Achieve accuracy on found global peaks
• Maintain diversity and guide search efficiently

Innovation

• Landscape-aware peak exploration technique
• Landscape-aware peak distinction method
• Adaptive reinitialization based on peak distribution