An Efficient Evolutionary Algorithm for Few-for-Many Optimization

2026-01-10

arXiv.org

AI Summary

This work addresses the challenge of effectively representing numerous conflicting objectives in high-dimensional multi-objective optimization using only a small set of solutions. To this end, it proposes the first dedicated evolutionary algorithm specifically designed for Few-for-Many (F4M) optimization. The algorithm employs a (μ+1) evolution strategy integrated with weighted Tchebycheff scalarization and an R2 indicator-guided environmental selection mechanism to generate a compact yet high-quality solution set that well covers the high-dimensional objective space. Additionally, the study introduces a general-purpose benchmark suite capable of transforming any multi-objective problem into an F4M instance. Experimental results demonstrate that the proposed algorithm significantly outperforms state-of-the-art methods across multiple high-dimensional benchmark problems, exhibiting superior convergence and solution set representativeness, particularly as the number of objectives increases.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Few-for-many (F4M) optimization, recently introduced as a novel paradigm in multi-objective optimization, aims to find a small set of solutions that effectively handle a large number of conflicting objectives. Unlike traditional many-objective optimization methods, which typically attempt comprehensive coverage of the Pareto front, F4M optimization emphasizes finding a small representative solution set to efficiently address high-dimensional objective spaces. Motivated by the computational complexity and practical relevance of F4M optimization, this paper proposes a new evolutionary algorithm explicitly tailored for efficiently solving F4M optimization problems. Inspired by SMS-EMOA, our proposed approach employs a $(\mu+1)$-evolution strategy guided by the objective of F4M optimization. Furthermore, to facilitate rigorous performance assessment, we propose a novel benchmark test suite specifically designed for F4M optimization by leveraging the similarity between the R2 indicator and F4M formulations. Our test suite is highly flexible, allowing any existing multi-objective optimization problem to be transformed into a corresponding F4M instance via scalarization using the weighted Tchebycheff function. Comprehensive experimental evaluations on benchmarks demonstrate the superior performance of our algorithm compared to existing state-of-the-art algorithms, especially on instances involving a large number of objectives. The source code of the proposed algorithm will be released publicly. Source code is available at https://github.com/MOL-SZU/SoM-EMOA.

Problem

• Few-for-Many optimization
• many-objective optimization
• Pareto front
• high-dimensional objective spaces
• representative solution set

Innovation

• Few-for-Many optimization
• evolutionary algorithm
• many-objective optimization
• R2 indicator
• Tchebycheff scalarization