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 $(μ+1)$-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.

翻译：少对多（F4M）优化是近期提出的一种新颖的多目标优化范式，旨在寻找一个能有效处理大量冲突目标的解的小型集合。与通常试图全面覆盖帕累托前沿的传统多目标优化方法不同，F4M优化强调寻找一个具有代表性的小型解集，以高效应对高维目标空间。受F4M优化的计算复杂性和实际相关性的启发，本文提出了一种专门为高效求解F4M优化问题而设计的新型进化算法。受SMS-EMOA的启发，我们提出的方法采用了一种由F4M优化目标引导的$(μ+1)$进化策略。此外，为了便于严格的性能评估，我们通过利用R2指标与F4M公式之间的相似性，专门为F4M优化提出了一套新颖的基准测试集。我们的测试集具有高度灵活性，允许任何现有的多目标优化问题通过使用加权切比雪夫函数的标量化，转化为相应的F4M实例。在基准测试上的全面实验评估表明，与现有的先进算法相比，我们的算法具有优越的性能，尤其是在涉及大量目标的实例上。所提出算法的源代码将公开发布。源代码可在 https://github.com/MOL-SZU/SoM-EMOA 获取。