An Efficient Evolutionary Algorithm for Few-for-Many Optimization

TL;DR

This paper introduces a new evolutionary algorithm tailored for Few-for-Many (F4M) optimization, emphasizing efficient solution set discovery in high-dimensional objective spaces, supported by a novel benchmark suite and superior experimental results.

Contribution

It proposes a specialized evolutionary algorithm for F4M optimization and develops a flexible benchmark test suite for evaluating such problems.

Findings

The algorithm outperforms existing methods on high-objective benchmarks.

The new benchmark suite effectively transforms multi-objective problems into F4M instances.

Experimental results demonstrate the algorithm's efficiency and robustness.

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.