Many-Objective Cover Problem: Discovering Few Solutions to Cover Many Objectives

Many-objective optimization (MaO) is a basic issue in various research areas. Although Pareto optimality is a common criterion for MaO, it may bring many troubles when facing a huge number (e.g., up to 100) of objectives. This paper provides a new perspective on MaO by introducing a many-objective cover problem (MaCP). Given m objectives, MaCP aims to find a solution set with size k ( \(1 < k \ll m\) ) to cover all objectives (i.e., each objective can be approximately optimized by at least one solution in this set). We prove the NP-hard property of MaCP and develop a clustering-based swarm optimizer (CluSO) with a convergence guarantee to tackle MaCP. Then, we propose a decoupling many-objective test suite (DC-MaTS) with practical significance and use it to evaluate CluSO. Extensive experimental results on various test problems with up to 100 objectives demonstrate both the efficiency and effectiveness of CluSO, while also illustrating that MaCP is a feasible perspective on MaO.