Few for Many: Towards Efficient and Flexible Many-Objective Optimization

Many-objective optimization (MaO) can be found in many areas. Most current MaO methods aim to approximate the Pareto set or find a single trade-off solution. They could become infeasible when the number of objectives is large. Some recent studies have demonstrated the efficiency of using a few solutions to synergistically optimize many objectives. This paper further refines and extends this idea for MaO. Specifically, we formulate this idea as a conditional set-optimization problem, termed the few-for-many (F4M) problem. Its optimization objective, referred to as the synergistic optimization index (SOI), is compatible with any user-specified scalarization method, enabling this formulation to flexibly model diverse MaO scenarios. Then, we introduce two specific forms of SOI: linear SOI and Tchebycheff SOI, followed by a theoretical analysis of their optimization complexity, monotonicity, and supermodularity. To apply the F4M formulation to MaO, we develop a greedy estimation-of-distribution algorithm (GEDA) and further design a generic multi-objective test suite (GMOTS). Extensive experimental studies illustrate the ability of GEDA in solving both continuous and discrete MaO problems. © 2025 IEEE.