Knee-oriented expensive many-objective optimization via aggregation-dominance: A multi-task perspective

Abstract

Given the costs to implement whole Pareto optimal solutions, users often prefer solutions of interest, like knee points, which represent naturally preferred solutions without a specific bias. Recent surrogate-assisted multi-objective evolutionary algorithms (SAMOEAs) incorporating knee identification techniques have been suggested, but most of them cannot find knee solutions for expensive many-objective optimization problems. This work proposes a Kriging-assisted evolutionary multi-task algorithm with aggregation-dominance. The aggregation-dominance approach identifies knee points on an estimated Pareto front, from which subproblems are created and solved in parallel via Kriging-assisted multi-task optimization for guiding search knee solutions. Additionally, our proposed infill solutions selection strategy focuses on re-evaluating solutions converging in regions of interest. Experimental results on knee-oriented benchmark problems show that our algorithm outperforms state-of-the-art methods, with aggregation-dominance surpassing five existing knee identification techniques. We also validate the algorithm’s performance on the portfolio allocation problem.