Objective Extraction for Many-Objective Optimization Problems: Algorithm and Test Problems
针对高维多目标优化中现有降维方法可能丢失帕累托解的问题，提出一种目标提取方法，将降维目标表示为原目标的线性组合以最大化冲突，并设计新测试框架和性能指标，实验验证了方法的有效性和鲁棒性。
For many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, the performance of most existing evolutionary multi-objective optimization algorithms generally deteriorates over the number of objectives. As some MaOPs may have redundant or correlated objectives, it is desirable to reduce the number of the objectives in such circumstances. However, the Pareto solution of the reduced MaOP obtained by most of the existing objective reduction methods, based on objective selection, may not be the Pareto solution of the original MaOP. In this paper, we propose an objective extraction method (OEM) for MaOPs. It formulates the reduced objective as a linear combination of the original objectives to maximize the conflict between the reduced objectives. Subsequently, the Pareto solution of the reduced MaOP obtained by the proposed algorithm is that of the original MaOP, and the proposed algorithm can thus preserve the dominance structure as much as possible. Moreover, we propose a novel framework that features both simple and complicated Pareto set shapes for many-objective test problems with an arbitrary number of essential objectives. Within this framework, we can control the importance of essential objectives. As there is no direct performance metric for the objective reduction algorithms on the benchmarks, we present a new metric that features simplicity and usability for the objective reduction algorithms. We compare the proposed OEM with three objective reduction methods, i.e., REDGA, L-PCA, and NL-MVU-PCA, on the proposed test problems and benchmark DTLZ5 with different numbers of objectives and essential objectives. Our numerical studies show the effectiveness and robustness of the proposed approach.