Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization
Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization
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DOI：
10.1007/11844297_54
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发表时间：
2006-09
期刊：
影响因子：
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通讯作者：
D. Brockhoff;E. Zitzler
中科院分区：
文献类型：
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作者：
D. Brockhoff;E. Zitzler
大多数用于逼近 Pareto 集的可用多目标进化算法 (MOEA) 都是针对低维问题（≤3 个目标）而设计和测试的。然而，众所周知，大量目标的问题会在帕累托集逼近的质量和运行时间方面造成额外的困难。此外，涉及的目标越多，决策过程就越困难。在这种情况下，问题就出现了：是否所有目标都是保持问题特征所必需的。人们还可能会问在什么条件下这种目标减少是可行的，以及如何计算一组最小目标。在本文中，我们提出了一个适合回答这三个问题的通用数学框架，以及相应的算法（精确算法和启发式算法）。启发式变体旨在直接集成到进化搜索过程中。此外，针对四个众所周知的测试问题的广泛实验表明，在所提出的方法的基础上，可以大幅降低维度。
Most of the available multiobjective evolutionary algorithms (MOEA) for approximating the Pareto set have been designed for and tested on low dimensional problems (≤3 objectives). However, it is known that problems with a high number of objectives cause additional difficulties in terms of the quality of the Pareto set approximation and running time. Furthermore, the decision making process becomes the harder the more objectives are involved. In this context, the question arises whether all objectives are necessary to preserve the problem characteristics. One may also ask under which conditions such an objective reduction is feasible, and how a minimum set of objectives can be computed. In this paper, we propose a general mathematical framework, suited to answer these three questions, and corresponding algorithms, exact and heuristic ones. The heuristic variants are geared towards direct integration into the evolutionary search process. Moreover, extensive experiments for four well-known test problems show that substantial dimensionality reductions are possible on the basis of the proposed methodology.