Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms
Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms
复制标题
DOI：
10.1109/tevc.2012.2185847
复制
发表时间：
2013-02
影响因子：
14.3
通讯作者：
D. Saxena;João A. Duro;A. Tiwari;K. Deb;Qingfu Zhang
中科院分区：
文献类型：
--
作者：
D. Saxena;João A. Duro;A. Tiwari;K. Deb;Qingfu Zhang
现有的多目标进化算法在处理多目标问题时面临着选择算子效率低、计算成本高、目标空间难以可视化等问题。虽然许多方法旨在通过增加标准选择算子的保真度来解决这些困难，但目标约简方法试图消除对描述帕累托最优前沿（POF）不重要的目标。如果发现基本目标的数量为两个或三个，则可以通过现有的moea解决问题。它意味着客观还原可以使一个原本无法解决的（多目标）问题变得可解决。即使当基本目标有四个或更多时，问题的简化表示也会对搜索效率、计算成本和决策产生有利影响。因此，开发通用和健壮的目标约简方法变得非常重要。本文分别提出了基于主成分分析和基于最大方差展开的线性和非线性目标约简算法框架。本文的主要贡献包括：1)增强了框架的核心组件，在适用于具有不同冗余程度的一系列问题方面具有更高的鲁棒性；处理不太接近真实POF的输入数据的机制；并依赖较少的参数，以尽量减少性能的可变性；2)提出误差度量来评估结果的质量；3)对所提算法所涉及的关键参数和输入数据的特征进行敏感性分析；4)在广泛的测试问题（扩大到50个目标）和两个现实问题上，研究所提出的算法与-à-vis优势关系保持算法的性能。
The difficulties faced by existing multiobjective evolutionary algorithms (MOEAs) in handling many-objective problems relate to the inefficiency of selection operators, high computational cost, and difficulty in visualization of objective space. While many approaches aim to counter these difficulties by increasing the fidelity of the standard selection operators, the objective reduction approach attempts to eliminate objectives that are not essential to describe the Pareto-optimal front (POF). If the number of essential objectives is found to be two or three, the problem could be solved by the existing MOEAs. It implies that objective reduction could make an otherwise unsolvable (many-objective) problem solvable. Even when the essential objectives are four or more, the reduced representation of the problem will have favorable impact on the search efficiency, computational cost, and decision-making. Hence, development of generic and robust objective reduction approaches becomes important. This paper presents a principal component analysis and maximum variance unfolding based framework for linear and nonlinear objective reduction algorithms, respectively. The major contribution of this paper includes: 1) the enhancements in the core components of the framework for higher robustness in terms of applicability to a range of problems with disparate degree of redundancy; mechanisms to handle input data that poorly approximates the true POF; and dependence on fewer parameters to minimize the variability in performance; 2) proposition of an error measure to assess the quality of results; 3) sensitivity analysis of the proposed algorithms for the critical parameter involved, and the characteristics of the input data; and 4) study of the performance of the proposed algorithms vis-à-vis dominance relation preservation based algorithms, on a wide range of test problems (scaled up to 50 objectives) and two real-world problems.