基于分解和超平面拟合的进化超多目标优化降维算法

目标降维是研究超多目标优化问题的一个重要方向，它通过恰当的算法设计，能够剔除一些对求解优化问题冗余的目标，达到极大简化优化问题的效果。在超多目标优化降维问题中，前沿界面呈现非线性的情形是最普遍也是最难处理的降维问题。该文提出一种基于分解和超平面拟合的算法(DHA)来处理这类目标降维问题，通过对进化过程中种群的有效分解，使得在几何上非线性分布的非劣解集近似分解为多个近似线性分布的子集，再用系数是稀疏的超平面结合一些扰动项去拟合这些非劣解子集，最后根据该超平面提取出原问题的本质目标集，达到去除冗余目标的效果。为了检验提出算法的有效性，采用DTLZ5(I, m), WFG3(I, m)和MAOP(I, m)作为测试问题集，与代表当今水平的著名算法进行比较。计算机仿真结果表明该文提出的算法无论前沿界面是线性或非线性的情形都具有优异的性能。

Objective Reduction Algorithm Based on Decomposition and Hyperplane Approximation for Evolutionary Many-Objective Optimization

Objective reduction is an important research direction in many-objective optimization. Through proper algorithm design, it can eliminate some redundant objectives to achieve the effect of greatly simplifying an optimization problem. Among the many-objective optimization problems with redundant objectives, the problems with nonlinear Pareto-Front are the most common and most difficult to tackle. In this paper, an algorithm based on Decomposition and Hyperplane Approximation (DHA) is proposed to deal with objective reduction problems with nonlinear Pareto-Front. The proposed algorithm decomposes a population with nonlinear geometric distribution into several subsets with approximate linear distribution in the process of evolution, and uses a hyperplane with sparse coefficients combined with some perturbation terms to fit these subsets, and then it extractes an essential objective set of original problem based on the coefficients of the fitting hyperplane. In order to test the performance of the proposed algorithm, this study compares it with some state-of-the-art algorithms in the benchmark DTLZ5(I, m), WFG3(I, m) and MAOP(I, m). The experimental results show that the proposed algorithm has good performance both in the problems with linear and nonlinear Pareto-Front.