Song Zhiming, Wang Maocai, Dai Guangming, Vasile Massimiliano
School of Computer, China University of Geosciences, Wuhan 430074, China.
School of Computer, China University of Geosciences, Wuhan 430074, China ; Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK.
ScientificWorldJournal. 2015;2015:439307. doi: 10.1155/2015/439307. Epub 2015 Mar 22.
As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m - 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m - 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.
众所周知，在一些温和条件下，具有(m)个目标函数的连续多目标优化问题的帕累托集是决策空间中一个分段连续的((m - 1))维流形。然而，如何利用这种正则性来设计多目标优化算法已成为研究重点。本文基于这种正则性，提出了一种基于回归分析的基于模型的多目标进化算法（MMEA - RA）来解决具有变量关联的连续多目标优化问题。在该算法中，优化问题通过概率分布被建模为决策空间中的一个有希望的区域，并且概率分布的质心是一个((m - 1))维分段连续流形。使用最小二乘法来构建这样一个模型。基于非支配排序的选择策略用于选择个体进入下一代。对新算法进行了测试，并与NSGA - II和RM - MEDA进行了比较。结果表明，在具有变量关联的测试实例上，MMEA - RA优于RM - MEDA和NSGA - II。同时，MMEA - RA比其他两种算法具有更高的效率。本文还指出并讨论了MMEA - RA的一些缺点。
