IEEE Trans Cybern. 2017 Sep;47(9):2678-2688. doi: 10.1109/TCYB.2017.2647742. Epub 2017 Jan 12.
A novel multiobjective technique is proposed for solving constrained optimization problems (COPs) in this paper. The method highlights three different perspectives: 1) a COP is converted into an equivalent dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: a) the original objective; b) a constraint-violation objective; and c) a niche-count objective; 2) a method of gradually reducing the constraint boundary aims to handle the constraint difficulty; and 3) a method of gradually reducing the niche size aims to handle the multimodal difficulty. A general framework of the design of dynamic constrained multiobjective evolutionary algorithms is proposed for solving DCMOPs. Three popular types of multiobjective evolutionary algorithms, i.e., Pareto ranking-based, decomposition-based, and hype-volume indicator-based, are employed to instantiate the framework. The three instantiations are tested on two benchmark suites. Experimental results show that they perform better than or competitive to a set of state-of-the-art constraint optimizers, especially on problems with a large number of dimensions.
本文提出了一种新颖的多目标技术，用于解决约束优化问题 (COPs)。该方法强调了三个不同的视角：1）将 COP 转换为具有三个目标的等效动态约束多目标优化问题 (DCMOP)：a）原始目标；b）违反约束目标；c）小生境计数目标；2）逐渐减小约束边界的方法旨在处理约束难度；3）逐渐减小小生境大小的方法旨在处理多模态难度。提出了一种用于解决 DCMOP 的动态约束多目标进化算法设计的通用框架。采用了三种流行的多目标进化算法，即基于 Pareto 排序、基于分解和基于 hype-volume 指标的算法，来实例化该框架。这三种实例在两个基准套件上进行了测试。实验结果表明，它们的性能优于或与一组最先进的约束优化器相当，特别是在维度较多的问题上。
