Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces
Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces
复制标题
处理决策空间和目标空间均具有约束的约束多目标优化问题
DOI：
10.1109/tevc.2019.2894743
复制
发表时间：
2019-10-01
影响因子：
14.3
通讯作者：
Wang, Yong
中科院分区：
文献类型：
--
作者：
Liu, Zhi-Zhong;Wang, Yong
约束多目标优化问题是实际应用中经常遇到的问题，通常涉及决策空间和目标空间的约束。然而，目前的人工CMOP从未同时考虑决策空间中的约束(即决策约束)和目标空间中的约束(即目标约束)。因此，它们模拟实际场景的能力有限。为了解决这个问题，本文构造了一组CMOP，称为DOC。首次尝试在人工CMOP的设计中同时考虑决策约束和目标约束。具体地，在DOC中，从现实世界的应用中收集各种决策约束(例如，不等式约束、等式约束、线性约束和非线性约束)，从而使得决策空间中的可行域具有不同的属性(例如，非线性、极小和多峰)。另一方面，设计了一些简单可控的目标约束，以减少目标空间中的可行域，使帕累托前沿具有不同的性质(如连续、离散、混合和退化)。作为一个整体，DOC对约束多目标进化算法(CMOEA)获得一组分布均匀且收敛良好的可行解提出了巨大的挑战。为了提高现有CMOEA在DOC上的性能，提出了一种简单高效的两阶段框架TOP。在顶部，第一阶段通过将CMOP转化为约束单目标优化问题来寻找有前景的可行域。然后在第二阶段，执行特定的CMOEA以获得最终解。将TOP应用于四个最先进的CMOEA中，实验结果表明该方法是非常有效的。
Constrained multiobjective optimization problems (CMOPs) are frequently encountered in real-world applications, which usually involve constraints in both the decision and objective spaces. However, current artificial CMOPs never consider constraints in the decision space (i.e., decision constraints) and constraints in the objective space (i.e., objective constraints) at the same time. As a result, they have a limited capability to simulate practical scenes. To remedy this issue, a set of CMOPs, named DOC, is constructed in this paper. It is the first attempt to consider both the decision and objective constraints simultaneously in the design of artificial CMOPs. Specifically, in DOC, various decision constraints (e.g., inequality constraints, equality constraints, linear constraints, and nonlinear constraints) are collected from real-world applications, thus making the feasible region in the decision space have different properties (e.g., nonlinear, extremely small, and multimodal). On the other hand, some simple and controllable objective constraints are devised to reduce the feasible region in the objective space and to make the Pareto front have diverse characteristics (e.g., continuous, discrete, mixed, and degenerate). As a whole, DOC poses a great challenge for a constrained multiobjective evolutionary algorithm (CMOEA) to obtain a set of well-distributed and well-converged feasible solutions. In order to enhance current CMOEAs’ performance on DOC, a simple and efficient two-phase framework, named ToP, is proposed in this paper. In ToP, the first phase is implemented to find the promising feasible area by transforming a CMOP into a constrained single-objective optimization problem. Then in the second phase, a specific CMOEA is executed to obtain the final solutions. ToP is applied to four state-of-the-art CMOEAs, and the experimental results suggest that it is quite effective.