Shift-Based Penalty for Evolutionary Constrained Multiobjective Optimization and Its Application
Shift-Based Penalty for Evolutionary Constrained Multiobjective Optimization and Its Application
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DOI：
10.1109/tcyb.2021.3069814
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发表时间：
2021-05-25
影响因子：
11.8
通讯作者：
Wang, Yong
中科院分区：
文献类型：
--
作者：
Ma, Zhongwei;Wang, Yong
本文提出了一种新的约束处理技术——基于位移的惩罚（ShiP），用于求解约束多目标优化问题。在ShiP中，首先根据相邻可行解的分布对不可行解进行位移。漂移程度由当前亲代种群和子代种群中可行解的比例自适应控制。然后，根据移位的不可行解违反约束的情况对其进行惩罚。这种两步法可以在进化的早期鼓励不可行的解从不同的方向接近/进入可行区域，在进化的后期引导不同的可行解向帕累托最优解发展。此外，ShiP可以实现从进化早期的多样性和可行性向进化后期的多样性和收敛性的适应性过渡。ShiP是灵活的，可以嵌入到三个著名的多目标优化框架。基准测试问题的实验表明，ShiP与其他代表性的cht具有很强的竞争力。此外，基于ShiP，我们提出了一种称为ShiP（+）的档案辅助约束多目标进化算法（CMOEA），该算法优于其他两种最先进的CMOEA。最后，将ShiP算法成功应用于城市公交线路的车辆调度中。
This article presents a new constraint-handling technique (CHT), called shift-based penalty (ShiP), for solving constrained multiobjective optimization problems. In ShiP, infeasible solutions are first shifted according to the distributions of their neighboring feasible solutions. The degree of shift is adaptively controlled by the proportion of feasible solutions in the current parent and offspring populations. Then, the shifted infeasible solutions are penalized based on their constraint violations. This two-step process can encourage infeasible solutions to approach/enter the feasible region from diverse directions in the early stage of evolution, and guide diverse feasible solutions toward the Pareto optimal solutions in the later stage of evolution. Moreover, ShiP can achieve an adaptive transition from both diversity and feasibility in the early stage of evolution to both diversity and convergence in the later stage of evolution. ShiP is flexible and can be embedded into three well-known multiobjective optimization frameworks. Experiments on benchmark test problems demonstrate that ShiP is highly competitive with other representative CHTs. Further, based on ShiP, we propose an archive-assisted constrained multiobjective evolutionary algorithm (CMOEA), called ShiP(+), which outperforms two other state-of-the-art CMOEAs. Finally, ShiP is applied to the vehicle scheduling of the urban bus line successfully.