IEEE Trans Cybern. 2016 Dec;46(12):2953-2965. doi: 10.1109/TCYB.2014.2359985. Epub 2014 Oct 8.
This paper proposes a novel fuzzy rule-based penalty function approach for solving single-objective nonlinearly constrained optimization problems. Of all the existing state-of-the-art constraint handling techniques, the conventional method of penalty can be easily implemented because of its simplicity but suffers from the lack of robustness. To mitigate the problem of parameter dependency, several forms of adaptive penalties have been suggested in literature. Instead of identifying a complex mathematical function to compute the penalty for constraint violation, we propose a Mamdani type IF-THEN rule-based fuzzy inference system that incorporates all the required criteria of self-adaptive penalty without formulating an explicit mapping. Effectiveness of the proposed constrained optimization algorithm has been empirically validated on the basis of the standard optimality theorems from the literature on mathematical programming. Simulation results show that fuzzy penalty not only surpasses its existing counterpart i.e., self adaptive penalty, but also remain competitive against several other standard as well as currently developed complex constraint handling strategies.
本文提出了一种基于模糊规则的新罚函数方法，用于解决单目标非线性约束优化问题。在所有现有的约束处理技术中，由于其简单性，传统的罚函数方法很容易实现，但缺乏鲁棒性。为了减轻参数依赖性的问题，文献中已经提出了几种形式的自适应罚函数。我们提出了一种基于 Mamdani 类型的 IF-THEN 规则的模糊推理系统，而不是识别复杂的数学函数来计算约束违反的罚函数，该系统包含了自适应罚函数的所有必要条件，而无需制定显式映射。所提出的约束优化算法的有效性已根据数学规划文献中的标准最优性定理进行了实证验证。仿真结果表明，模糊罚函数不仅优于现有的自适应罚函数，而且在与其他几种标准以及当前开发的复杂约束处理策略的竞争中也具有竞争力。
