Fuzzy Optimization with Multi-Objective Evolutionary Algorithms: a Case Study

2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making Pub Date : 2007-04-01 DOI:10.1109/MCDM.2007.369417

Gracia Sánchez, F. Jiménez

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引用次数: 18

Abstract

This paper outlines a real-world industrial problem for product-mix selection involving 8 decision variables and 21 constraints with fuzzy coefficients. On one hand, a multi-objective optimization approach to solve the fuzzy problem is proposed. Modified S-curve membership functions are considered. On the other hand, an ad hoc Pareto-based multi-objective evolutionary algorithm to capture multiple non dominated solutions in a single run of the algorithm is described. Solutions in the Pareto front corresponds with the fuzzy solution of the former fuzzy problem expressed in terms of the group of three (xrarr, mu, alpha), i.e., optimal solution - level of satisfaction - vagueness factor. Decision-maker could choose, in a posteriori decision environment, the most convenient optimal solution according to his level of satisfaction and vagueness factor. The proposed algorithm has been evaluated with the existing methodologies in the field and the results have been compared with the well-known multi-objective evolutionary algorithm NSGA-II

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模糊优化与多目标进化算法:一个案例研究

本文提出了一个包含8个决策变量和21个模糊系数约束的现实工业产品组合选择问题。一方面，提出了一种求解模糊问题的多目标优化方法。考虑了改进的s曲线隶属函数。另一方面，描述了一种特别的基于pareto的多目标进化算法，该算法在一次运行中捕获多个非支配解。Pareto前的解对应于前一个模糊问题的模糊解，用三组(xrarr, mu, alpha)表示，即最优解-满意度-模糊因子。在事后决策环境中，决策者可以根据自己的满意程度和模糊性因素选择最方便的最优方案。用该领域现有的方法对该算法进行了评估，并将结果与著名的多目标进化算法NSGA-II进行了比较

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2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making

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