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首页> 外文期刊>IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics >An interactive fuzzy satisficing method for multiobjectivenonconvex programming problems with fuzzy numbers through coevolutionarygenetic algorithms
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An interactive fuzzy satisficing method for multiobjectivenonconvex programming problems with fuzzy numbers through coevolutionarygenetic algorithms

机译：协同进化遗传算法求解带模糊数的多目标非凸规划问题的交互式模糊满足方法

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摘要

In this paper, by considering the experts' fuzzy understanding ofnthe nature of the parameters in the problem-formulation process,nmultiobjective nonconvex nonlinear programming problems with fuzzynnumbers are formulated and an interactive fuzzy satisficing methodnthrough coevolutionary genetic algorithms is presented. Using thenΑ-level sets of fuzzy numbers, the corresponding nonfuzzynΑ-programming problem is introduced. After determining the fuzzyngoals of the decision maker, if the decision maker specifies the degreenΑ and the reference membership values, the corresponding extendednPareto optimal solution can be obtained by solving the augmented minimaxnproblems for which the coevolutionary genetic algorithm, called GENOCOPnIII, is applicable. In order to overcome the drawbacks of GENOCOP III,nthe revised GENOCOP III is proposed by introducing a method forngenerating an initial feasible point and a bisection method forngenerating a new feasible point efficiently. Then an interactive fuzzynsatisficing method for deriving a satisficing solution for the decisionnmaker efficiently from an extended Pareto optimal solution set isnpresented together with an illustrative numerical example
机译：本文在考虑问题专家对问题本质的模糊理解的基础上，提出了具有模糊数的多目标非凸非线性规划问题，提出了一种基于协同进化遗传算法的交互式模糊满足方法。使用随后的模糊数集，引入了相应的非模糊化编程问题。在确定了决策者的模糊目标之后，如果决策者指定了度和参考成员值，则可以通过求解扩展的最小极大问题来获得相应的扩展的nPareto最优解，该问题可以应用称为GENOCOPnIII的协进化遗传算法。为了克服GENOCOP III的缺点，提出了一种改进的GENOCOP III，该方法引入了一种生成初始可行点的方法和一种二分法来高效生成一个新的可行点。然后，提出了一种交互式模糊满足方法，该方法从扩展的帕累托最优解集中有效地为决策者提供满足解，并给出了一个示例性的数值示例。

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