In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective 0-1 programming problems involving fuzzy numbers are formu...
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In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective 0-1 programming problems involving fuzzy numbers are formulated. Using the alpha-level sets of fuzzy numbers, the corresponding nonfuzzy alpha-programming problem is introduced. The fuzzy goals of the decision maker (DM) for the objective functions are quantified by eliciting the corresponding linear membership functions. Through the introduction of an extended Pareto optimality concept, if the DM specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the DM efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. (C) 1998 Elsevier Science B.V. All rights reserved.
Recently, genetic algorithms (GAs), a new learning paradigm that models a natural evolution mechanism, have received a great deal of attention regarding their potential as optimization techniques for solving combinato...
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Recently, genetic algorithms (GAs), a new learning paradigm that models a natural evolution mechanism, have received a great deal of attention regarding their potential as optimization techniques for solving combinatorial optimization problems. In this paper, we focus on multiobjective 0-1 programming problems as a generalization of the traditional single objective ones. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for each of the objective functions. After eliciting the linear membership functions through the interaction with the decision maker, we adopt the fuzzy decision of Bellman and Zadeh or minimum-operator for combining them. In order to investigate the applicability of the conventional GAs for the solution of the formulated problems, a lot of numerical simulations are performed by assuming several genetic operators. Then, instead of using the penalty function for treating the constraints, we propose three types of revised GAs which generate only feasible solutions, Illustrative numerical examples demonstrate both feasibility and efficiency of the proposed methods.
In this paper, we deal with a multiobjective 0-1 programming problem involving fuzzy random variable coefficients. Introducing fuzzy goals for the objective functions, we consider the problem to maximize the degrees o...
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In this paper, we deal with a multiobjective 0-1 programming problem involving fuzzy random variable coefficients. Introducing fuzzy goals for the objective functions, we consider the problem to maximize the degrees of possibility that the objective function values satisfy the fuzzy goals, which becomes a multiobjective stochastic 0-1 programming problem. Using the expectation model in stochastic programming, we reformulate the problem as a multiobjective 0-1 linear fractional programming problem. In order to find a satisficing solution for a decision maker, we propose an interactive satisficing method based on the reference point method and show that the problem to be solved is reduced to a mixed 0-1 programming problem. (C) 2004 Elsevier Ltd. All rights reserved.
In this paper, we focus on a multiobjective 0-1 programming problem with block angular structure by incorporating fuzzy goals of the decision maker. Having elicited the linear membership functions of the decision make...
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ISBN:
(纸本)0780329031
In this paper, we focus on a multiobjective 0-1 programming problem with block angular structure by incorporating fuzzy goals of the decision maker. Having elicited the linear membership functions of the decision maker, if we adopt the fuzzy decision for aggregating them, the original problem reduces into a single objective 0-1 programming problem with block angular structure. For solving the reduced problem by exploiting its special structure, we propose a genetic algorithm with decomposition procedures which generates only feasible solutions. Through a lot of numerical experiments, both feasibility and efficiency of the proposed method are demonstrated.
In this paper, an interactive fuzzy satisficing method for a multiobjective 0-1 programming problem is presented by incorporating the desirable features of both the interactive fuzzy programming methods and genetic al...
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In this paper, an interactive fuzzy satisficing method for a multiobjective 0-1 programming problem is presented by incorporating the desirable features of both the interactive fuzzy programming methods and genetic algorithms. By considering the imprecise nature of human judgements, the fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting linear membership functions. If the DM specifies the reference membership levels for all of the membership functions, the corresponding Pareto optimal solution which is, in the minimax sense, nearest to the requirement can be obtained by solving the minimax problem. To generate Pareto optimal solutions by applying the proposed genetic algorithm which is modified to generate only feasible solutions, the algorithm is further revised by providing some new mechanism for forming an initial population after the first interaction with the DM. illustrative numerical examples demonstrate the both feasibility and efficiency of the proposed methods.
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