The Degree-Constrained Minimum Spanning Tree problem is to find a minimum spanning tree of the given graph, subject to constraints on node degrees. The dc-MST problem is NP-complete. This paper investigates the dc-MST...
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The Degree-Constrained Minimum Spanning Tree problem is to find a minimum spanning tree of the given graph, subject to constraints on node degrees. The dc-MST problem is NP-complete. This paper investigates the dc-MST problem with fuzzy weights. According to different decision criteria, three models are proposed: expected dc-MST model, a-dc-MST model and the most dc-MST model. Finally, a hybrid intelligent algorithm approach with a tree-based genetic representation is designed to solve these models, and numerical examples are provided to illustrate its effectiveness.
In this paper, we associate a vector maximum optimization (VOP) problem to the related real valued programming problem depending on the following approaches, the minimum operator and the second is product operator. Fo...
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In this paper, we associate a vector maximum optimization (VOP) problem to the related real valued programming problem depending on the following approaches, the minimum operator and the second is product operator. For the above two operators we use a suitable transformation functions to reformulate the (VOP) to the fuzzy problem (FP). A characterization of this transformation functions of the both approaches will be given. We present the relation between the efficient solution and solution of VOP and FP by the minimum and product operator. (c) 2004 Elsevier Inc. All rights reserved.
A method for solving single- and multi-objective probabilistic linear programming problems with a joint constraint is presented. It is assumed that the parameters in the probabilistic linear programming problems are r...
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A method for solving single- and multi-objective probabilistic linear programming problems with a joint constraint is presented. It is assumed that the parameters in the probabilistic linear programming problems are random variables, and the probabilistic problem is converted to an equivalent deterministic mathematical programming problem. In this paper the parameters are generally considered as normal and log-normal random variables. A non-linear programming method is used to solve the single-objective deterministic problem, and a fuzzy programming method is used to solve the multi-objective deterministic problem. Finally, a numerical example is presented to illustrate the methodology.
In this paper, a fuzzy quadratic minimum spanning tree problem is formulated as expected value model, chance-constrained programming and dependent-chance programming according to different decision criteria. Then the ...
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In this paper, a fuzzy quadratic minimum spanning tree problem is formulated as expected value model, chance-constrained programming and dependent-chance programming according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a simulation-based genetic algorithm using Prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents. Finally, a numerical example is provided for illustrating the effectiveness of the genetic algorithm. (c) 2004 Published by Elsevier Inc.
In this paper we propose a robust approach for solving the scheduling problem of parallel machines with sequence-. dependent set-up costs. In the literature, several mathematical models and solution methods have been ...
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In this paper we propose a robust approach for solving the scheduling problem of parallel machines with sequence-. dependent set-up costs. In the literature, several mathematical models and solution methods have been proposed to solve such scheduling problems, but most of which are based on the strong assumption that input data are known in a deterministic way. In this paper, a fuzzy mathematical programming model is formulated by taking into account the uncertainty in processing times to provide the optimal solution as a trade-off between total set-up cost and robustness in demand satisfaction. The proposed approach requires the solution of a non-linear. mixed integer programming (NLMIP), that can be formulated as an equivalent, mixed integer linear programming (MILP) model. The resulting MILP model in real applications could be intractable due to its NP-hardness. Therefore, we propose a solution method technique, based on the solution of an approximated model, whose dimension is remarkably reduced with respect to the: original counterpart. Numerical experiments conducted on the basis of data taken from a real application show that the average deviation of the reduced model solution over the optimum is less than 1.5%. (C) 2003 Elsevier B.V. All rights reserved.
Three types of system performances-the expected system lifetime, a-system lifetime, and system reliability-characterized in the context of credibility are investigated in this paper. Some fuzzy simulations are designe...
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Three types of system performances-the expected system lifetime, a-system lifetime, and system reliability-characterized in the context of credibility are investigated in this paper. Some fuzzy simulations are designed to estimate these system performances. In order to formulate general standby redundancy optimization problems with fuzzy lifetimes, a spectrum of standby redundancy fuzzy programming models are proposed. fuzzy simulation, neural network, and genetic algorithm are also integrated to produce a hybrid intelligent algorithm for solving those models. Finally, some numerical experiments on multi-stage system and network system are provided. (c) 2005 Elsevier Ltd. All rights reserved.
This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approa...
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This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approach, several given levels of tolerable violation for system constraints are permitted. This is realized through a relaxation of the critical constraints using violation variables, such that the model's decision space can be expanded. Thus, solutions from the violation analysis will not necessarily satisfy all of the model's original constraints. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions can be generated through this approach. Considerable information regarding decisions of facility expansion and waste flow allocation within the waste management system were generated. The modeling results help to generate a number of decision alternatives under various system conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability. (C) 2002 Elsevier Science Ltd. All rights reserved.
Li and Yu (fuzzy Sets and Systems 101 (1999) 109) argued that the model of Yang et al. for fuzzy programming (fuzzy Sets and Systems 41 (1991) 39) is correct only for a specific type of piecewise linear membership fun...
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Li and Yu (fuzzy Sets and Systems 101 (1999) 109) argued that the model of Yang et al. for fuzzy programming (fuzzy Sets and Systems 41 (1991) 39) is correct only for a specific type of piecewise linear membership function and proposed their model for other type of membership functions. This study generalizes the model of Yang et al. A numerical example indicates that the model of Li and Yu is inapplicable to a fuzzy programming problem that involves more than one membership function, whereas the proposed model gives the optimal solution. (C) 2002 Elsevier Science B.V. All rights reserved.
＜正＞ The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling ...
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＜正＞ The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy travelling time. In order to compare different paths with fuzzy travelling time, some concepts are proposed: expected shortest path, α-path and the most credible path. Correspondingly, by using the concepts as decision criteria, some fuzzy programming models for TSP are proposed based on credibility theory. The deterministic equivalents of the models are also given. Finally, a simulated annealing method is designed to solve these models, and a numerical example is provided to illustrate its effectiveness.
＜正＞ This paper considers to locate multiple new uncapacitated facilities on a plane bounded by a convex polygon under minisum, maximin and minimax criteria to meet fuzzy demands of customers. Some fuzzy programming...
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＜正＞ This paper considers to locate multiple new uncapacitated facilities on a plane bounded by a convex polygon under minisum, maximin and minimax criteria to meet fuzzy demands of customers. Some fuzzy programming models are initiated for this problem, where Euclidean distances are assumed as the scenario. And some hybrid intelligent algorithms are designed for solving the proposed models.
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