In this paper we propose an evolutionary algorithm to estimate the minimum (nadir) objective values over the efficient set in multiple objective linearprogramming problems (MOLP). Nadir values provide valuable inform...
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ISBN:
(纸本)9783642010194
In this paper we propose an evolutionary algorithm to estimate the minimum (nadir) objective values over the efficient set in multiple objective linearprogramming problems (MOLP). Nadir values provide valuable information for characterizing the ranges of the objective function values over the efficient set. However, they are very hard to compute in the general case. The proposed algorithm uses a population of weight vectors with particular characteristics, which are then used as parameters in the optimization of weighted-sums of the objective functions. The population evolves through a process of selection, recombination and mutation. The algorithm has been tested on a number of random MOLP problems for which the nadir point is known. A result comparison with an exact method is shown and discussed.
This paper treats a multiobjective linear programming problem in which the coefficients contained in the objective function of the problem are fuzzy random variables. First, in order to take into account ambiguities o...
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This paper treats a multiobjective linear programming problem in which the coefficients contained in the objective function of the problem are fuzzy random variables. First, in order to take into account ambiguities of judgment by a human decision maker, fuzzy objectives are introduced. Subsequently, we consider a problem of maximizing the possibility and necessity of the objective function value to satisfy the fuzzy objectives. Since these degrees vary stochastically, a formulation is based on the fractile optimization. model in a stochastic programming method. A process is presented for equivalent transformation to a deterministic multiobjective nonlinear fractional programming method. For the transformed multiobjectiveprogramming problem, an interactive fuzzy satisficing method that derives a satisfactory solution of the decision maker through interactions with the decision maker is proposed. It is shown that the global optimum solution of problems solved iteratively by an interactive process can be derived by means of an extended Dinkelbach-type algorithm. (C) 2005 Wiley Periodicals, Inc.
In this paper, we propose a modification of Benson's algorithm for solving multiobjectivelinear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson's ori...
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In this paper, we propose a modification of Benson's algorithm for solving multiobjectivelinear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson's original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of epsilon-nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjectivelinear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method.
The geometric duality theory of Heyde and Lohne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson's outer approximation method (B...
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The geometric duality theory of Heyde and Lohne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson's outer approximation method (Benson 1998a,b) while the dual problem can be solved by a dual variant of Benson's algorithm (Ehrgott et al. 2007). Duality theory then assures that it is possible to find the (weakly) nondominated set of the primal MOLP by solving its dual. In this paper, we propose an algorithm to solve the dual MOLP approximately but within specified tolerance. This approximate solution set can be used to calculate an approximation of the weakly nondominated set of the primal. We show that this set is a weakly E-nondominated set of the original primal MOLP and provide numerical evidence that this approach can be faster than solving the primal MOLP approximately.
This paper presents a novel method for solving the multi-objective linearprogramming problems with mixed fuzzy-stochastic resources. A fuzzifying technique is first proposed to treat the stochastic resources constrai...
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ISBN:
(纸本)0780387481
This paper presents a novel method for solving the multi-objective linearprogramming problems with mixed fuzzy-stochastic resources. A fuzzifying technique is first proposed to treat the stochastic resources constraints as fuzzified chance constraints, as a result of this, the stochastic constraints are treated in a fuzzy environment. Then, based on the max-min operator, an improve approach is presented to solve all the fuzzy-efficient solutions for the multiobjective fuzzy-stochastic linearprogramming problems. The proposed method pursues not only the highest membership degree in the objective but also a better utilization of each constrained resource. Finally, a numerical example is given to illustrate the method.
As an approach to the optimization of systems containing fuzziness and uncertainty, the probabilistic programming method including uncertainty based on probability theory and the fuzzy mathematical programming method ...
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As an approach to the optimization of systems containing fuzziness and uncertainty, the probabilistic programming method including uncertainty based on probability theory and the fuzzy mathematical programming method representing fuzziness in terms of fuzzy theory are typical ones that have been developed in various forms. In the present research, we target multiobjective linear programming problems in which the coefficients included in the program are random variables. We develop a formulation based on the probabilistic maximization model in which the probability that several objective functions are below certain values is maximized under the stochastic constraint condition that the constraints need not be satisfied all the time but only above a certain probability. For the multiobjective probability maximization model, the fuzzy target of the decision maker is introduced. Also, an interactive algorithm based on the reference point method that derives a solution satisfactory to the decision maker by interaction with the decision maker is applied. The new decision making process is a combination of the probabilistic programming method and the fuzzy programming method. (C) 2003 Wiley Periodicals, Inc.
This article describes LUSE, a system for exploration of rural land use allocations (total area devoted to each kind of use) by multiobjective linear programming methods. The objectives pursued are maximization of gro...
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This article describes LUSE, a system for exploration of rural land use allocations (total area devoted to each kind of use) by multiobjective linear programming methods. The objectives pursued are maximization of gross margin, employment in agriculture, land use naturalness and traditional rural landscape, and minimization of production costs and use of agrochemicals. The constraints oil the areas devoted to the land uses considered in addition to those imposed by their joint and individual availabilities, are that they must reach levels considered to satisfy existing demand for those uses or their products, and that the areas devoted to maize and fodder must be sufficient for maintenance of dairy farm production. The program generates comprehensive samples of the Pareto-optimal set, and also allows interactive convergence on a solution that is satisfactory to the decision-maker or interactive exploration of the Paretooptimal set. The system is currently parameterized for use in an area of Galicia (N.W. Spain), but is easily adaptable to other geographic locations. (C) 2006 Elsevier Ltd. All rights reserved.
In order to extend worldwide the processing business of the petrochemical plant, its potential business partners can themselves concurrently simulate production plans with high quality technical and economic features....
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ISBN:
(纸本)9789608457720
In order to extend worldwide the processing business of the petrochemical plant, its potential business partners can themselves concurrently simulate production plans with high quality technical and economic features. In the simulation process, a large number of divergent goals are under attention. Therefore, the plant computer will use the multi-objective linearprogramming as a tool for negotiations. The dialog between a partner and the plant computer consists in two steps, namely processing demand and plant response, performed repeatedly until the business makes sense or it shows unacceptable. In the first case, can be signed the processing contract.
This paper describes a visual cryptography method for the elimination of pixel expansion and the improvement of contrast. The proposed method uses the probability concept to construct a multiobjectivelinear programmi...
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This paper describes a visual cryptography method for the elimination of pixel expansion and the improvement of contrast. The proposed method uses the probability concept to construct a multiobjective linear programming model for general access structures. Then, the solution space of the model is explored by goal programming. The advantages of the proposed method are fourfold. First, it can avoid expanding the shadow images. Second, it can reach better contrast. Third, it can deal with general access structures and get the desired contrast levels. Fourth, it can be easily extended to deal with the problems of multiple secret images. Experiments on several access structures show that the proposed method is effective against pixel expansion and is capable of contrast improvement. (c) 2006 Society of Photo-Optical Instrumentation Engineers.
The vendor selection problem (VSP) is a critical element of the numerous managerial decisions in the consideration of both outsourcing and integrated supply chain management. Many papers in the literature have dealt w...
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The vendor selection problem (VSP) is a critical element of the numerous managerial decisions in the consideration of both outsourcing and integrated supply chain management. Many papers in the literature have dealt with VSPs from a multicriteria perspective, but few have looked into the implications of such decisions in a multiechelon supply chain with the explicit consideration of multiple time-phased demands. A new integrated supply chain model is proposed for a multiechelon supply chain. This model takes into account the usual cost objective and other important criteria in a multiechelon supply chain ranging from the most upstream suppliers' quality to end customers' satisfaction level through a large-scale multiobjectivelinear programme (MOLP). Furthermore, various Pareto optimal solutions can be graphically presented to facilitate decision making and negotiations with existing and potential suppliers.
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