It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This pape...
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It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure. (c) 2004 Published by Elsevier Inc.
This paper deals with multiobjective linear programming problems involving fuzzy random variable coefficients and provides new solution concepts based on M alpha-Pareto optimality and stochastic programming models. Fu...
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ISBN:
(纸本)0780392981
This paper deals with multiobjective linear programming problems involving fuzzy random variable coefficients and provides new solution concepts based on M alpha-Pareto optimality and stochastic programming models. Fuzzy goals are introduced to consider the imprecise of the decision maker's judgment for objective functions. After the formulated problem is transformed into the deterministic one, an interactive algorithm based on the reference point method is constructed to solve the deterministic problem.
We propose an interactive interior point method for finding the best compromise solution to a multiple objective linearprogramming problem. We construct a sequence X-0,X-1,...,X-k,... of smaller and smaller polytopes...
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We propose an interactive interior point method for finding the best compromise solution to a multiple objective linearprogramming problem. We construct a sequence X-0,X-1,...,X-k,... of smaller and smaller polytopes which shrink towards the compromise solution. During the kth iteration, we move from the center of polytope Xk-1 to the center of polytope X-k by performing a local optimization which consists of maximizing a linear function over an ellipsoid. (C) 2001 Elsevier Science B.V. All rights reserved.
In this paper we examine the design and implementation issues relating to the search process for a solution to an interactive multiobjectivelinear optimization problem (MOLP). A solution methodology proposed by Dror ...
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In this paper we examine the design and implementation issues relating to the search process for a solution to an interactive multiobjectivelinear optimization problem (MOLP). A solution methodology proposed by Dror and Gass is employed. The primary objective of the design process is to investigate the advantages of using interactive graphics in the presentation of alternative solutions and to direct the solution search. We find several features useful, including three-dimensional perspective views, graph animation, interactive highlighting, and interactive detail inspection. (C) 2001 Elsevier Science Inc. All rights reserved.
The aim of this paper is to develop a duality theory for linearmultiobjectiveprogramming verifying similar properties as in the scalar case. We use the so-called "strongly proper optima" and we characteriz...
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The aim of this paper is to develop a duality theory for linearmultiobjectiveprogramming verifying similar properties as in the scalar case. We use the so-called "strongly proper optima" and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima. (C) 1999 Elsevier Science Ltd. All rights reserved.
Zimmermann (1978) proposed a fuzzy method for solving multiple objective decision problems whose main difficulty is in specifying the membership functions of the objectives. We have considered two different approaches...
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We present a method useful in solving a special class of large-scale multiobjective integer problems depending on the decomposition algorithm. These problems involve fuzzy parameters on the right-hand side of the inde...
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We present a method useful in solving a special class of large-scale multiobjective integer problems depending on the decomposition algorithm. These problems involve fuzzy parameters on the right-hand side of the independent constraints. The presented solution method is based upon a combination of the decomposition algorithm coupled with the weighting method together with the branch-and-bound method. An illustrative numerical example is given to clarify the theory and the method discussed in this paper. (C) 1999 Elsevier Science B.V. All rights reserved.
This paper proposes a multiobjective linear programming (MLP) model on injection oilfield recovery system. A modified interior-point algorithm to MLP problems has been constructed by using concepts of Kamarkar's i...
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This paper proposes a multiobjective linear programming (MLP) model on injection oilfield recovery system. A modified interior-point algorithm to MLP problems has been constructed by using concepts of Kamarkar's interior point algorithm and the Analytic Hierarchy Process (AHP). This algorithm is shown to likely be more efficient than other MLP's algorithms in the application of decision making on the petroleum industry through the demonstration of a numerical example. The MLP model's optimal solution allows decision makers to optimally design the developing plan of the injection oilfield recovery system. (C) 1998 Elsevier Science Ltd. All rights reserved.
In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order ...
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In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linearprogramming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.
This paper shows how a formal modeling framework, Evolutionary Systems Design (ESD), for evolutionary problem definition and solution, can be used for problem adaptation and restructuring in optimization problems, as ...
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This paper shows how a formal modeling framework, Evolutionary Systems Design (ESD), for evolutionary problem definition and solution, can be used for problem adaptation and restructuring in optimization problems, as developed for multiobjective linear programming (MOLP). Restructuring through a heuristic controls/goals/values referral process and adaptation are discussed for interactive MOLP, and illustrated by a numerical example.
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