A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary...
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A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions and Wolfe and Mond-Weir type duality results are given in terms of the right differentials of the functions. The duality results are stated by using the concepts of generalized semilocally convex functions.
Most of the known methods for finding the efficient set of a multipleobjective linear programming (MOLP) problem are bottom-up search methods. Main difficulties of the known bottom-up search methods are to find all e...
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Most of the known methods for finding the efficient set of a multipleobjective linear programming (MOLP) problem are bottom-up search methods. Main difficulties of the known bottom-up search methods are to find all efficient extreme points adjacent to and to enumerate all efficient faces incident to an efficient degenerate extreme point. Main drawbacks of these methods are that the computational cost is still large and an implementation of them is still difficult. In this paper we propose a new local bottom-up search method for finding all maximal efficient faces for an MOLP problem. Our method is based on the maximal descriptor index sets for efficient edges and extreme rays for the MOLP problem in which the maximal descriptor index sets for edges and extreme rays incident to an efficient degenerate extreme point are easily found on the basis of solving some special linear programming problems. In addition, all efficient extreme points adjacent to and all efficient faces incident to an efficient extreme point can be easily found without using the simplex tables corresponding to bases of this point. Our method can overcome difficulties caused by the degeneracy of faces and is easy to implement. Some comparisons of our method with the known bottom-up search methods are presented. A numerical example is given to illustrate the method.
In this paper we consider solution generation method for multipleobjective linear programming problems. The set of efficient or Pareto optimal solutions for the problems can be regarded as global information in multi...
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In this paper we consider solution generation method for multipleobjective linear programming problems. The set of efficient or Pareto optimal solutions for the problems can be regarded as global information in multipleobjective decision making situation. In the past three decades as solution generation techniques various conventional algorithms based on simplex-like approach with heavy computational burden were developed. Therefore, the development of novel and useful directions in efficient solution generation method have been desired. The purpose of this paper is to develop theoretical results and computational techniques of the efficient solution generation method based on extreme ray generation method that sequentially generates efficient points and rays by adding inequality constraints of the polyhedral feasible region. (C) 2003 Elsevier B.V. All rights reserved.
In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the DPreinvexity type-I functions, we...
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In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the DPreinvexity type-I functions, we also study the optimality solutions for multipleobjective nonlinear programming problems. We also establish and illustrate the duality theorems (weak, strong, and converse) for the Wolf-type and Mond-Weir-type for multipleobjective nonlinear programming problems using these new generalizations of the D-Preinvexity type-I functions.
Although goal programming is one of the most used techniques for modeling and solving multi-objective optimization problems due to modeling elegance and mathematical simplicity. However, the existing goal programming ...
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Although goal programming is one of the most used techniques for modeling and solving multi-objective optimization problems due to modeling elegance and mathematical simplicity. However, the existing goal programming methods have some deficiencies in assigning the weights and then finding the solution per the objectives' priority to tackle the incommensurabilty in heterogeneous objectives. Therefore, this article proposes an efficient scalarization technique to solve the multi-objective optimization problem by introducing a modified goal function. The performance of the proposed method is evaluated using some closeness measure to the ideal solution for several test problems. A real application of the proposed method is illustrated in finding the best locations to establish municipal solid waste (MSW) management intermediate facilities in Nashik city (India). The model selects the three best locations out of the given eight potential locations to establish facilities by considering environmental and economic objectives. Overall, this study provides a theoretical advancement supported by a real-life MSW management application.
An algorithm for enumerating all nondominated vectors of multipleobjective integer linear programs is presented. The method tests different regions where candidates can be found using an auxiliary binary problem for ...
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An algorithm for enumerating all nondominated vectors of multipleobjective integer linear programs is presented. The method tests different regions where candidates can be found using an auxiliary binary problem for tracking the regions already explored. An experimental comparision with our previous efforts shows the method has relatively good time performance.
In this paper, we propose an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of ...
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In this paper, we propose an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of reference directions and weighted sums. Reference directions for the linear functions, and weighted sums for combining the quadratic function with the linear ones are used as parameters to implement the free search of nondominated solutions. The idea leads to the parametric linear complementarity problem formulation. An approach to deal with this type of problems is given as well. The approach is illustrated with a numerical example. (C) 1997 Elsevier Science B.V.
In this paper, we will consider the computation of objective function values when a nondominated frontier is searched in multipleobjective quadratic-linear programming (MOQLP). Reference directions and weighted-sums ...
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In this paper, we will consider the computation of objective function values when a nondominated frontier is searched in multipleobjective quadratic-linear programming (MOQLP). Reference directions and weighted-sums constitute a methodological basis for the search. This idea leads to a parametric linear complementarity model formulation. A critical task of making a search procedure efficient, is to compute the changes in quadratic and linear objective functions efficiently when a search direction is changed or a basis change is performed, Those changes in objective functions can be computed by a so-called direct or indirect method. The direct method is a straightforward one and based on the use of unit changes in basic decision variables. Instead, the indirect method utilizes some other basic variables of the model. We will introduce the indirect method and make theoretical and empirical comparisons between the methods. Based on the comparisons, we point out that the indirect method is clearly much more efficient than the direct one. (C) 1998 Elsevier Science B.V.
In the present paper a complete procedure for solving multipleobjective Integer Linear programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was pr...
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In the present paper a complete procedure for solving multipleobjective Integer Linear programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.
multipleobjective linear fractional programming (MOLFP) is an important field of research. Using some branch and bound techniques, we have developed a new interactive method for MOLFP that drastically reduces the com...
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multipleobjective linear fractional programming (MOLFP) is an important field of research. Using some branch and bound techniques, we have developed a new interactive method for MOLFP that drastically reduces the computational effort needed, while providing guidance for the decision maker in the choice of his/her preferred solutions. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions while constraining the others. Several linear programming problems, organized in a tree structure, are generated as the search evolves. The whole idea is simple and it results in a fast and very intuitive approach to exploring the non-dominated set of solutions in MOLFP, and eventually to finding the preferred solution.
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