In this present article we have given some multiobjective programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used mos...
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In this present article we have given some multiobjective programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used most general type of invexity assumptions involved with the functions which are related to the programming problems. It is to be pointed out that the objective functions in such programs contain terms like support functions which in turn are able to give results on particular classes of programs involving quadratic terms. Our results in particular give as special cases some earlier results on symmetric duals given in the current literature. (c) 2004 Published by Elsevier B.V.
The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed ...
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The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.
The ideal Power System Operation is achieved when various objectives like cost of generation, system transmission losses, environmental pollution etc. are simultaneously attained with minimum values. These cannot be h...
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ISBN:
(纸本)9810557027
The ideal Power System Operation is achieved when various objectives like cost of generation, system transmission losses, environmental pollution etc. are simultaneously attained with minimum values. These cannot be handled by single objective techniques as the above three objectives may be conflicting in nature in certain domain. Therefore, multiobjective programming techniques have to be employed as these are capable of minimizing more than one objective simultaneously. In this paper, three objectives of multiobjective Optimal Power Flow (MOPF) problem -cost of generation, system transmission losses, environmental pollution are considered and MOPF problem is attempted sequentially using sequential Goal programming (SGP). Six strategies have been developed for IEEE 5, 14 and 30 bus systems. The optimal stategy has been identified by the Power Systems Operator using Regret Analysis.
Real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criter...
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Real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory. Here we propose a method for solving these kinds of models through a fuzzy compromise programming approach. To formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced. This concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their a-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis. (C) 2004 Elsevier B.V. All rights reserved.
In this paper, a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable. By considering the concept of Pareto optimal s...
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In this paper, a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable. By considering the concept of Pareto optimal solution and substituting d-invexity for convexity, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions and duality in the sense of Mond-Weir and Wolfe for nondifferentiable multiobjective programming are given. (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper, first and second order sufficient conditions are established for strict local Pareto minima of orders 1 and 2 to multiobjective optimization problems with an arbitrary feasible set and a twice different...
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In this paper, first and second order sufficient conditions are established for strict local Pareto minima of orders 1 and 2 to multiobjective optimization problems with an arbitrary feasible set and a twice differentiable objective function are provided. For this aim, the concept of support function to a multiobjective problem is introduced, so that the scalar case in particular is contained. The obtained results generalize the classical ones of this case. Furthermore, particularizing to a feasible set defined by equality and inequality constraints, first and second order optimality conditions in primal form as well as dual form (by means of a Lagrange multiplier rule) are obtained.
This paper is concerned with a problem where K (n x n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, a...
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This paper is concerned with a problem where K (n x n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, as measured by an appropriate index, for each of the K matrices. A multiobjective programming approach for this problem, which seeks to optimize a weighted function of the K indices, is proposed, and illustrative examples are provided using a set of proximity matrices from the psychological literature. These examples show that, by solving the multiobjective programming model under different weighting schemes, the quantitative analyst can uncover information about the relationships among the matrices and often identify one or more permutations that provide good to excellent index values for all matrices. (C) 2002 Elsevier Science (USA).
In this note we present a new multiplier rule for a constrained multiobjective programming problem with continuous data by using the concept of unbounded approximate Jacobians recently developed by Jeyakumar and Luc [...
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In this note we present a new multiplier rule for a constrained multiobjective programming problem with continuous data by using the concept of unbounded approximate Jacobians recently developed by Jeyakumar and Luc [SIAM J. Control Optim., 36 ( 1998), pp. 1815 1832].
In the restructured electricity industry, the engineering aspects of planning need to be reformulated even though the goal to attain remains substantially the same, requiring various objectives to be simultaneously ac...
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In the restructured electricity industry, the engineering aspects of planning need to be reformulated even though the goal to attain remains substantially the same, requiring various objectives to be simultaneously accomplished to achieve the optimality of the power system development and operation. In many cases, these objectives contradict each other and cannot be handled by conventional single optimization techniques. In this paper, a multiobjective formulation for the siting and sizing of DG resources into existing distribution networks is proposed. The methodology adopted permits the planner to decide the best compromise between cost of network upgrading, cost of power losses, cost of energy not supplied, and cost of energy required by the served customers. The implemented technique is based on a genetic algorithm and an E-constrained method that allows obtaining a set of noninferior solutions. Application examples are presented to demonstrate the effectiveness of the proposed procedure.
This paper examines the tradeoffs between different uses of forests in three communes in the mountain region in northern Sweden. The most important uses of the forests include timber production, preservation of biodiv...
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This paper examines the tradeoffs between different uses of forests in three communes in the mountain region in northern Sweden. The most important uses of the forests include timber production, preservation of biodiversity, reindeer grazing and recreation. Management outcomes with respect to the different uses are measured in terms of the net present value (NPV) of timber production profits, the sum of deadwood volume over time, the minimum periodic lichen production, and a minimum periodic recreation index (RI). The analysis shows that the forests can be managed to achieve dramatically different mixes of NPV. deadwood volume, and lichen production, whereas the RI varies only within a narrow range. To maximize the NPV, lichen production would reduce by 40% from its maximum level, and the volume of deadwood would be close to 0 in period 2 and thereafter. Maximization of deadwood volume would lead to the maximum lichen production, while the NPV would fall below 0. Maximization of lichen production reduces the NPV by at least 20%, and could reduce the amount of deadwood by up to 75%. When lichen production is restricted to its maximum, there is a wide range of possible choices with respect to the mix of the NPV and deadwood volume. The marginal cost of increasing the deadwood volume ranges from 1.12 to 20 SEK/m(3). The choice between lichen production and deadwood volume is most flexible when the NPV is fixed at approximately 93% of its maximum. (C) 2003 Elsevier B.V. All rights reserved.
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