In this paper, optimality for multiobjective programming problems having invex objective and constraint functions (with respect to the same function eta) is considered. An equivalent vector programming problem is cons...
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In this paper, optimality for multiobjective programming problems having invex objective and constraint functions (with respect to the same function eta) is considered. An equivalent vector programming problem is constructed by a modification of the objective function. Furthermore, an eta-Lagrange function is introduced for a constructed multiobjective problem and modified saddle point results are presented.
Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order (F, rho)-conve...
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Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order (F, rho)-convexity assumptions. These results generalize the duality results recently given by Aghezzaf and Hachimi involving generalized first order (F, rho)-convexity conditions. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, the so-called eta-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function eta. In th...
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In this paper, the so-called eta-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function eta. In this method, an equivalent eta-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated eta-approximated vector optimization problem. Finally, the description of the eta-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.
This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the gre...
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This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the greater area of Thessaloniki and was part of a project aiming at the compliance with air quality standards in five major cities in Greece. The methodological approach comprises two stages: in the first stage, the availability of several measures contributing to a certain extent to reducing atmospheric pollution indicates a combinatorial problem and favors the use of Integer programming. More specifically, Multiple Objective Integer programming is used in order to generate alternative efficient combinations of the available policy measures on the basis of two conflicting objectives: public expenditure minimization and social acceptance maximization. In the second stage, these combinations of control measures (i.e., the control strategies) are then comparatively evaluated with respect to a wider set of criteria, using tools from Multiple Criteria Decision Analysis, namely, the well-known PROMETHEE method. The whole procedure is based on the active involvement of local and central authorities in order to incorporate their concerns and preferences, as well as to secure the adoption and implementation of the resulting solution.
It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce...
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It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce a set of sufficient conditions reversing that implication. Thus, we study some properties of the isoperimetric problems and their applications to the analysis of economic models.
Integrated watershed management is required to ensure the reasonable use of resources and reconcile interactions among natural and human systems. In the present study, an interval fuzzy multiobjective programming (IFM...
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Integrated watershed management is required to ensure the reasonable use of resources and reconcile interactions among natural and human systems. In the present study, an interval fuzzy multiobjective programming (IFMOP) method was used to solve an integrated watershed management problem. Based on system analysis, an IFMOP model suitable for a lake watershed system {IFMOPLWS} was developed and applied to the Lake Qionghai watershed in China. Scenario analysis and an interactive approach were used in the solution process. In this manner, various system components were incorporated into one framework for holistic consideration and optimization. Integrality and uncertainty, as well as the multiobjective and dynamic characteristics of the watershed system, were well addressed. Using two scenarios, two planning schemes were generated. Agriculture, tourism, macroeconomics, cropland use, water supply, forest coverage, soil erosion, and water pollution were fully interpreted and compared to identify a preferable planning alternative for local agencies. This study showed that the IFMOPLWS is a powerful tool for integrated watershed management planning and can provide a solid base for sustainable watershed management.
In this paper, we show with a counterexample, that the method proposed by Sedeno-Noda and Gonzalez-Martin for the biobjective integer minimum flow problem is not able to find all efficient integer points in objective ...
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In this paper, we show with a counterexample, that the method proposed by Sedeno-Noda and Gonzalez-Martin for the biobjective integer minimum flow problem is not able to find all efficient integer points in objective space. (c) 2004 Elsevier Ltd. All rights reserved.
The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized in...
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The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized invexity assumptions. A close relationship between these problems and multiobjective fractional symmetric dual problems is also presented. (C) 2005 Elsevier Inc. All rights reserved.
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.
For a linear-programming problem with q ( greater than or equal to 2) objective functions (that is, a multiobjective linear-programming problem), we propose a method for ranking the full set or a subset of efficient e...
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For a linear-programming problem with q ( greater than or equal to 2) objective functions (that is, a multiobjective linear-programming problem), we propose a method for ranking the full set or a subset of efficient extreme-point solutions. The idea is to enclose the given efficient solutions, as represented by q-dimensional points in objective space, within an annulus of minimum width, where the width is determined by a hypersphere that minimizes the maximum deviation of the points from the surface of the hypersphere. We argue that the hypersphere represents a surface of compromise and that the point closest to its surface should be considered as the "best" compromise efficient solution. Also, given a ranked (sub)set of efficient solutions, a procedure is given that associates to each efficient solution a set of q positive weights that causes the efficient solution to be optimal with respect to the given set of efficient solutions. (C) 2002 Elsevier Science B.V. All rights reserved.
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