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...
详细信息
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.
This paper is devoted to the study of a class of multiobjective programming problems involving the support functions of a compact convex set and twice differentiable functions. In order to extend some theoretical resu...
详细信息
This paper is devoted to the study of a class of multiobjective programming problems involving the support functions of a compact convex set and twice differentiable functions. In order to extend some theoretical results of the mathematical programming, here the new classes of generalized invex functions, named second-order B - (p, r) - invex functions, are introduced. Furthermore, the general Mond- Weir type second order dual associated with the multiobjective problem is derived. Based upon the new generalized invexity assumption in the functions involved, several duality results including weak duality, strong duality and strict converse duality are established and proved. This paper will extend notions of convexity and larger the classes of optimization problems.
This paper presents a reference point-based interactive algorithm, which has been specifically designed to deal with stochastic multiobjective programming problems. This algorithm combines the classical information us...
详细信息
This paper presents a reference point-based interactive algorithm, which has been specifically designed to deal with stochastic multiobjective programming problems. This algorithm combines the classical information used in this kind of methods, i.e. values that the decision maker regards as desirable for each objective, with information about the probabilities the decision maker wishes to accept. This novel aspect allows the method to fully take into account the randomness of the final outcome throughout the whole solution process. These two pieces of information have been introduced in an adapted achievement-scalarizing function, which assures each solution obtained to be probability efficient.
We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an effic...
详细信息
We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in oProgress in Optimizationo, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101-116). As special cases of our duality relations, we give some known duality results.
Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. multiobjective programming is an operations research methodology th...
详细信息
Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient Set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.
The conflict between environmental protection of reservoir water quality and the economic development by different uses of land within a watershed is a problem that constantly confronts public officials in regional pl...
详细信息
The conflict between environmental protection of reservoir water quality and the economic development by different uses of land within a watershed is a problem that constantly confronts public officials in regional planning, as experienced in many developing countries. This analysis applied multiobjective linear programming (MOLP) techniques to land resource allocation in order to evaluate the sustainable strategy of land development in a reservoir region. The information incorporated into the optimization objectives include economic benefits characterized by income and employment level, and water quality impacts related to the total discharges of target pollutants. The constraint set thereby consists of the limitations of carrying capacity of various land-use programs and assimilative capacity corresponding to different pollution impacts on water quality. The practical implementation is assessed by a case study of the Tweng-Wen reservoir watershed system in Taiwan. By using the compromise programming technique and the multiobjective simplex method, it shows that increasing the residential area is a feasible option if pollution can be controlled properly in these new communities, but livestock husbandry should not be allowed under any circumstance within the Tweng-Wen reservoir watershed.
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...
详细信息
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 paper, a pair of Wolfe type higher-order nondifferentiable symmetric dual programs over arbitrary cones has been studied and then well-suited duality relations have been established considering K-F convexity a...
详细信息
In this paper, a pair of Wolfe type higher-order nondifferentiable symmetric dual programs over arbitrary cones has been studied and then well-suited duality relations have been established considering K-F convexity assumptions. An example which satisfies the weak duality relation has also been depicted.
In this paper, we introduce a new class of generalized (F, alpha, rho, theta)-d-V-univex functions for a nonsmooth multiobjective programming problem. Sufficient optimality conditions under generalized (F, alpha, rho,...
详细信息
In this paper, we introduce a new class of generalized (F, alpha, rho, theta)-d-V-univex functions for a nonsmooth multiobjective programming problem. Sufficient optimality conditions under generalized (F, alpha, rho, theta)-d-V-univex functions are established for a feasible solution to be an efficient solution. Appropriate duality theorems for a Mond-Weir-type dual are also presented under the aforesaid assumptions. (C) 2010 Elsevier Ltd. All rights reserved.
A pair of Mond-Weir type second-order symmetric dual multiobjective programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under pseudoinvexity/K-F-convexity assumption...
详细信息
A pair of Mond-Weir type second-order symmetric dual multiobjective programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under pseudoinvexity/K-F-convexity assumptions. (C) 2009 Elsevier Ltd. All rights reserved.
暂无评论