In this paper, we introduce mathematical programs with vector optimization constraints. For these problems, we establish two models in both the weak Pareto solution and Pareto solution setting. Some new existence resu...
详细信息
In this paper, we introduce mathematical programs with vector optimization constraints. For these problems, we establish two models in both the weak Pareto solution and Pareto solution setting. Some new existence results are obtained under rather weak conditions. We establish also equivalences between mathematical programs with vector optimization constraints and mathematical programs with vector variational inequality constraints.
We suggest a pair of second-order symmetric dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong and converse duality theorems under F-convex...
详细信息
We suggest a pair of second-order symmetric dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong and converse duality theorems under F-convexity conditions. (c) 2004 Elsevier B.V. All rights reserved.
In this paper, a new approach for a solution of a nonlinear multiobjective programming problem is introduced. An equivalent eta-approximated vector optimization problem is constructed by a modification of the objectiv...
详细信息
In this paper, a new approach for a solution of a nonlinear multiobjective programming problem is introduced. An equivalent eta-approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem. The connection between (weak) efficient points in the original multiobjective programming problem and its equivalent eta-approximated vector optimization problem is proved. In this way, optimality conditions for nonlinear constrained multiobjective programming problems having invex and/or generalized invex objective and constraint functions (with respect to the same functions eta) are obtained. (c) 2005 Elsevier Ltd. All rights reserved.
This study proposes a fuzzy approach for solving the multiobjective and multilevel knapsack problems (KPs). The problem was first formulated as a multilevel programming problem with multiple decision makers (DMs). The...
详细信息
This study proposes a fuzzy approach for solving the multiobjective and multilevel knapsack problems (KPs). The problem was first formulated as a multilevel programming problem with multiple decision makers (DMs). Then the degree of satisfaction of each DM was established and represented by their individual membership functions. The recursive formulation of dynamic programming was used to solve the decisions of the interrelated stages. The overall satisfaction of the decision was obtained through this stage-wise operation on the hierarchical structure. Capacity allocation was developed and a step-by-step solution procedure was illustrated. A detailed comparison between multiobjective and multilevel KPs was also carried out. Finally, the possible use of turnpike theorem in KPs was scrutinized in the fuzzy domain. (c) 2005 Elsevier Ltd. All rights reserved.
In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are c...
详细信息
In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are convex. A sufficient condition for the connectedness of G-proper efficient solution set is established when objective functions are strictly quasiconvex.
This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with Psubset of or equal toR(m) being the underlying ordering cone, called semistrictly (R-m\-int P)-quas...
详细信息
This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with Psubset of or equal toR(m) being the underlying ordering cone, called semistrictly (R-m\-int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit (R-m\-int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.
The transfer capability on a transmission path is limited by constraints on acceptability, voltage security, small-signal stability, and transient stability. For a large interconnected power grid, these constraints ar...
详细信息
The transfer capability on a transmission path is limited by constraints on acceptability, voltage security, small-signal stability, and transient stability. For a large interconnected power grid, these constraints are influenced significantly by the interactions among path flows in different control areas. When a critical transmission path capability is limited by one of these constraints, it may be necessary to coordinate the interarea power transfers so as to improve the transfer capability on the constrained path without compromising on the security criteria. Based on such considerations, this paper presents a novel multiobjective methodology in which global strategies are developed for the improvement and coordination of transmission path transfers. The problem is formulated with respect to various constraints into suitable optimization problems. An efficient nonlinear programming algorithm with sufficient line search step is incorporated for finding optimal solutions while also incorporating security and stability constraints. The MW benefits for the transfer capability from the coordination procedure are explicitly demonstrated after the optimization process. The effectiveness of the methodology is illustrated by case studies on improving the capability of the California-Oregon Intertie (COI) for large-scale WECC western American power system models.
Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing...
详细信息
Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing that the theorems of Ref. 1 are not true. Then, by modifying the assumptions of these theorems, we establish two new sufficient optimality theorems for (weak) Pareto-optimal solutions of (MOP);moreover, we give generalized sufficient optimality theorems for (MOP).
This paper introduces a new method to estimate the weakly efficient set for the multiobjective Linear Fractional programming problem. The main idea is based on the procedure proposed by Tzeng and Hsu (In: G.H. Tzeng, ...
详细信息
This paper introduces a new method to estimate the weakly efficient set for the multiobjective Linear Fractional programming problem. The main idea is based on the procedure proposed by Tzeng and Hsu (In: G.H. Tzeng, H.F. Wang, U.P. Wen, L. Yu (Eds.), Multiple Criteria Decision Making, Springer, New York, 1994, pp. 459-470), called CONNISE. However, as we will explain in this paper, the CONNISE method is not always convergent for problems with more than two objectives. For this reason, we have developed a new method, called "The Controlled Estimation Method", based on the same concept as CONNISE regarding the decision-maker being able to control distances between points from the estimation set he/she wants to find, while ensuring the method is convergent with problems with more than two objectives. Thus, we propose an algorithm able to calculate a discrete estimation of the weakly efficient set that verifies this property of the CONNISE method, but further, improves it thanks to its convergence and the fact that it satisfies the three good properties suggested by Sayin (Math. programming 87(3) (2000) 543): Coverage, Uniformity, and Cardinality. (C) 2003 Elsevier Ltd. All rights reserved.
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.
暂无评论