检索结果-内蒙古大学图书馆

Global optimization in practice: An application to interactive multiple objective linear programming

JOURNAL OF GLOBAL OPTIMIZATION 1998年第4期12卷 353-372页

作者： Benson, HP Lee, D McClure, P Univ Florida Dept Informat & Decis Sci Gainesville FL 32611 USA Korea Ind Technol Assoc Kangnam Gu Seoul 135703 South Korea Becker Groves Inc Ft Pierce FL 34954 USA

A multiple objective linear programming problem (F') involves the simultaneous maximization of two or more conflicting linear objective functions over a nonempty polyhedron X. Many of the most popular methods for solving this type of problem, including many well-known interactive methods, involve searching the efficient set X-E of the problem. Generally however, X-E is a complicated, nonconvex set. As a result, concepts and methods from global optimization may be useful in searching X-E. In this paper, we will explain in theory, and show via an actual application to citrus rootstock selection in Florida, how the potential usefulness of the well-known interactive method STEM for solving problem (P) in this way, can depend crucially upon how accurately certain global optimization problems involving minimizations over X-E are solved. In particular, we will show both in theory and in practice that the choice of whether to use the popular but unreliable "payoff table" approach or to use one of the lesser known, more accurate global optimization methods to solve these problems can determine whether STEM succeeds or fails as a decision aid. Several lessons and conclusions of transferable value derived from this research are also given.

关键词： multiple objective linear programming optimization over the efficient set interactive methods global optimization citrus rootstock selection

来源：评论

学校读者我要写书评

暂无评论

Maximal descriptor set characterizations of efficient faces in multiple objective linear programming

引用

OPERATIONS RESEARCH LETTERS 2003年第2期31卷 124-128页

作者： Jorge, JM Univ La Laguna Dept Estadist Invest Operat & Computac San Cristobal la Laguna 38271 Tenerife Spain

In this paper we present the concept of maximal descriptor set as a way of identifying faces of a polyhedron in a unique form. This concept is based on the implicit representation of a face through its maximal set of binding inequalities. By making use of this notion it is possible to derive new practical tests to characterize the efficiency of arbitrary faces in a multiple objective linear program, some of which can be seen as extensions of other well-known results on efficiency for general points (not necessarily vertices). (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multiple objective linear programming efficient solution efficient face maximal descriptor set vector maximization

来源：评论

学校读者我要写书评

暂无评论

USING QUALITATIVE DATA IN multiple objective linear-programming

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1990年第1期48卷 81-87页

作者： KORHONEN, P WALLENIUS, J HELSINKI SCH ECON & BUSINESS ADM RUNEBERGINKATU 14-16SF-00100 HELSINKIFINLAND

In this paper we consider the problem of incorporating qualitative data in multiple objective linear programming. We show how the weight assessment technique in the Analytic Hierarchy Process (AHP) can be utilized in multiple objective linear programming, when only qualitative (subjective, judgemental) data is available. Using the AHP, we first quantify the qualitative relationships between the row variables and the decision variables for our model. The row variables may have the status of an objective function or a constraint. Then we apply our visual and dynamic decision support system called VIG for solving the resulting multiple objective linear programming problem. We develop the approach and describe an application to strategic management. [ABSTRACT FROM AUTHOR]

关键词： Analytic Hierarchy Process interactive multiple objective linear programming reference direction visual

来源：评论

学校读者我要写书评

暂无评论

THE RANGE OF THE EFFICIENT FRONTIER IN multiple objective linear-programming

引用

MATHEMATICAL programming 1984年第1期28卷 84-95页

作者： RHODE, R WEBER, R Institute of Operations Research Department of Economics University of Saarland D-6600 Saarbrücken 11 West Germany

Because a rational decision maker should only select an efficient alternative in multiple criterion decision problems, the efficient frontier defined as the set of all efficient alternatives has become a central solution concept in multiple objective linear programming. Normally this set reduces the set of available alternatives of the underlying problem. There are several methods, mainly based on the simplex method, for computing the efficient frontier. This paper presents a quite different approach which uses a nonlinear parametric program, solved by Wolfe's algorithm, to determine the range of the efficient frontier.

关键词： Efficiency multiple objective linear programming multiple objective Quadratic-linear programming Parametric Quadratic programming Range of the Efficient Frontier Wolfe's algorithm

来源：评论

学校读者我要写书评

暂无评论

Solving Bilevel linear Programs Using multiple objective linear programming

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2009年第2期140卷 197-212页

作者： Glackin, J. Ecker, J. G. Kupferschmid, M. US Mil Acad Dept Math Sci West Point NY 10996 USA Rensselaer Polytech Inst Dept Math Sci Troy NY 12180 USA Rensselaer Polytech Inst Acad & Res Comp Troy NY 12180 USA

We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound algorithm when the number of leader variables is small.

关键词： Bilevel linear programming multiple objective linear programming Efficient set Rational reaction set Simplex algorithm pivot

来源：评论

学校读者我要写书评

暂无评论

Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver

引用

OPTIMIZATION 2019年第10期68卷 2039-2054页

作者： Ciripoi, Daniel Loehne, Andreas Weissing, Benjamin Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany

The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for one convex polyhedron are, for example, the polar, the conical hull and the image under affine transformation. The concept of a P-representation of a convex polyhedron is introduced. It is shown that many polyhedral calculus operations can be expressed explicitly in terms of P-representations. We point out that all the relevant computational effort for polyhedral calculus consists in computing projections of convex polyhedra. In order to compute projections we use a recent result saying that multiple objective linear programming (MOLP) is equivalent to the polyhedral projection problem. Based on the MOLP solver bensolve a polyhedral calculus toolbox for Matlab and GNU Octave is developed. Some numerical experiments are discussed.

关键词： Polyhedron polyhedral set polyhedral convex analysis polyhedron computations multiple objective linear programming

来源：评论

学校读者我要写书评

暂无评论

On Optimization Over the Efficient Set of a multiple objective linear programming Problem

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2017年第1期172卷 236-246页

作者： Sun, Erjiang Southern Calif Edison Rosemead CA 91770 USA

In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multiple objective linear program problem. Instead of solving the problem directly, we introduce a new problem of minimizing the objective function subject to some linear constraints with additional binary variables. We show under certain conditions that the two problems are equivalent. When the objective function of the original problem is a linear or convex function, the new problem is a linear or convex programming problem, respectively, with some binary variables. These problems can be solved as mixed-integer programs with current state-of-art mixed-integer programming solvers.

关键词： multiple objective linear programming Efficient set Weakly efficient set Global optimization Mixed-integer programming

来源：评论

学校读者我要写书评

暂无评论

LEXICOGRAPHIC OPTIMALITY IN THE multiple objective linear-programming - THE NUCLEOLAR SOLUTION

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1992年第3期57卷 355-359页

作者： MARCHI, E OVIEDO, JA UNIV NACL SAN LUIS CONSEJO NACL INVEST CIENTIFICAS & TECNICASINST MATEMAT APLICADA SAN LUISRA-5700 SAN LUISARGENTINA

In this paper we study the problem of multiple objective linear programming (MOLP). We introduce a new solution concept which is related to that of the nucleolus of n-person cooperative game theory. We prove that a general MOLP problem always has a solution in the new sense. The points in the nucleolus are efficient in the classic way. We prove existence and at the same time we introduce a constructing algorithm for computing it.

关键词： multiple objective linear programming LEXICOGRAPHIC ORDER NUCLEOLAR SOLUTION ALGORITHM

来源：评论

学校读者我要写书评

暂无评论

USING multiple objective linear-programming TO EVALUATE MULTI-PARTICIPANT AGROFORESTRY SYSTEMS

引用

AGROFORESTRY SYSTEMS 1988年第2期7卷 185-195页

作者： WOJTKOWSKI, PA BRISTER, GH CUBBAGE, FW School of Forest Resources University of Georgia Athens USA

multiple objective linear programming is used to evaluate a simulated two-participant maize/cassava/leucaena/teak agroforestry system. Examples using two different price ratios are presented along with possible methods to optimize the system with regard to the interests of the two profit seeking participants. A third example examines possible solutions to a system involving a profit seeking forester and a non-monetary subsistence farmer.

关键词： agroforestry economics linear programming multiple objective linear programming

来源：评论

学校读者我要写书评

暂无评论

Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming

引用

OPERATIONAL RESEARCH 2022年第1期22卷 165-198页

作者： Ghazi, Amineh Lotfi, Farhad Hosseinzadeh Sanei, Masoud Islamic Azad Univ Dept Math Cent Tehran Branch Tehran Iran Islamic Azad Univ Dept Math Sci & Res Branch Tehran Iran

Data envelopment analysis (DEA) models use the frontier of the production possibility set (PPS) to evaluate decision making units (DMUs). However, the explicit-form equations of the frontier cannot be obtained using the traditional DEA models. To fill this gap, the current paper proposes an algorithm to generate all strong-efficient DMUs and the explicit-form equations of the strong-efficient frontier and the strong defining hyperplanes for the PPS with the variable returns to scale (VRS) technology. The algorithm is based on a multiple objective linear programming (MOLP) problem in the DEA methodology, which is solved through the multicriteria simplex method. Also, Isermann's test is employed to specify strong-efficient nonbasic variables in each strong-efficient multicriteria simplex table. Before presenting the algorithm, a theoretical framework is introduced to characterize the relationships between the feasible region in the decision space of the MOLP problem and the PPS with the VRS technology. It is shown that the algorithm which has four phases is finitely convergent and has less computational complexity than other algorithms in the related literature. Finally, two examples are used to illustrate the algorithm.

关键词： Data envelopment analysis multiple objective linear programming Efficient frontier Defining hyperplane

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：