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

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

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USING QUALITATIVE DATA IN multiple objective linear-programming

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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.

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

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

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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

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Solving Bilevel linear Programs Using multiple objective linear programming

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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

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

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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

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

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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

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

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

作者： WOJTKOWSKI, PA BRISTER, GH CUBBAGE, FW 1. School of Forest Resources University of Georgia 30602 Athens GA 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： multiple objective linear programming linear programming agroforestry economics

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

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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

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An α-fuzzy goal approximate algorithm for solving fuzzy multiple objective linear programming problems

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SOFT COMPUTING 2007年第3期11卷 259-267页

作者： Lu, Jie Ruan, Da Wu, Fengjie Zhang, Guangquan Univ Technol Sydney Fac Informat Technol Broadway NSW 2007 Australia CEN SCK Belgian Nucl Res Ctr B-2400 Mol Belgium

multiple conflicting objectives in many decision making problems can be well described by multiple objective linear programming (MOLP) models. This paper deals with the vague and imprecise information in a multiple objective problem by fuzzy numbers to represent parameters of an MOLP model. This so-called fuzzy MOLP (or FMOLP) model will reflect some uncertainty in the problem solution process since most decision makers often have imprecise goals for their decision objectives. This study proposes an approximate algorithm based on a fuzzy goal optimization under the satisfactory degree alpha to handle both fuzzy and imprecise issues. The concept of a general fuzzy number is used in the proposed algorithm for an FMOLP problem with fuzzy parameters. As a result, this algorithm will allow decision makers to provide fuzzy goals in any form of membership functions.

关键词： optimization multiple objective linear programming fuzzy multiple objective linear programming approximate algorithm

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A multiple objective linear programming approach to power generation planning with demand-side management (DSM)

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International Transactions in Operational Research 1996年第3-4期3.0卷 305-317页

作者： Martins, A.G. Coelho, D. Antunes, H. Clímaco, J. University of Coimbra Portugal and INESC Portugal Coimbra Polytechnic Institute Portugal and INESC Portugal

The optimization of an economic indicator has traditionally been the sole objective function of mathematical programming models for power generation expansion planning. Recently, however, other evaluation aspects, such as environmental concerns, were also given an explicit role as objective functions in mathematical models. Models become thus more realistic so that decision makers are able to grasp the inherent conflicts and trade-offs among the distinct objectives in selecting a best compromise plan. A significant change in the planning processes has also occurred concerning new planning methodologies integrating demand-side management (DSM) techniques, in an attempt to change the levels and forms of electricity use by the consumers. This paper presents a multiple objective linear programming model for power generation expansion planning incorporating DSM. The objective functions are the total expansion cost, the environmental impact associated with the installed power capacity and the environmental impact associated with the energy output. DSM is included by modelling it as a new generating group along with the generating alternatives from the supply side. Five categories of constraints are considered related to the reliability of the supply system, the availability of the generating units, the capacity of the DSM-equivalent generating group, the total capacity installed throughout the planning period, the pollutant emissions. Some results are presented derived by using an interactive method, aimed at assisting decision makers in a progressive and selective search of good compromise solutions. © 1996 Blackwell Publishing Ltd.

关键词： Decision support systems Demand-side management Integrated resource planning Mathematical modelling multiple objective linear programming Power generation planning

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