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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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An energy planning approach based on mixed 0-1 multiple objective linear programming

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International Transactions in Operational Research 1999年第2期6卷 231-244页

作者： Mavrotas, G. Diakoulaki, D. Papayannakis, L. Laboratory of Industrial and Energy Economics ational Technical University of Athens Department of Chemical Engineering Greece

multiple objective linear programming (MOLP) models have been widely used in the energy sector for taking into account several conflicting objectives pursued in energy planning. However, continuous variables are not suffcient to accurately represent discrete phenomena encountered in many practical decision situations, such as the power generation expansion problem. This paper presents a new approach based on a mixed 0-1 MOLP model and applied to the Greek electricity generation sector for identifying the number and output of each type of power units needed to satisfy the expected electricity demand in the future. The core of the model is a branch and bound algorithm, which has been properly modified for the multi-objective case and is capable of generating the whole set of effcient solutions. The results provided by this method is the extraction of the effcient combinations of the power generation units, and for each combination the effcient solutions determining electricity production from each unit. © 1999 Blackwell Publishing Ltd.

关键词： Integer programming multiple objective linear programming Power generation

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An approach to updating weights in multiple objective linear programming

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 1999年第2期16卷 185-202页

作者： San Pedro, JC Univ Philippines Inst Math Sci & Phys Los Banos Philippines

In this paper, we present a systematic approach to updating weights in multiple objective linear programming. We develop a number of extensions to the simplex theory which leads to the identification of (a) alternative weight vectors for which a current efficient solution remains optimal, and (b) adjacent efficient solutions. We also give an example to illustrate the proposed approach.

关键词： weight-update method multiple objective linear programming

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A comparative study of two key algorithms in multiple objective linear programming

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JOURNAL OF ALGORITHMS & COMPUTATIONAL TECHNOLOGY 2019年第13期13卷 -页

作者： Nyiam, Paschal B. Salhi, Abdellah Univ Essex Dept Math Sci Wivenhoe Pk Colchester CO4 3SQ Essex England

multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.

关键词： multiple objective linear programming parametric simplex algorithm outer-approximation algorithm most preferred nondominated point multiple criteria decision making

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Data Mining Using multiple objective linear programming

Data Mining Using Multiple Objective Linear Programming

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The Second International Conference on Information and Management Sciences

作者： Chen-Kou Yu Nan Jeon Institute of Technology, Yan-shui, Tainan County, Taiwan, China

This paper develops a data mining technique using multiple objective linear programming. This method replaces the applications of discriminant analysis, a tradition method, for data analysis. The multiple objective li... 详细信息

关键词： data mining multiple objective linear programming fuzzy programming

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An Extension Of Scalarization-Based Approach To Fuzzy multiple objective linear programming With Fuzzy Parameters

An Extension Of Scalarization-Based Approach To Fuzzy Multip...

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The Second International Conference on Information and Management Sciences

作者： Fengjie Wu Jie Lu and Guangquan Zhang Faculty of Information University of Technology Sydney PO Box 123 Broadway NSW 2007 Australia

＜正＞ This paper focuses on fuzzy multiple objective linear programming （FMOLP） problems with fuzzy parameters in objective functions. B ased on the results of fuzzy linear programming （FLP） proposed by Zhang et al, this paper firstly proposes related definitions and concepts about FMOLP problems with fuzzy parameters. It then extends scalarization-based approach for converting a FMOLP problem into a crisp programming problem, and uses the extended approach to solve the original FMOLP problem. Finally, an example is presented for demonstrating the proposed approach.

关键词： Optimization Decision support technology multiple objective linear programming Fuzzy multiple objective linear programming.

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AN INTERACTIVE ALGORITHM FOR SOLVING multiple-objective INTEGER linear-programming PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第3期79卷 443-450页

作者： NARULA, SC VASSILEV, V LINKOPING INST TECHNOL S-58183 LINKOPINGSWEDEN BULGARIAN ACAD SCI BU-1113 SOFIABULGARIA

We propose a reference direction based interactive algorithm to solve multiple objective integer linear programming (MOILP) problems. At each iteration of the solution procedure, the algorithm finds (weak) nondominated solutions to the relaxed MOILP problem. Only at certain iterations, if the DM so desires, an additional mixed integer programming problem is solved to find an integer (weak) nondominated solution which is close to the current continuous (weak) nondominated solution to the relaxed MOILP problem. In the proposed algorithm, DM has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.

关键词： multiple CRITERIA multiple objective linear programming REFERENCE POINT

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AN INTERIOR multiple-objective PRIMAL-DUAL linear-programming ALGORITHM USING EFFICIENT ANCHORING POINTS

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1995年第9期46卷 1121-1132页

作者： ARBEL, A TEL AVIV UNIV DEPT IND ENGNIL-69978 TEL AVIVISRAEL

We present an interior multiple objective linear programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.

关键词： INTERIOR-POINT linear programming KARMARKARS ALGORITHM MULTICRITERIA DECISION MAKING multiple objective linear programming

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