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A weight space-based approach to fuzzy multiple-objective linear programming

DECISION SUPPORT SYSTEMS 2003年第4期34卷 427-443页

作者： Borges, AR Antunes, CH INESC P-3000033 Coimbra Portugal ISEC Coimbra Polytech Inst P-3030601 Coimbra Portugal Univ Coimbra Dept Elect Engn P-3030030 Coimbra Portugal

In this paper, the effects of uncertainty on multiple-objective linear programming models are studied using the concepts of fuzzy set theory. The proposed interactive decision support system is based on the interactive exploration of the weight space. The comparative analysis of indifference regions on the various weight spaces (which vary according to intervals of values of the satisfaction degree of objective functions and constraints) enables to study the stability and evolution of the basis that correspond to the calculated efficient solutions with changes of some model parameters. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multiple-objective linear programming fuzzy sets interactive methods weight space efficient solutions decision support systems

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Using lexicographic parametric programming for searching a non-dominated set in multiple-objective linear programming

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Journal of Multi-Criteria Decision Analysis 1996年第4期5卷 291-300页

作者： Korhonen, Pekka Halme, Merja Helsinki School of Economics and Business Administration Helsinki SF-00100 Runeberginkatu 14-16 Finland

In this paper we propose an approach which makes it possible to search non-dominated and only non-dominated solutions in multiple-objective linear programming. The approach is based on the use of a reference direction and lexicographic parametric programming. The requisite theory is developed in the paper. The use of the approach is illustrated with a numerical example. © 1996 John Wiley & Sons, Ltd.

关键词： Efficiency Lexicographic parametric programming multiple-objective linear programming Non-dominated criterion values Reference directions

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Asymptotic sign-solvability, multiple objective linear programming, and the nonsubstitution theorem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2006年第3期64卷 541-555页

作者： Cayton, L. Herring, R. Holder, A. Holzer, J. Nightingale, C. Stohs, T. Trinity Univ Math San Antonio TX USA Univ Calif San Diego La Jolla CA 92093 USA Oberlin Coll Oberlin OH 44074 USA Univ Wisconsin Madison WI 53706 USA Mills Coll Oakland CA 94613 USA Univ Nebraska Lincoln NE USA

In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to address a dynamic version of the nonsubstitution theorem.

关键词： multiple-objective linear programming asymptotic programming sign-solvability nonsubstitution theorem computational economics

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Using objective values to start multiple objective linear programming algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第3期128卷 587-596页

作者： Arbel, A Korhonen, P Helsinki Sch Econ Helsinki 00100 Finland Tel Aviv Univ Dept Ind Engn IL-69978 Tel Aviv Israel

We introduce in this paper a new starting mechanism for multiple-objective linear programming (MOLP) algorithms. This makes it possible to start an algorithm from any solution in object:ive space. The original problem is first augmented in such a way that a given starting solution is feasible. The augmentation is explicitly or implicitly controlled by one parameter during the search process, which verifies the feasibility (efficiency) of the final solution. This starting mechanism can be applied either to traditional algorithms, which search the exterior of the constraint polytope, or to algorithms moving through the interior of the constraints. We provide recommendations on the suitability of an algorithm for the various locations of a starting point in objective space. Numerical considerations illustrate these ideas. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： multiple-objective linear programming interactive starting solution aspiration levels scalarizing functions reference direction interior-point algorithms

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A λ-Cut and Goal-programming-Based Algorithm for Fuzzy-linear multiple-objective Bilevel Optimization

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2010年第1期18卷 1-13页

作者： Gao, Ya Zhang, Guangquan Ma, Jun Lu, Jie Univ Technol Sydney Fac Engn & Informat Technol Broadway NSW 2007 Australia

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a lambda-cut and goal-programming- based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using.-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a.-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a.-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm.

关键词： Bilevel programming decision making fuzzy sets goal programming multiple-objective linear programming optimization

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Inverse DEA under inter-temporal dependence using multiple-objective programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期240卷 447-456页

作者： Jahanshahloo, G. R. Soleimani-damaneh, M. Ghobadi, S. Islamic Azad Univ Sci & Res Branch Dept Math Tehran Iran Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran Aalto Univ Sch Business Dept Informat & Serv Econ FI-00076 Helsinki Finland

This paper deals with the inverse Data Envelopment Analysis (DEA) under inter-temporal dependence assumption. Both problems, input-estimation and output-estimation, are investigated. Necessary and sufficient conditions for input/output estimation are established utilizing Pareto and weak Pareto solutions of linear multiple-objective programming problems. Furthermore, in this paper we introduce a new optimality notion for multiple-objective programming problems, periodic weak Pareto optimality. These solutions are used in inverse DEA, and it is shown that these can be characterized by a simple modification in weighted sum scalarization tool. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis Inverse DEA Inter-temporal dependence multiple-objective linear programming Efficiency

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Outcome space partition of the weight set in multiobjective linear programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2000年第1期105卷 17-36页

作者： Benson, HP Sun, E Univ Florida Warrington Coll Business Adm Gainesville FL 32611 USA

Approaches for generating the set of efficient extreme points of the decision set of a multiple-objective linear program (P) that are based upon decompositions of the weight set W-0 suffer from one of two special drawbacks. Either the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for problem (P) can be decomposed into a partition based upon the outcome set Y of the problem, where the elements of the partition are in one-to-one correspondence with the efficient extreme points of Y. As a result, the drawbacks of the decompositions of W-0 based upon the decision set of problem (P) disappear. The article explains also how this new partition offers the potential to construct algorithms for solving large-scale applications of problem (P) in the outcome space, rather than in the decision space.

关键词： multiple-objective linear programming vector maximization efficient points weight set

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Using aspiration levels in an interior primal-dual multiobjective linear programming algorithm

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Journal of Multi-Criteria Decision Analysis 1996年第1期5卷 61-71页

作者： Arbel, Ami Korhonen, Pekka Industrial Engineering Department Tel-Aviv University Tel-Aviv 69978 Israel Helsinki School of Economics and Business Administration Helsinki 0100 Runeberginkatu 14-16 Finland

We introduce in this paper a new multiple-objective linear programming (MOLP) algorithm. The algorithm is based on the single-objective path-following primal-dual linear programming algorithm and combines it with aspiration levels and the use of achievement scalarizing functions. The resulting algorithm falls in the class of interactive MOLP algorithms, as it requires interaction with the decision maker (DM) during the iterative process to obtain statements of aspirations for levels of objectives of the MOLP problem. The interior point algorithm is then used to trace a path of interates from a current (interior) solution and approach as closely as desired a non-dominated solution corresponding to the optimum of the achievement scalarizing function. The timing of the interaction with the DM is dependent on the progress of the interior algorithm. It can take place every few, pre-specified, iterations or after the duality gap achieved for the stated aspirations has fallen below a certain threshold. It is expected that an interior algorithm will speed up the overall process of searching and finding the most preferred MOLP solution-especially in large-scale problems-by avoiding the need for numerous pivot operations and their corresponding interactive sessions inherent in simplex-based algorithms. © 1996 John Wiley & Sons, Ltd.

关键词： Aspiration levels Interior point algorithms multiple-objective linear programming Path-following primal-dual algorithm Scalarizing functions

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Resource allocation based on efficiency analysis

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MANAGEMENT SCIENCE 2004年第8期50卷 1134-1144页

作者： Korhonen, P Syrjänen, M Helsinki Sch Econ Helsinki 00101 Finland

The purpose of this paper is to develop an approach to a resource-allocation problem that typically appears in organizations with a centralized decision-making environment, for example, supermarket chains, banks, and universities. The central unit is assumed to be interested in maximizing the total amount of outputs produced by the individual units by allocating available resources to them. We will develop an interactive formal approach based on data envelopment analysis (DEA) and multiple-objective linear programming (MOLP) to find the most preferred allocation plan. The units are assumed to be able to modify their production in the current production possibility set within certain assumptions. Various assumptions are considered concerning returns to scale and the ability of each unit to modify its production plan. Numerical examples are used to illustrate the approach.

关键词： resource allocation data envelopment analysis frontier analysis multiple-objective linear programming

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OPTIMIZING A linear FUNCTION OVER AN EFFICIENT SET

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第3期83卷 541-563页

作者： ECKER, JG SONG, JH 1. Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York

The problem (P) of optimizing a linear function d(T)x over the efficient set for a multiple-objective linear program (M) is difficult because the efficient set is typically nonconvex. Given the objective function direction d and the set of domination directions D, if d(T) pi greater than or equal to 0 for all nonzero pi epsilon D), then a technique for finding an optimal solution of (P) is presented in Section 2. Otherwise, given a current efficient point ($) over cap chi, if there is no adjacent efficient edge yielding an increase in d(T)x, then a cutting plane d(T)x = dT chi is used to obtain a multiple-objective linear program (($) over bar M) with a reduced feasible set and an efficient set ($) over bar E To find a better efficient point, we solve the problem (I-i) of maximizing c(i)(T) chi, over the reduced feasible set in (($) over bar M) sequentially for i. If there is a x(i) epsilon ($) over bar E that is an optimal solution of (I-i) for some i and d(T) chi(i) > dT ($) over cap chi, then we can choose chi(i) as a current efficient point. Pivoting on the reduced feasible set allows us to find a better efficient point or to show that the current efficient point ($) over cap chi is optimal for (P). Two algorithms for solving (P) in a finite sequence of pivots are presented along with a numerical example.

关键词： multiple-objective linear programming EFFICIENT SETS DOMINATION CONES NONCONVEX OPTIMIZATION

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