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Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem

FUZZY OPTIMIZATION AND DECISION MAKING 2016年第3期15卷 237-253页

作者： Rivaz, S. Yaghoobi, M. A. Hladik, M. Univ Yasuj Dept Math Yasuj Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Appl Math Kerman Iran Charles Univ Prague Fac Math & Phys Dept Appl Math Malostranske Nam 25 Prague 11800 Czech Republic

The current research concerns multiobjective linear programming problems with interval objective functions coefficients. It is known that the most credible solutions to these problems are necessarily efficient ones. To solve the problems, this paper attempts to propose a new model with interesting properties by considering the minimax regret criterion. The most important property of the new model is attaining a necessarily efficient solution as an optimal one whenever the set of necessarily efficient solutions is nonempty. In order to obtain an optimal solution of the new model, an algorithm is suggested. To show the performance of the proposed algorithm, numerical examples are given. Finally, some special cases are considered and their characteristic features are highlighted.

关键词： multiobjective linear programming Interval programming Minimax regret criterion Necessarily efficient solutions

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Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2008年第2期68卷 257-276页

作者： Shao, Lizhen Ehrgott, Matthias Univ Auckland Dept Engn Sci Auckland 1 New Zealand Univ Nantes Lab Informat Nantes Atlantique Nantes France

In this paper, we propose a modification of Benson's algorithm for solving multiobjective linear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson's original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of epsilon-nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjective linear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method.

关键词： multiobjective linear programming radiotherapy treatment planning epsilon-efficient solution

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NEGO - GROUP DECISION SUPPORT SYSTEM

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INFORMATION & MANAGEMENT 1985年第5期8卷 237-246页

作者： KERSTEN, GE MANAGEMENT ORG & DEV INST DEPT MANAGEMENT SYSTWARSAWPOLAND

Formulating the policy of a plan for an organization by its members can be called group decision making (GDM). A combination of 2 major decision-making frameworks, maximizing and satisficing, may be used to describe GDM. In the satisficing approach, decision makers (DM) formulate demands in the form of constraints, then they take into account preferences or wants, which take the form of objective functions, when choosing from among different decisions. GDM has 2 stages: 1. The DM makes a decision. 2. DMs negotiate to reach a compromise decision. Negotiating is an iterative process that is completed when all demands have been met. NEGO is a group decision support system that assists DMs in finding a compromise. An example is presented to illustrate how NEGO can be used to help solve GDM problems that can be modeled as multiobjective linear programming problems. NEGO is not helpful to solving problems in which 2 decision makers have the same objective but different criteria.

关键词： Decision Support System Negotiations Group Decision Making multiobjective Decision Making multiobjective linear programming Goal programming

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A multiobjective based approach for mathematical programs with linear flexible constraints

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APPLIED MATHEMATICAL MODELLING 2012年第12期36卷 6264-6274页

作者： Yaghoobi, M. A. Pourkarimi, L. Mashinchi, M. Razi Univ Dept Math Kermanshah 67149 Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Math Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced. (C) 2012 Elsevier Inc. All rights reserved.

关键词： multiobjective linear programming Efficiency Maximal efficient face Flexible constraint

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Optimal Planning of University Technology Transfer Measures With FDANP-F-FlowSort and an Extended multiobjective PROMETHEE V

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IEEE ACCESS 2022年 10卷 56629-56651页

作者： Tibay, Edgar Quinones, Renissa Quinones, Hubert Selerio, Egberto, Jr. Shane Evangelista, Samantha Lourdes Aro, Joerabell Maturan, Fatima May Atibing, Nadine Yamagishi, Kafferine Ocampo, Lanndon Cebu Technol Univ Prod Extens & Resource Generat Cebu Philippines Cebu Technol Univ Ctr Appl Math & Operat Res Cebu Philippines Cebu Technol Univ Dept Tourism Management Cebu 6000 Philippines

This work offers an integrated methodological framework for decision support in planning the implementation of measures that address the barriers to university technology transfer (UTT). The planning problem consists of two parts: 1) identifying the high priority measures;2) optimally implementing these measures over a specified planning horizon subject to resource constraints. Treated as a multi-criteria sorting problem under uncertainty, the high priority measures are determined via fuzzy DEcision MAking Trial and Evaluation Laboratory (DEMATEL) and analytic network process (ANP) for evaluating the barriers, and the fuzzy FlowSort (F-FlowSort) for classifying the priority of the various measures. Then, an extended multi-objective extension of the Preference Ranking Organization METHod for Enrichment Evaluations V (PROMETHEE V) is offered to determine the degree of implementation of the high priority measures over multiple periods. Demonstrated in an actual case study with 29 identified measures under 24 previously known barriers, findings reveal six high priority measures, which include designing a sustained partnership, engaging in joint research ventures, establishing partnerships from international financial institutions, streamlining objectives to full support of the technology readiness levels, establishing a holistic system approach towards technology readiness levels, and establishing agreements to have access to the industry laboratory facilities. The implementation plan, represented as a set of Pareto optimal solutions, is obtained through the augmented epsilon -constraint (AUGMECON) algorithm for the epsilon -constrained multi-objective linear programming formulation of the extended PROMETHEE V. Layers of sensitivity analysis were performed to test the robustness of the results to changes in the parameters. Finally, policy insights are provided to key decision-makers for advancing UTT.

关键词： University technology transfer multi-period planning analytic network process fuzzy FlowSort PROMETHEE V multiobjective linear programming

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Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program

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JOURNAL OF HAZARDOUS MATERIALS 2013年第Feb.15期246卷 257-266页

作者： Zhang, Xiaodong Huang, Gordon Univ Texas Austin Jackson Sch Geosci Bur Econ Geol Austin TX 78713 USA Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada

Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different pi levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help the decision makers justify and/or adjust their waste management strategies based on their implicit knowledge and preferences. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Municipal solid waste management Greenhouse gas emission control Fuzzy possibilistic programming multiobjective linear programming

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A new hybrid algorithm of simulated annealing and simplex downhill for solving multiple-objective aggregate production planning on fuzzy environment

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NEURAL COMPUTING & APPLICATIONS 2019年第6期31卷 1823-1834页

作者： Zaidan, A. A. Atiya, Bayda Abu Bakar, M. R. Zaidan, B. B. Univ Pendidikan Sultan Idris Dept Comp Fac Arts Comp & Creat Ind Tanjong Malim Malaysia Univ Putra Malaysia Dept Math Fac Sci Serdang Malaysia

Aggregate production planning (APP) is a significant level that seeks efficient production systems. In actual condition, APP decisions, production inputs, and relevant planning parameters are intrinsically imprecise, which results in significant complexities in the generation of master production schedules. Thus, this paper proposes a hybridization of a fuzzy programming, simulated annealing (SA), and simplex downhill (SD) algorithm called fuzzy-SASD to establish multiple-objective linear programming models and consequently resolve APP problems in a fuzzy environment. The proposed strategy is dependent on Zimmerman's approach for handling all inexact operating costs, data capacities, and demand variables. The SD algorithm is employed to balance exploitation and exploration in SA, thereby efficient and effective (speed and quality) solution for the APP model. The proposed approach produces rates for efficient solutions of APP in large-scale problems that are 33, 83, and 89% more efficient than those of particle swarm optimization (PSO), standard algorithm (SA), and genetic algorithm (GA), respectively. Moreover, the proposed approach produces a significantly low average rate for computational time at only 64, 77, and 24% compared with those of GA, PSO, and SA, respectively. Experimental results indicate that the fuzzy-SASD is the most effectual of all approaches.

关键词： Aggregate production planning Simulated annealing multiobjective linear programming Simplex downhill approach

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An interactive fuzzy satisficing method for multiobjective optimal control problems in linear distributed-parameter systems

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FUZZY SETS AND SYSTEMS 1999年第2期102卷 237-246页

作者： Sakawa, M Inuiguchi, M Kato, K Ikeda, T Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 739 Japan

In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： linear distributed-parameter systems multiobjective optimal control multiobjective linear programming fuzzy programming fuzzy goals fuzzy satisficing methods

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Interactive decision making for large-scale multiobjective linear programs with fuzzy numbers

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FUZZY SETS AND SYSTEMS 1997年第2期88卷 161-172页

作者： Sakawa, M Kato, K Department of Industrial and Systems Engineering Faculty of Engineering Hiroshima University Higashi-Hiroshima 739 Japan

In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy numbers are formulated. Through the use of the alpha-level sets of fuzzy numbers, an extended Pareto optimality concept, called the alpha-Pareto optimality is introduced. To generate a candidate for the satisficing solution which is also alpha-Pareto optimal, decision maker is asked to specify the degree alpha and the reference objective values. It is shown that the corresponding alpha-Pareto optimal solution can be easily obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive decision-making method for deriving a satisficing solution for the decision maker efficiently from an alpha-Pareto optimal solution set is presented. (C) 1997 Elsevier Science B.V.

关键词： large-scale linear programming multiobjective linear programming block angular structure fuzzy numbers interactive decision making

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Goal-programming-assisted visual cryptography method with unexpanded shadow images for general access structures

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OPTICAL ENGINEERING 2006年第9期45卷 097001-1-097001页

作者： Hsu, Ching-Sheng Hou, Young-Chang Ming Chuan Univ Dept Informat Management Taoyuan 333 Taiwan Tamkang Univ Dept Informat Management Tamsui 251 Taiwan

This paper describes a visual cryptography method for the elimination of pixel expansion and the improvement of contrast. The proposed method uses the probability concept to construct a multiobjective linear programming model for general access structures. Then, the solution space of the model is explored by goal programming. The advantages of the proposed method are fourfold. First, it can avoid expanding the shadow images. Second, it can reach better contrast. Third, it can deal with general access structures and get the desired contrast levels. Fourth, it can be easily extended to deal with the problems of multiple secret images. Experiments on several access structures show that the proposed method is effective against pixel expansion and is capable of contrast improvement. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

关键词： goal programming multiobjective linear programming visual cryptography

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