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

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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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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Filtering Algorithms for Biobjective Mixed Binary linear Optimization Problems with a Multiple-Choice Constraint

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INFORMS JOURNAL ON COMPUTING 2020年第1期32卷 57-73页

作者： Jornada, Daniel Leon, V. Jorge Ford Motor Co Global Data Insights & Analyt Dearborn MI 48124 USA Texas A&M Univ Dept Engn Technol & Ind Distribut College Stn TX 77843 USA Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA

This paper deals with a class of biobjective mixed binary linear programs having a multiple-choice constraint, which are found in applications such as Pareto set-reduction problems, single-supplier selection, and investment decisions, among others. Two objective space-search algorithms are presented. The first algorithm, termed line search and linear programming filtering, is a two-phase procedure. Phase 1 searches for supported Pareto outcomes using the parametric weighted sum method, and Phase 2 searches for unsupported Pareto outcomes by solving a sequence of auxiliary mixed binary linear programs. An effective linear programming filtering procedure excludes arty previous outcomes found to be dominated. The second algorithm, termed linear programming decomposition and filtering, decomposes the mixed binary problem by iteratively fixing binary variables and uses the linear programming filtering procedure to prune out any dominated outcomes. Computational experiments show the effectiveness of the linear programming filtering and suggest that both algorithms run faster than existing general-purpose objective space-search procedures.

关键词： biobjective mixed binary programming optimization over the efficient set dominance filtering multiobjective linear programming Pareto set reduction

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Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

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EXPERT SYSTEMS WITH APPLICATIONS 2013年第2期40卷 563-574页

作者： Katagiri, Hideki Uno, Takeshi Kato, Kosuke Tsuda, Hiroshi Tsubaki, Hiroe Hiroshima Univ Fac Engn Higashihiroshima Hiroshima 7398527 Japan Univ Tokushima Inst Socioarts & Sci Tokushima 7708502 Japan Hiroshima Inst Technol Fac Appl Informat Sci Saeki Ku Hiroshima 7315193 Japan Doshisya Univ Fac Sci & Engn Kyotanabe 6100394 Japan Inst Stat Math Dept Data Sci Tachikawa Tokyo 1908562 Japan

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： multiobjective linear programming Random fuzzy variable Possibility Necessity Possibilistic value at risk (pVaR) Pareto optimal solution Interactive algorithm

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A fuzzy satisficing method for multiobjective linear optimal control problems

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FUZZY SETS AND SYSTEMS 1996年第2期78卷 223-229页

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

In this paper, we propose ct fuzzy satisficing method for the solution of multiobjective linear continuous optimal control problems. To solve these multiobjective linear continuous optimal control problems, we first discretize the time and replace the system of differential equations by difference equations. By introducing suitable auxiliary variables, approximate linear multiobjective programming problems are formulated. Then 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 we adopt the fuzzy decision for combining them, it is shown that the formulated problem can be reduced to a linear programming problem and the satisficing solution for the decision maker can be obtained through the simplex method of linear programming. An Illustrative numerical example is provided to indicate the efficiency of the proposed method.

关键词： multiobjective linear control problems multiobjective linear programming fuzzy goals fuzzy decision fuzzy satisficing method

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APPLICATION OF FLEXIBILITY ANALYSIS FOR COMPROMISE SOLUTION IN LARGE-SCALE linear-SYSTEMS

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 1989年第2期22卷 189-194页

作者： SHIMIZU, Y Research Reactor Institute Kyoto University Osaka 590-04 Japan

This paper describes the use of flexibility analysis with uncertain parameters involved in linear models. Due to the presence of various judgments of value in large-scale systems, the previous formulation developed under single-objective optimization is revised by use of the minimum aspiration level, which plays an important role in multiobjective optimization. An improved algorithm to compute the flexibility index in an iterative manner is also presented. The proposed approach is applied to a post-optimal analysis of the dynamic allocation planning of an electric power system. Such consideration is shown to be of special importance in increasing reliability at the planning stage of problem-solving in uncertain systems.

关键词： Electric System Flexibility Analysis Large-Scale System Minimum Aspiration Level multiobjective linear programming Process System

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Approximating the nondominated set of an MOLP by approximately solving its dual problem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2008年第3期68卷 469-492页

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

The geometric duality theory of Heyde and Lohne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson's outer approximation method (Benson 1998a,b) while the dual problem can be solved by a dual variant of Benson's algorithm (Ehrgott et al. 2007). Duality theory then assures that it is possible to find the (weakly) nondominated set of the primal MOLP by solving its dual. In this paper, we propose an algorithm to solve the dual MOLP approximately but within specified tolerance. This approximate solution set can be used to calculate an approximation of the weakly nondominated set of the primal. We show that this set is a weakly E-nondominated set of the original primal MOLP and provide numerical evidence that this approach can be faster than solving the primal MOLP approximately.

关键词： multiobjective linear programming Geometric duality epsilon-nondominated set Approximation Radiotheraphy treatment planning

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IDENTIFYING THE EFFICIENT EXTREME-POINTS OF THE 3-OBJECTIVE linear-programming PROBLEM

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1993年第1期44卷 81-85页

作者： BRYSON, N HOWARD UNIV SCH BUSINESSDEPT INFORMAT SYST & ANALWASHINGTONDC 20059 USA

In this paper a new method for generating the set of efficient extreme-points for the three-objective linear programming problem is presented. This method successfully exploits the fact that vectors that are strictly efficient in associated multi-objective problems of lower dimensions are also efficient in the full multi-objective problem.

关键词： multiobjective linear programming PARAMETRIC linear programming

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Coupling distinct MOLP interactive approaches with a novel DEA hybrid model

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2022年第5期29卷 3207-3228页

作者： Henriques, Carla Luque, Mariano Marcenaro-Gutierrez, Oscar Coimbra Business Sch Polytech Inst Coimbra Quinta Agr P-3040316 Coimbra Portugal Univ Coimbra INESC Coimbra DEEC Polo 2 P-3030290 Coimbra Portugal Univ Malaga Programa Doctorado Econ & Empresa PhD Programme Econ & Business Malaga Spain Univ Malaga Dept Appl Econ Math C Ejido 6 Malaga 29071 Spain Univ Malaga Dept Appl Econ Stat & Econometr C Ejido 6 Malaga 29071 Spain

We propose a modelling framework which allows considering different priorities and individual expansion and contraction scales for distinct types of inputs and outputs, through the Weighted Russell Directional Distance Model (WRDDM). An equivalence model between the WRDDM and the super-ideal point model has also been established, which is then incorporated into several interactive multiobjective linear programming (MOLP) approaches. The use of these diverse interactive methodologies allows obtaining the benchmark Decision Making Units (DMUs) which best suit the decision maker's (DM) preferences. This feature can be useful since traditional Data Envelopment Analysis (DEA) models tend to completely neglect the DM's preferences and value judgements in the computation of the DMUs used as a reference of best practices. Therefore, with this tool the DMs have the possibility of translating into the decision-making process management constraints (namely, budgetary) and aspiration levels regarding the inputs and outputs, providing much more realistic support for actual decision-making.

关键词： data envelopment analysis weighted Russell directional distance model multiobjective linear programming interactive approaches

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A vector linear programming approach for certain global optimization problems

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JOURNAL OF GLOBAL OPTIMIZATION 2018年第2期72卷 347-372页

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

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal (Math Program 141(1-2): 103-120, 2013) on quasi-concave problems and Shao and Ehrgott (Optimization 65(2): 415-431, 2016) on multiplicative linear programs. Furthermore, it improves results of Lohne and Wagner (J Glob Optim 69(2): 369-385, 2017) on minimizing the difference f = g-h of two convex functions g, h where either g or h is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.

关键词： Global optimization DC programming multiobjective linear programming linear vector optimization

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