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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第3期192卷 891-903页

作者： Garcia Caceres, Rafael Guillermo Araoz Durand, Julian Arturo Palacios Gomez, Fernando Univ Politecn Cataluna Dept Math & Operat Res Barcelona Spain Pontificia Univ Javeriana Dep Product Proc Sch Engn Bogota Colombia Univ Andes Dept Ind Engn Bogota Colombia

This paper presents the theoretical foundations of the new integral analysis method (IAM), and its application to it facility location problem. This methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages: definition of the problem, cardinal analysis, ordinal analysis and integration analysis. The method uses the concepts of stochastic multicriteria acceptability analysis (SMAA), Monte Carlo simulation, optimization techniques and elements of probability. The proposed method (IAM) was used to determine optimal locations for the retail stores of it Colombian coffee marketing company. (c) 2007 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis multiple objective programming Combinatorial optimization Simulation Integral analysis method

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Robust portfolio modeling with incomplete cost information and project interdependencies

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期190卷 679-695页

作者： Liesio, Juuso Mild, Pekka Salo, Ahti Aalto Univ Syst Anal Lab Helsinki 02015 Finland

Robust portfolio modeling (RPM) [Liesio, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488-1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplete cost information and variable budget levels. These extensions lead to a multi-objective zero-one linear programming problem with interval-valued objective function coefficients for which all non-dominated solutions are determined by a tailored algorithm. The extended RPM framework permits more comprehensive modeling of portfolio problems and provides support for advanced benefit-cost analyses. It retains the key features of RPM by providing robust project and portfolio recommendations and by identifying projects on which further attention should be focused. The extended framework is illustrated with an example on product release planning. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiple criteria decision analysis project portfolio selection incomplete information robustness multiple objective programming

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The search-and-remove algorithm for biobjective mixed-integer linear programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期268卷 281-299页

作者： Soylu, Banu Erciyes Univ Dept Ind Engn TR-38039 Kayseri Turkey

In this study, an exact algorithm, called the search-and-remove (SR) algorithm, is proposed to compute the Pareto frontier of biobjective mixed-integer linear programming problems. At each stage of the algorithm, efficient slices (all integer variables are fixed in a slice) are searched with the dichotomic search algorithm and found slices are recorded and excluded from the decision space with the help of Tabu constraints. The algorithm is also enhanced with lower and upper bounds, which are updated at each stage of the algorithm. The SR algorithm continues until it is proved that all efficient slices of the biobjective mixed-integer linear programming (BOMILP) problem are found. The algorithm finally returns a set of potentially efficient slices including all efficient slices of the problem. Then, an upper envelope finding algorithm merges the Pareto frontiers of these slices to the Pareto frontier of the original problem. A computational analysis is performed on several benchmark problems and the performance of the algorithm is compared with state of the art methods from the literature. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Biobjective mixed-integer linear programming Integer programming Bound sets

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Using system dynamics for simulation and optimization of one coal industry system under fuzzy environment

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第9期38卷 11552-11559页

作者： Xu, Jiuping Li, Xiaofei Sichuan Univ Uncertainty Decis Making Lab Chengdu 610064 Peoples R China

In this paper, we have developed a model that integrates system dynamics with fuzzy multiple objective programming (SD-FMOP). This model can be used to study the complex interactions in a industry system. In the process of confirming sensitive parameters and fuzzy variables of the SD model, we made use of fuzzy multi-objective programming to help yield the solution. We adopted the chance-constraint programming model to convert the fuzzy variables into precise values. We use genetic algorithm to solve FMOP model, and obtain the Pareto solution through the programming models. It is evident that FMOP is effective in optimizing the given system to obtain the decision objectives of the SD model. The results recorded from the SD model are in our option, reasonable and credible. These results may help governments to establish more effective policy related to the coal industry development. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Coal industry planning Fuzzy set theory System dynamics multiple objective programming Simulation

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Measure of efficiency in DEA with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights restrictions

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APPLIED MATHEMATICS AND COMPUTATION 2004年第1期156卷 175-187页

作者： Jahanshahloo, GR Soleimani-damaneh, M Nasrabadi, E Teacher Training Univ Fac Math Sci & Comp Engn Tehran 15618 Iran Sharif Univ Technol Fac Ind Engn Tehran Iran

In this paper, a fuzzy comparison of fuzzy numbers is defined and a slack-based measure (SBM model) in data envelopment analysis (DEA) is extended to be a fuzzy DEA model, using it. Proposed measure is employed for evaluation and ranking of all decision making units, using a fuzzy concept called fuzzy profit. Also, it is shown that the introduced model is convenient for using weights restrictions. Furthermore, we compare the results of proposed model with Guo and Tanaka's results [Fuzzy Sets Syst. 119 (2001) 149] by representing a numerical example introduced by them. (C) 2003 Elsevier Inc. All rights reserved.

关键词： DEA fuzzy DEA fuzzy linear programming efficiency goal programming multiple objective programming

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On bi-objective combinatorial optimization with heterogeneous objectives

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期319卷 89-101页

作者： Cosson, Raphael Santana, Roberto Derbel, Bilel Liefooghe, Arnaud Univ Lille CNRS UMR 9189 CRIStAL Cent LilleInria F-59000 Lille Nord France Univ Basque Country UPV EHU San Sebastian State Two Spain Univ Littoral Cote dOpale UR 4491 LISIC F-62228 Calais Hauts De France France

The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective functions, in terms of multi-modality and search difficulty. Building on recent efforts leveraging the so-called single- objective NK-landscapes to model such a setting, we conduct a three-fold empirical analysis on the impact of objective heterogeneity on the landscape properties and search difficulty of bi-objective optimization problems. Firstly, for small problems, we propose two techniques based on studying the distribution of the solutions in the objective space. Secondly, for large problems, we investigate the ability of existing landscape features to capture the degree of heterogeneity among the two objectives. Thirdly, we study the behavior of two state-of-the-art multi-objective evolutionary algorithms, namely MOEA/D and NSGA-II, when faced with a range of problems with different degrees of heterogeneity. Although one algorithm is found to consistently outperform the other, the dynamics of both algorithms vary similarly with respect to objective heterogeneity. Our analysis suggests that novel approaches are needed to understand the fundamental properties of heterogeneous bi-objective optimization problems and to tackle them more effectively.

关键词： multiple objective programming Combinatorial optimization Evolutionary computations Landscape analysis Automated algorithm selection

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Weak efficiency for multiobjective variational problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期155卷 373-379页

作者： Arana-Jiménez, M Rufián-Lizana, A Osuna-Gómez, R IES Andres Benitez Cadiz 11407 Spain Univ Sevilla Dept Estadist & Invest Operat E-41012 Seville Spain

Sometimes, to locate efficient solutions for multiobjective variational problems (MVPs) is quite costly, so in this paper we tackle the study of weakly efficient solutions for MVPs. A new concept of weak vector critical point which generalizes other ones already existent, and a new class of pseudoinvex functions are introduced. We will apply a new approach to prove that the new class of pseudoinvex functions is equivalent to the class of functions whose weak vector critical points are weakly efficient solution for MVPs. (C) 2003 Published by Elsevier B.V.

关键词： nonlinear programming multiple objective programming variational problems pseudoinvexity weakly efficient solutions

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Finding a representative nondominated set for multi-objective mixed integer programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期272卷 61-77页

作者： Ceyhan, Gokhan Koksalan, Murat Lokman, Banu Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkey

In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Mixed integer programming Nondominated point Representative subset

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E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第1期246卷 218-231页

作者： Ruiz, Ana B. Sindhya, Karthik Miettinen, Kaisa Ruiz, Francisco Luque, Mariano Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Univ Jyvaskyla Dept Math Informat Technol FI-40014 Agora Finland

Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto optimal solutions is calculated in a pre-processing stage before the decision maker is involved. When the decision maker interacts with the solution process in the interactive decision making stage, no new optimization problem is solved, thus, avoiding the waiting time for the decision maker to obtain new solutions according to her/his preferences. In this stage, starting from the worst possible objective function values, the decision maker is shown a set of points in the objective space, from which (s)he chooses one as the preferable point. At successive iterations, (s)he always sees points which improve all the objective values achieved by the previously chosen point. In this way, the decision maker remains focused on the solution process, as there is no loss in any objective function value between successive iterations. The last post-processing stage ensures the Pareto optimality of the final solution. A real-life engineering problem is used to demonstrate how E-NAUTILUS works in practice. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： multiple objective programming Interactive methods multiple criteria optimization Computational cost Trading-off

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A fuzzy multiple objective nonlinear optimization problem and its duality results

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019年第2期36卷 1361-1373页

作者： Gupta, S. K. Dangar, D. Ahmad, I. Al-Homidan, S. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttarakhand India Marwari Coll Dept Math Ranchi Bihar India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran Saudi Arabia

In this study, we propose a formulation of a Mond-Weir type dual program for a multiobjective nonlinear optimization problem under fuzzy environment. To deal with the multiobjectivity in the formulation, we consider the concept of weak Pareto optimal solution in the fuzzy sense. We use the Hukuhara metric/difference to define the distance/difference between two fuzzy numbers. Further, we establish weak and strong duality theorems under fuzzy pseudo/quasi-convexity assumptions. Moreover, we also validate these duality relations using various numerical illustrations.

关键词： multiple objective programming Fuzzy valued function Mond-Weir type duality Partial ordering Hukuhara difference

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