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On the Lexicographic Centre of multiple objective Optimization

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第2期168卷 600-614页

作者： Zhang Jiangao Yang, Shitao Chongqing Univ Fac Construct Management & Real Estate Chongqing 400045 Peoples R China Sichuan Univ State Key Lab Hydraul & Mt River Engn Chengdu 610064 Peoples R China Florida Inst Technol Nathan M Bisk Coll Business 150 W Univ Blvd Melbourne FL 32901 USA

We study the lexicographic centre of multiple objective optimization. Analysing the lexicographic-order properties yields the result that, if the multiple objective programming's lexicographic centre is not empty, then it is a subset of all efficient solutions. It exists if the image set of multiple objective programming is bounded below and closed. The multiple objective linear programming's lexicographic centre is nonempty if and only if there exists an efficient solution to the multiple objective linear programming. We propose a polynomial-time algorithm to determine whether there is an efficient solution to multiple objective linear programming, and we solve the multiple objective linear programming's lexicographic centre by calculating at most the same number of dual linear programs as the number of objective functions and a system of linear inequalities.

关键词： multiple objective programming Lexicographic order Lexicographic centre Efficient solution Image set theta-image set

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multiple-objective analysis of integrated relief supply and network restoration in humanitarian logistics operations

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2016年第1期54卷 49-68页

作者： Ransikarbum, Kasin Mason, Scott J. Clemson Univ Dept Ind Engn Clemson SC 29634 USA

While logistics research recently has placed increased focus on disruption management, few studies have examined the response and recovery phases in post-disaster operations. We present a multiple objective, integrated network optimisation model for making strategic decisions in the supply distribution and network restoration phases of humanitarian logistics operations. Our model provides an equity-based solution for constrained capacity, budget and resource problems in post-disaster logistics management. We conduct designed experiments for this NP-hard problem to analyse important aspects of the integrated problem for both small- and large-sized networks: full vs. partial restoration and pooled vs. separate budgeting approach. Finally, we apply the model to a Hazus-generated regional case study based on an earthquake scenario and generate efficient Pareto frontiers to understand the trade-off between the objectives of interest.

关键词： disruption management humanitarian logistics response and recovery equity multiple objective programming Hazus

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Modeling and optimization of multi objective non-linear programming problem in intuitionistic fuzzy environment

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APPLIED MATHEMATICAL MODELLING 2015年第16期39卷 4617-4629页

作者： Singh, Sujeet Kumar Yadav, Shiv Prasad Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

In dealing with real world practical optimization problems, a decision maker usually faces a state of uncertainty as well as hesitation, due to various unpredictable factors. Sometimes it is necessary to optimize, several non-linear and conflicting objectives simultaneously. To deal with the uncertain parameters which arise in such situations, intuitionistic fuzzy numbers are utilized. We formulate a multiobjective non-linear programming problem in intuitionistic fuzzy environment. We propose a linear ranking function and utilize it to convert the intuitionistic fuzzy model into a crisp model. After converting the problem into equivalent crisp problem, we propose a non-linear membership function and develop various approaches for solving it by using different operators and fuzzy programming technique. We apply our methodologies for justification to a numerical problem in manufacturing systems. (C) 2015 Elsevier Inc. All rights reserved.

关键词： multiple objective programming Intuitionistic fuzzy number Accuracy function Nonlinear programming

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Dynamic programming for spanning tree problems: application to the multi-objective case

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OPTIMIZATION LETTERS 2015年第3期9卷 437-450页

作者： Pugliese, Luigi Di Puglia Guerriero, Francesca Santos, Jose Luis Univ Calabria Dept Mech Energy & Management Engn I-87036 Arcavacata Di Rende CS Italy Univ Coimbra Dept Math P-3001454 Coimbra Portugal

The aim of this paper is to provide a dynamic programming formulation for the spanning tree problem (), which allows several instances of the classical to be addressed. The spanning tree structure is modelled with states and transition between states, defining a state-space. Several properties are shown and optimality conditions are given. Once the theoretical fundamentals of the proposed formulation are derived, the multi-objective spanning tree problem () is addressed. This problem arises in the telecommunications and transportation sectors. In these contexts, handling different criteria simultaneously plays a crucial role. The scientific literature provides several works that focus on the bi-objective version of the considered problem, in which only two criteria are taken into account. To the best of our knowledge, no works provide optimal methods to address the with an arbitrary number of objective functions. In this paper we extend the proposed dynamic programming formulation to model and solve the with criteria.

关键词： Dynamic programming Spanning tree problems multiple objective programming Pareto front

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Robustness in nonsmooth nonlinear multi-objective programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期247卷 370-378页

作者： Zamani, Moslem Soleimani-damaneh, Majid Kabgani, Alireza Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran Inst Res Fundamental Sci IPM Sch Math Tehran Iran

Recently Georgiev, Luc, and Pardalos (2013), [Robust aspects of solutions in deterministic multiple objective linear programming, European Journal of Operational Research, 229(1), 29-36] introduced the notion of robust efficient solutions for linear multi-objective optimization problems. In this paper, we extend this notion to nonlinear case. It is shown that, under the compactness of the feasible set or convexity, each robust efficient solution is a proper efficient solution. Some necessary and sufficient conditions for robustness, with respect to the tangent cone and the non-ascent directions, are proved. An optimization problem for calculating a robustness radius followed by a comparison between the newly-defined robustness notion and two existing ones is presented. Moreover, some alterations of objective functions preserving weak/proper/robust efficiency are studied. (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 Robust solution Nonsmooth optimization Clarke generalized gradient Proper efficiency

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Wolfe type higher order multiple objective nondifferentiable symmetric dual programming with generalized invex function

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Journal of Mathematical Modelling and Algorithms in Operations Research 2014年第4期13卷 557-577页

作者： Tripathy, Arun Kumar Devi, Gayatri Department of Mathematics Trident Academy of Technology F2/A Chandaka Industrial Estate Infocity Area Bhubaneswar 751024 Odisha India Department of Computer Science and Engineering Ajaya Binaya Institute of Technology Markat Nagar CDA Sector-1 Cuttack 753014 Odisha India

In this paper, a new class of higher order (φ, ρ)-invex function is introduced with an example, in which the sublinearity and convexity assumption on φ with respect to third argument is relaxed. A pair of higher order Wolfe type multiobjective symmetric dual for a class of nondifferentiable multiobjective programming involving square root term is presented and the weak duality, strong duality and converse duality theorems are established with their proofs under higher order (φ, ρ)-invexity and (φ, ρ)-incavity assumption. Self duality theorem is proved for the proposed dual program. These results are used to discuss Wolfe type higher-order symmetric minimax mixed integer dual problems. A numerical example is developed where the results of weak and strong duality theorems can be applied. Discussion on some particular cases shows that our results generalize earlier results in related domain. © Springer Science+Business Media Dordrecht 2014.

关键词： Higher order (φ, ρ)-invexity multiple objective programming Pareto optimal solution Schwartz inequality Square root term

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A Method for Generating a Well-Distributed Pareto Set in multiple objective Mixed Integer Linear Programs Based on the Decision Maker's Initial Aspiration Level

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2016年第4期33卷 1650031-1650031页

作者： Razavyan, S. Islamic Azad Univ South Tehran Branch Dept Math Tehran Iran

This paper attempt to generate a representative subset of the Pareto optimal set for multiple objective mixed integer linear programming problem using the weighted L-1 norm distance. The procedure presented in this paper is somewhat similar to the one used in the ideal-point methods and its aim is to generate at each iteration the closest-points to the ideal vector corresponding to the decision maker's initial aspiration level for a new tradeoff parameter. Unlike most of the known algorithms for generating a discrete representation of the Pareto optimal set, the procedure generates at each iteration a nondominated point by solving only one mixed integer linear programming problem. The obtained solution minimizes the weighted L1 norm distance to the ideal vector with respect to the distance between the ideal vector and previously found vectors. More generally, this approach is able to generate all Pareto optimal solutions, where all of the decision variables are restricted to be integer. In order to explain the presented details, several illustrative examples are provided.

关键词： multiple objective programming integer programming Pareto optimal discrete representation ideal-point

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House selection via the internet by considering homebuyers' risk attitudes with S-shaped utility functions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第1期241卷 188-201页

作者： Ho, Hui-Ping Chang, Ching-Ter Ku, Cheng-Yuan Chien Kuo Technol Univ Dept Int Business Adm Changhua Taiwan Chang Gung Univ Dept Informat Management Taoyuan Taiwan Natl Chiao Tung Univ Dept Informat Management & Finance Hsinchu Taiwan

The widespread use of the Internet has significantly changed the behavior of homebuyers. Using online real estate agents, homebuyers can rapidly find some modern houses that meet their needs;however, most current online housing systems provide limit features. In particular, existing systems fail to consider homebuyers' housing goals and risk attitudes. To increase effectiveness, online real estate agents should provide an efficient matching mechanism, personalized service and house ranking with the aim of increasing both buyers' satisfaction and deal rate. An efficient online real estate agent should provide an easy way for homebuyers to find (rank) a suitable house (alternatives) with consideration of their different housing philosophies and risk attitudes. In order to comprehend these ambiguous housing goals and risk attitudes, it is also indispensable to determine a satisfaction level for each fuzzy goal and constraint. In this study, we propose fuzzy goal programming with an S-shaped utility function as a decision aid to help homebuyers in choosing their preferred house via the Internet in an easy way. With the use of a decision aid, homebuyers can specify their housing goals and constraints with different priority levels and thresholds as a matching mechanism for a fuzzy search, while the matching mechanism can be translated into a standard query language for a regular relational database. Moreover, a laboratory experiment is conducted on a real case to demonstrate the effectiveness of the proposed approach. The results indicate that the proposed method provides better customer satisfaction than manual systems in housing selection service. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Decision support systems multiple objective programming Fuzzy goal programming Utility functions Risk attitude

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A novel portfolio selection model based on fuzzy goal programming with different importance and priorities

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EXPERT SYSTEMS WITH APPLICATIONS 2015年第20期42卷 6898-6912页

作者： Kocadagli, Ozan Keskin, Ridvan Mimar Sinan Fine Arts Univ Dept Stat TR-34380 Istanbul Turkey Celal Bayar Univ Fac Econ & Adm Sci Dept Econometr TR-45030 Manisa Turkey

Despite the risk return tradeoff is main concern of financial theory;the rational investment decisions requires considering many criteria simultaneously. In addition to determining a certain importance and priority among these criteria, modeling the investor behaviors in accordance with market trends provides much more realistic approach. However, the researchers mostly overlook to evaluate these concepts simultaneously. This article introduces a novel fuzzy portfolio selection model that takes into accounts the risk preferences in accordance with the market moving trends as well as the risk return tradeoff, and allows the decision makers to define a certain importance and priority among their objectives. To construct this model, firstly the portfolio return, risk and beta coefficient are assumed as main objectives including the possibilistic uncertainties. To define possibilistic uncertainty, the specific fuzzy membership functions are constituted for these objectives with respect to the risk preferences of investors and market moving trends. By means of the fuzzy goal programming techniques, a novel portfolio selection model is developed using these specific fuzzy membership functions. In the application section, three investment terms are examined in the Istanbul Stock Exchange National 30 Index. While ISE30 index has the upward (bullish) and the downward (bearish) moving trends in the first two implementations, the third implementation includes a scenario in which the investors desire to chase the ISE30 index. In the analyses, the proposed model is compared with the classical Mean Variance, Mean-Absolute-Deviation and Maxmin models in terms of their portfolio returns based on the selling prices in the test periods. As a result, the proposed model gives superior performance than the classical models because it takes into account the investor preferences in accordance with market moving trend. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Fuzzy goal programming Portfolio selection model Risk preferences of investors Capital Asset Pricing Model

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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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