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On a general duality model in multiobjective fractional programming with n-set functions

MATHEMATICAL AND COMPUTER MODELLING 2011年第1-2期54卷 490-496页

作者： Preda, Vasile Stancu-Minasian, Ioan M. Beldiman, Miruna Stancu, Andreea-Madalina Acad Romana Inst Math Stat & Appl Math Bucharest 050711 Romania Univ Bucharest Dept Math & Comp Sci Bucharest 010014 Romania

We consider some types of generalized convexity and discuss duality results for a fractional programming problem involving (F, b, phi, rho, theta)-univex n-set functions. Almost all results presented until now in the literature were obtained under the assumption that the function F is sublinear or, in the last time, convex in the third argument. In our approach, we suppose that F is a quasiconvex function in the third argument. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming n-set function Duality Generalized convexity

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An Approach to multiobjective programming Problems based on Fuzzy Random Theory

An Approach to Multiobjective Programming Problems based on ...

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The Twelfth Asia Pacific Industrial Engineering ＆ Management Systems Conference(APIEMS 2011)

作者： Youshe Yang~1 and Mingfa Zheng~2 1 College of Science,Air Force Engineering,Xi'an,Shanxi,710051,China 2 College of Science,Air Force Engineering University,Xi'an,Shanxi,710051,China

In this paper,based on the fuzzy random theory, the fuzzy random multiobjective programming(FR-MOP) problems are *** first investigate the expected value model,and study its *** on the proposed model,the expected-value efficient solution and the expected-value weakly efficient solution are defined. To solve the FRMOP problems,a method,called method of main objective function,is presented,whose results can provide theoretical foundation for designing solution ***,a numerical example are given to explain the solution method.

关键词： credibility theory fuzzy random variable multiobjective programming expected-value efficient solution

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A multilevel and multistage efficiency evaluation of innovation systems: A multiobjective DEA approach

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EXPERT SYSTEMS WITH APPLICATIONS 2016年 62卷 63-80页

作者： Carayannis, Elias G. Grigoroudis, Evangelos Goletsis, Yorgos George Washington Univ Washington DC 20052 USA Tech Univ Crete Sch Prod Engn & Management GR-73100 Khania Greece Univ Ioannina Dept Econ GR-45110 Ioannina Greece

Evaluating the efficiency of innovation systems can serve as a substantial enabling tool for policymaking serving to identify best practices and develop potential improvements of actions and strategies. It also serves to provide valuable insight in understanding the nature and dynamics of innovation process at its different stages and levels. The main aim of the paper is to present an integrated assessment and classification framework for national and regional innovation efficiency. The proposed model is based on Data Envelopment Analysis and is formulated as a multiobjective mathematical program in order to consider the objectives and constraints of the different stages and levels of the innovation process. Additionally, the model copes with DEA inconsistencies when ratio measures are employed. In the second part of the study, a multicriteria decision aid approach, based on an ordinal regression model, is applied in order to study how environmental factors on innovation and entrepreneurship affect the estimated efficiency scores. The proposed approach is applied to a set of 23 European countries and their 185 corresponding regions. The results show that there are large differences regarding the efficiency scores of the different stages and levels, implying the existence of significant divergences from the expected norm concerning innovation efficiency. The contribution of the paper lies (i) in the proposed multiobjective model, which is able to model the multiple stages and levels of the innovation process and handle ratio measures without requiring the same set of inputs and outputs at different levels and (ii) in the presented application of the model in the efficiency evaluation of innovation systems, including a meta-analysis of the results based on the framework of the Quadruple Innovation Helix. Such an approach may provide a valuable tool for country/region comparison and policy formulation. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Data envelopment analysis multiobjective programming Multistage efficiency Multilevel efficiency Ordinal regression analysis Innovation systems

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On sufficient optimality conditions for multiobjective control problems

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JOURNAL OF GLOBAL OPTIMIZATION 2016年第4期64卷 721-744页

作者： de Oliveira, Valeriano Antunes Silva, Geraldo Nunes UNESP Univ Estadual Paulista Dept Matemat Aplicada Inst Biociencias Letras & Ciencias Exatas Campus Sao Jose Do Rio Preto BR-15051000 Sao Jose Do Rio Preto SP Brazil

This paper is devoted to presenting optimality conditions for the sufficiency of the maximum principle for multiobjective optimal control problems with nonsmooth data. Such conditions are the most general as possible in the sense that problems in which the set of necessary conditions from the maximum principle are also sufficient, necessarily obey them. A variation of such conditions is also presented, under which the set of optimal solutions of the multiobjective problem can be determined by resolving a related scalar weighting problem.

关键词： Optimal control Optimality conditions Generalized convexity multiobjective programming

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Inventory management under uncertainty: A military application

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COMPUTERS & INDUSTRIAL ENGINEERING 2016年 96卷 96-107页

作者： Bean, Wilna L. Joubert, Johan W. Luhandjula, M. K. Univ Pretoria Dept Ind & Syst Engn ZA-0002 Pretoria South Africa CSIR Built Environm Transport Syst & Operat POB 395 ZA-0001 Pretoria South Africa Univ S Africa Dept Decis Sci POB 392 ZA-0003 Pretoria South Africa

Inventory management under uncertainty is a widely investigated field and many different types of inventory models have been used to address inventory problems in practice. However, a look at the literature reveals that few papers are devoted to inventory planning and management in environments characterised by uncertainty resulting from extreme events. In this paper a fuzzy-stochastic multi objective modelling approach is used to address the problem of managing inventory in an environment characterised by uncertainty. The model is applied specifically to the military environment and determines the required stock level for a single item, based on three different scenarios. A numerical example is provided for the sake of illustration and the reliability of the model tested through simulation. The results are compared with those obtained from the well known (r, Q) and (s, S) inventory models in the literature. This comparison showed that the hybrid model presented in this paper is more reliable in extreme scenarios. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Inventory management Fuzzy-stochastic programming multiobjective programming Military stock Uncertainty

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Fast Model Predictive Control for Multilevel Cascaded H-Bridge STATCOM With Polynomial Computation Time

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2016年第8期63卷 5231-5243页

作者： Zhang, Yonglei Wu, Xiaojie Yuan, Xibo Wang, Yingjie Dai, Peng China Univ Min & Technol Sch Informat & Elect Engn Xuzhou 221116 Peoples R China Univ Bristol Dept Elect & Elect Engn Bristol BS8 1UB Avon England

To solve the issue of exponentially increasing computational burden of finite control set model predictive control (FCS-MPC) for multilevel converters, a fast MPC scheme for multilevel cascaded H-bridge STATCOM is presented. The proposed approach consists of three steps. First, with the partially stratified optimization approach, the multiobjective programming of MPC is divided into two suboptimization problems, i.e., current-control MPC and voltage-balancing MPC. Second, a dynamic programming algorithm is proposed for the optimization of current-control MPC. Third, a mixed algorithm, which combines dynamic programming and greedy algorithm (0-1 programing), is proposed to select the optimal switching combination from all the redundant switching combinations for the voltage balancing MPC achieving a global optimization. Through the analysis of the time complexity, with the proposed scheme, the total computation of FCS-MPC can be reduced to polynomial time from exponential time. The proposed approaches will not deteriorate the control performance. The control performance is validated by simulation results and the effectiveness is further demonstrated by implementing the algorithm on a low-cost DSP (TMS320F28335) in real time.

关键词： Cascaded H-bridge (CHB) static synchronous compensator (STATCOM) dynamic programming model predictive control (MPC) multiobjective programming partially stratified optimization

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Using multiobjective optimization to map the entropy region

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期63卷 45-67页

作者： Csirmaz, Laszlo Cent European Univ Budapest Hungary Renyi Inst Budapest Hungary

Mapping the structure of the entropy region of at least four jointly distributed random variables is an important open problem. Even partial knowledge about this region has far reaching consequences in other areas in mathematics, like information theory, cryptography, probability theory and combinatorics. Presently, the only known method of exploring the entropy region is, or equivalent to, the one of Zhang and Yeung from 1998. Using some non-trivial properties of the entropy function, their method is transformed to solving high dimensional linear multiobjective optimization problems. Benson's outer approximation algorithm is a fundamental tool for solving such optimization problems. An improved version of Benson's algorithm is presented, which requires solving one scalar linear program in each iteration rather than two or three as in previous versions. During the algorithm design, special care is taken for numerical stability. The implemented algorithm is used to verify previous statements about the entropy region, as well as to explore it further. Experimental results demonstrate the viability of the improved Benson's algorithm for determining the extremal set of medium-sized numerically ill-posed optimization problems. With larger problem sizes, two limitations of Benson's algorithm is observed: the inefficiency of the scalar LP solver, and the unexpectedly large number of intermediate vertices.

关键词： multiobjective programming Effective solutions Entropy region Benson's algorithm Entropy inequality

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On solving a multiobjective fixed charge problem with imprecise fractional objectives

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APPLIED SOFT COMPUTING 2016年 40卷 64-69页

作者： Upmanyu, M. Saxena, R. R. Univ Delhi Dept Math Delhi 110007 India Univ Delhi Dept Math Deen Dayal Upadhyaya Coll Delhi 110007 India

The fixed charge problem is a special type of nonlinear programming problem which forms the basis of many industry problems wherein a charge is associated with performing an activity. In real world situations, the information provided by the decision maker regarding the coefficients of the objective functions may not be of a precise nature. This paper aims to describe a solution algorithm for solving such a fixed charge problem having multiple fractional objective functions which are all of a fuzzy nature. The enumerative technique developed not only finds the set of efficient solutions but also a corresponding fuzzy solution, enabling the decision maker to operate in the range obtained. A real life numerical example in the context of the ship routing problem is presented to illustrate the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Fixed charge problem multiobjective programming Fractional programming Fuzzy objective function

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On Benson's scalarization in multiobjective optimization

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OPTIMIZATION LETTERS 2016年第8期10卷 1757-1762页

作者： Soleimani-damaneh, Majid Zamani, Moslem Univ Tehran Sch Math Stat & Comp Sci Coll Sci Tehran Iran Inst Res Fundamental Sci IPM Sch Math Tehran 193955746 Iran

In this paper, a popular scalarization problem in multiobjective optimization, introduced by Benson, is considered. In the literature it was proved that, under convexity assumption, the set of properly efficient points is empty when the Benson's problem is unbounded. In this paper, it is shown that this result is still valid in general case without convexity assumption.

关键词： multiobjective programming Scalarization Benson's problem

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multiobjective project portfolio selection with fuzzy constraints

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期245卷 7-29页

作者： Perez, F. Gomez, T. Univ Malaga Dept Appl Econ Math Campus El Ejido S-N E-29071 Malaga Spain

Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s.

关键词： Project portfolio selection multiobjective programming Fuzzy numbers

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