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Optimality and duality for V-invex non-smooth multiobjective programming problems

OPTIMIZATION 2008年第5期57卷 635-641页

作者： Mishra, S. K. Wang, S. Y. Lai, K. K. City Univ Hong Kong Dept Management Sci Kowloon Hong Kong Peoples R China GB Pant Univ Agr & Technol Coll Basic Sci & Humanities Dept Math Stat & Comp Sci Pantnagar Uttar Pradesh India Chinese Acad Sci Inst Syst Sci Beijing Peoples R China Hunan Univ Coll Business Adm Changsha 410082 Hunan Peoples R China

We consider non-smooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several optimality conditions under various (generalized) V-invexity assumptions and certain regularity conditions are presented. Further, we introduce a Mond-Weir type dual and establish duality relations under the aforesaid assumptions.

关键词： multiobjective programming locally Lipschitz functions V-invex functions sufficient optimality conditions duality

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Possibilistic Mean Models for Linear programming Problems with Discrete Fuzzy Random Variables

Possibilistic Mean Models for Linear Programming Problems wi...

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Hideki Katagiri Takeshi Uno Kosuke Kato Graduate School of Engineering Hiroshima University 1-4-1 Kagamiyama Higashi-Hiroshima 739-8527 Japan Institute of Socio-Arts and Sciences The University of Tokushima 1-1 Minamijosanjima-cho Tokushima-shi Tokushima 770-8502 JAPAN Faculty of Applied Information Science Hiroshima Institute of Technology 2-1-1 Miyake Saeki-ku Hiroshima 731-5193 JAPAN

ISBN: (纸本)9781479906505

This paper considers linear programming problems where objective functions involve fuzzy random variables. New decision making models, called possibilistic mean model, are proposed in order to maximize the mean (expectation) of the degrees of possibility and necessity with respect to attained objective function values. It is shown that the original fuzzy random programming problems are transformed into deterministic nonlinear ones which can be solved by conventional nonlinear programming techniques.

关键词： fuzzy random variable multiobjective programming possibility measure necessity measure Random variable linear programming Pareto optimisation Fuzzy Objective function

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A two-slope achievement scalarizing function for interactive multiobjective optimization

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COMPUTERS & OPERATIONS RESEARCH 2012年第7期39卷 1673-1681页

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

The use of achievement (scalarizing) functions in interactive multiobjective optimization methods is very popular, as indicated by the large number of algorithmic and applied scientific papers that use this approach. Key parameters in this approach are the reference point, which expresses desirable objective function values for the decision maker, and weights. The role of the weights can range from purely normalizing to fully preferential parameters that indicate the relative importance given by the decision maker to the achievement of each reference value. Technically, the influence of the weights in the solution generated by the achievement scalarizing function is different, depending on whether the reference point is achievable or not. Besides, from a psychological point of view, decision makers also react in a different way, depending on the achievability of the reference point. For this reason, in this work, we introduce the formulation of a new achievement scalarizing function with two different weight vectors, one for achievable reference points, and the other one for unachievable reference points. The new achievement scalarizing function is designed so that an appropriate weight vector is used in each case, without having to carry out any a priori achievability test. It allows us to reflect the decision maker's preferences in a better way as a part of an interactive solution method, and this can cause a quicker convergence of the method. The computational efficiency of this new formulation is shown in several test examples using different reference points. (C) 2011 Elsevier Ltd. All rights reserved,

关键词： multiobjective programming Interactive methods Reference point methods Pareto optimality

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Convexificators and strong Kuhn-Tucker conditions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2012年第4期64卷 550-557页

作者： Golestani, M. Nobakhtian, S. Univ Isfahan Dept Math Esfahan 81745163 Iran

This study is devoted to constraint qualifications and strong Kuhn-Tucker necessary optimality conditions for nonsmooth multiobjective optimization problems. The main tool of the study is the concept of convexificators. Mangasarian-Fromovitz type constraint qualification and several other qualifications are proposed and their relationships are investigated. In addition, sufficient optimality conditions are studied. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Optimality conditions Nonsmooth optimization Convexificator Constraint qualification

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Connections Between Single-Level and Bilevel multiobjective Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2012年第1期153卷 60-74页

作者： Ruuska, Sauli Miettinen, Kaisa Wiecek, Margaret M. Univ Jyvaskyla Dept Math Informat Technol Jyvaskyla Finland

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors, and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiobjective optimization problems.

关键词： Two-level optimization multiobjective programming Multicriteria optimization Binary relations

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Interval programming models for matrix games with interval payoffs

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OPTIMIZATION METHODS & SOFTWARE 2012年第1期27卷 1-16页

作者： Li, Deng-Feng Nan, Jiang-Xia Zhang, Mao-Jun Fuzhou Univ Sch Management Fuzhou 350108 Fujian Peoples R China Dalian Univ Coll Informat Engn Dalian 116622 Liaoning Peoples R China Dalian Univ Technol Dept Econ Dalian 116024 Liaoning Peoples R China

The aim of this paper is to study how to solve a type of matrix game with interval payoffs. In this paper, the interval inequality relations and the concept of solutions of the matrix game with interval payoffs are defined. Based on the fuzzy ranking index defined, the solution of the matrix game with interval payoffs can be obtained through solving a pair of bi-objective linear programming models derived from the constructed auxiliary interval programming models. It is shown that the models proposed in this paper extend those of the classical matrix game. The validity and applicability of the proposed methodology are illustrated with a numerical example.

关键词： interval matrix game multiobjective programming uncertainty mathematical theory optimization

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Optimal expansion of a drinking water infrastructure system with respect to carbon footprint, cost-effectiveness and water demand

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2012年 110卷 194-206页

作者： Chang, Ni-Bin Qi, Cheng Yang, Y. Jeffrey Univ Cent Florida Dept Civil Environm & Construct Engn Orlando FL 32816 USA Univ Cent Florida Dept Ind Engn & Management Syst Orlando FL 32816 USA US EPA Off Res & Dev Natl Risk Management Res Lab Cincinnati OH 45268 USA

Urban water infrastructure expansion requires careful long-term planning to reduce the risk from climate change during periods of both economic boom and recession. As part of the adaptation management strategies, capacity expansion in concert with other management alternatives responding to the population dynamics, ecological conservation, and water management policies should be systematically examined to balance the water supply and demand temporally and spatially with different scales. To mitigate the climate change impact, this practical implementation often requires a multiobjective decision analysis that introduces economic efficiencies and carbon-footprint matrices simultaneously. The optimal expansion strategies for a typical water infrastructure system in South Florida demonstrate the essence of the new philosophy. Within our case study, the multiobjective modeling framework uniquely features an integrated evaluation of transboundary surface and groundwater resources and quantitatively assesses the interdependencies among drinking water supply, wastewater reuse, and irrigation water permit transfer as the management options expand throughout varying dimensions. With the aid of a multistage planning methodology over the partitioned time horizon, such a systems analysis has resulted in a full-scale screening and sequencing of multiple competing objectives across a suite of management strategies. These strategies that prioritize 20 options provide a possible expansion schedule over the next 20 years that improve water infrastructure resilience and at low life-cycle costs. The proposed method is transformative to other applications of similar water infrastructure systems elsewhere in the world. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Water supply multiobjective programming Systems analysis Regionalization Carbon footprint Adaptive water resources management

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Probabilistic reactive power procurement in hybrid electricity markets with uncertain loads

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ELECTRIC POWER SYSTEMS RESEARCH 2012年第1期82卷 68-80页

作者： Kargarian, Amin Raoofat, Mahdi Mohammadi, Mohammad Islamic Azad Univ Safashahr Branch Dept Elect & Comp Engn Safashahr Iran Shiraz Univ Sch Elect & Comp Engn Dept Power & Control Eng Shiraz Iran

This paper presents a novel probabilistic algorithm for optimal reactive power provision in hybrid electricity markets. The proposed algorithm is a six-stage multiobjective nonlinear constrained optimization problem which takes into account load forecasting inaccuracies. Considering a set of probable forecasted loads, a three-component expected total market payment function is suggested being minimized as cost function of the first stage. Besides economic issues, expected voltage security margin, deviation from multilateral and pool based energy transactions, deviation from spinning reserve contracts, having adequate local reactive power reserve in each voltage control area of the system and transmission congestion probability are well thought out in stages 2-5 as technical aspects of the market. Finally, in the last stage, using different weighting factors to compromise between all objects, a probabilistic multiobjective function is presented to find the best reactive power market schedule. The proposed algorithm is applied on IEEE 24-bus test system. As a benchmark, Monte Carlo Simulation method is utilized to simulate the market of given period of time to evaluate results of the proposed algorithm, and satisfactory results are achieved. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Hybrid electricity markets Local reactive power reserve Monte Carlo Simulation multiobjective programming Probabilistic reactive power market System security

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Improving fleet utilization for carriers by interval scheduling

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第1期218卷 261-269页

作者： Lee, Soonhui Turner, Jonathan Daskin, Mark S. Homem-de-Mello, Tito Smilowitz, Karen Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Univ Adolfo Ibanez Sch Business Santiago Chile

Carriers are under increasing pressure to offset rising fuel charges with cost cutting or revenue generating schemes. One opportunity for cost reduction lies in asset management. This paper presents resource allocation scheduling models that can be used to assign truck loads to delivery times and trucks when delivery times are flexible. The paper makes two main contributions. First, we formulate the problem as a multi-objective optimization model - minimizing the number of trucks needed as well as the costs associated with tardiness or earliness - and demonstrate how improvements in fleet usage translate into savings which carriers can use as incentives to promote flexible delivery times for customers. Second, we show that a two-phase model with a polynomial algorithm in the second phase is able to produce optimal schedules in a reasonable time. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Multi-machine scheduling Flexible delivery times Fleet size reduction Penalty costs multiobjective programming

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Interactive multiobjective optimization approach to the input-output design of opening new branches

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 530-538页

作者： Park, K. Sam Shin, Dong Eun Korea Univ Sch Business Seoul 136701 South Korea

We demonstrate a real-world application of the interactive multiple objective optimization (MOO) approach to the simultaneous setting of input and output amounts for the opening of new branches. As illustrated by the case example, all the branches of a fast-food company employ multiple inputs to generate multiple outputs. The company launches several new branches each year and, therefore, needs to plan the quantities of inputs and outputs to be used and produced before their operations. Such input-output settings are a vital practical problem that arises whenever a new branch is opened in a host of different industries. In this paper, we show in detail the entire process of the application from modeling the case problem to generating its solution. In the modeling stage, a data envelopment analysis model and a statistical method are subsequently utilized to form a nonlinear MOO problem for the input-output settings. To solve this problem, we then develop and apply an interactive MOO method, which combines the two earlier interactive methods (Geoffrion et al., 1972;Zionts and Wallenius, 1976), while compensating for their drawbacks and capturing their positive aspects. (C) 2012 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Interactive approach Nonlinear programming Data envelopment analysis Input-output design New branches

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