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multiobjective higher-order symmetric duality involving generalized cone-invex functions

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第12期60卷 3187-3192页

作者： Gupta, S. K. Jayswal, Anurag Indian Inst Technol Patna Dept Math Patna 800013 Bihar India Birla Inst Technol Mesra Dept Appl Math Ranchi 835215 Bihar India

In this paper, a pair of Mond-Weir type multiobjective higher-order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher-order K-preinvexity/K-pseudoinvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also discussed. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Cone constraints Efficiency Duality

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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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Semistrictly quasiconvex mappings and non-convex vector optimization

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2004年第1期59卷 129-145页

作者： Flores-Bazán, F Univ Concepcion Dept Ingn Matemat Concepcion Chile

This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with Psubset of or equal toR(m) being the underlying ordering cone, called semistrictly (R-m\-int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit (R-m\-int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.

关键词： non-convex vector functions weakly efficient solution vector optimization multiobjective programming asymptotic cone

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GENERALIZED QUASICONVEXITIES, CONE SADDLE-POINTS, AND MINIMAX THEOREM FOR VECTOR-VALUED FUNCTIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第2期81卷 355-377页

作者： TANAKA, T NIIGATA UNIV GRAD SCH SCI & TECHNOLDEPT MATH SCINIIGATA 95021JAPAN

We establish the following theorems: (i) an existence theorem for weak type generalized saddle points;(ii) an existence theorem for strong type generalized saddle points;(iii). a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are bawd on a few key observations and also on the Browder coincidence. theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.

关键词： MINIMAX THEOREMS multiobjective programming VECTOR OPTIMIZATION VECTOR-VALUED FUNCTIONS CONE CONVEXITY DEMICONTINUITY CONE SADDLE POINTS POINTED CONVEX CONES

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A Hierarchical Self-Adaptive Data-Analytics Method for Real-Time Power System Short-Term Voltage Stability Assessment

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2019年第1期15卷 74-84页

作者： Zhang, Yuchen Xu, Yan Dong, Zhao Yang Zhang, Rui Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

As one of the most complex and largest dynamic industrial systems, a modern power grid envisages the wide-area measurement protection and control (WAMPAC) system as the grid sensing backbone to enhance security, reliability, and resiliency. However, based on the massive wide-area measurement data, how to realize real-time short-term voltage stability (STVS) assessment is an essential yet challenging problem. This paper proposes a hierarchical and self-adaptive data-analytics method for real-time STVS assessment covering both the voltage instability and the fault-induced delayed voltage recovery phenomenon. Based on a strategically designed ensemble-based randomized learning model, the STVS assessment is achieved sequentially and self-adaptively. Besides, the assessment accuracy and the earliness are simultaneously optimized through the multiobjective programming. The proposed method has been tested on a benchmark power system, and its exceptional assessment accuracy, speed, and comprehensiveness are demonstrated by comparing with existing methods.

关键词： Data-analytics ensemble learning extreme learning machine multiobjective programming short-term voltage stability (STVS) smart grid

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Second-order efficiency conditions and sensitivity of efficient points

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第3期98卷 569-592页

作者： Bolintineanu, S El Maghri, M Univ Perpignan Lab Anal Nonlineaire & Optimisat F-66025 Perpignan France

The paper deals with necessary and sufficient efficiency conditions of first and second order in vector differential optimization in Banach spaces. The conditions presented ensure the Frechet sensitivity of efficient (Pareto) points for a perturbed problem. In finite dimension, weaker conditions ensure the Lipschitz sensitivity and existence of directional derivatives of perturbed efficient points.

关键词： vector optimization multicriteria optimization multiobjective programming efficiency weak efficiency proper efficiency post-Pareto analysis efficiency conditions sensitivity analysis

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Note on Mond-Weir type nondifferentiable second order symmetric duality

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OPTIMIZATION LETTERS 2008年第4期2卷 599-604页

作者： Husain, Z. Ahmad, I. Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this paper, we point out some inconsistencies in the earlier work of Ahmad and Husain (Appl. Math. Lett. 18, 721-728, 2005), and present the correct forms of their strong and converse duality theorems.

关键词： Nondifferentiable programming multiobjective programming Second order symmetric duality

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A hybrid genetic algorithm model for transshipment management decisions

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2009年第2期122卷 703-713页

作者： Sharma, Dinesh K. Jana, R. K. Univ Maryland Eastern Shore Dept Business Management & Accounting Princess Anne MD 21853 USA Indian Inst Social Welf & Business Management Kolkata India

Transshipment is a critical area of supply chain management that may lead to cost reductions and improved services for companies to make greater profits and to become more competitive. In this study, we present a transshipment planning model for the petroleum refinery industry. The main objective of the model is to minimize the total transshipment cost, maximize production, satisfy storage requirements at depots and meet the demand for oil in these sales areas. To accommodate imprecision, the goals are defined in a fuzzy sense and a fuzzy goal programming (FGP) model is developed. To provide flexibility to the decision-maker, we integrate a genetic algorithm (GA) within the FGP framework in such a way that it can find solutions for different sets of target and tolerance values of the goals in a single run. A case example is presented to demonstrate the usefulness of the integrated technique. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Transshipment planning Genetic algorithm multiobjective programming Fuzzy goal programming

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A game-theoretic approach for the web services scheduling problem

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EXPERT SYSTEMS WITH APPLICATIONS 2014年第10期41卷 4743-4751页

作者： Fontanini, W. Ferreira, P. A. V. Ctr Informat Technol Renato Archer BR-13069901 Campinas SP Brazil Univ Estadual Campinas Fac Elect & Comp Engn BR-13082852 Campinas SP Brazil

We address the design of an Internet-based business process composed of several web services by using multiobjective optimization and game-theoretic methods. Adopting a suitable representation for the business process, we present a mathematical optimization problem which considers several quality-of-service objectives: cost, execution time, reliability, availability and reputation. The web service scheduling problem is formulated as a multiobjective mixed-integer linear optimization problem and solved through a goal optimization method. The optimal solution of the scheduling problem assigns suppliers to all the tasks that comprise the business process, thus establishing the revenues - utilities - of all the suppliers. We then model the interaction between the suppliers as an incomplete information (Bayesian) game: the structure of the game is common knowledge of all the suppliers, but each supplier knows only his/her own utility function. A characterization of the Bayes-Nash equilibria of the game is provided. The paper includes numerical examples. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： E-commerce Scheduling Integer programming multiobjective programming Game theory

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A multiobjective APPROACH TO DESIGN FRANCHISE OUTLET NETWORKS

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1994年第1期45卷 71-81页

作者： CURRENT, JR STORBECK, JE OHIO STATE UNIV DEPT MANAGEMENT SCICOLUMBUSOH 43210 USA

The economic goals and the resulting locational objectives of a franchisor and its individual franchisees are frequently in conflict. For example, one goal of the franchisor is to maximize system-wide market coverage, while the corresponding goal of the franchisee is to maximize his or her individual market share. Consequently, the optimal facility siting scheme from one perspective may be suboptimal from the other. That is, the facility siting scheme which maximizes system-wide coverage will not necessarily maximize the market shares of the individual franchises which make up the system. In this paper we introduce a multiobjective integer programming model to design franchise networks. The model selects franchise locations and identifies individual franchise market areas. Constraints in the formulation guarantee that all franchise locations are assigned at least a minimal threshold market area with sufficient demand to ensure economic survival. An underlying assumption of the model is that a rationing mechanism exists to assign demand to various franchise locations. Consequently, the model is most appropriate for service delivery franchises in which the franchisor can define and enforce exclusive franchise territories for the various franchise outlets. The purpose of this model is to generate alternative siting configurations which demonstrate the inherent trade-offs between the objectives of the franchisor and the individual franchisees. Given these various location alternatives, it is expected that the franchisor will then evaluate them in terms of other criteria such as the likelihood of the individual franchisee's success, pricing strategies for the various sites, total costs, total profit, and the effects of the response of competitors. Consequently, the proposed model should be viewed as an aid for one aspect of the decision process, i.e. the generation of alternative courses of action.

关键词： FRANCHISE NETWORK DESIGN multiobjective programming

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