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Some results on symmetric duality of multiobjective programmes with generalized (F,ρ) invexity

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期168卷 333-339页

作者： Ojha, DB Mukherjee, RN Banaras Hindu Univ Inst Technol Dept Appl Math Varanasi 221005 Uttar Pradesh India

In this present article we have given some multiobjective programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used most general type of invexity assumptions involved with the functions which are related to the programming problems. It is to be pointed out that the objective functions in such programs contain terms like support functions which in turn are able to give results on particular classes of programs involving quadratic terms. Our results in particular give as special cases some earlier results on symmetric duals given in the current literature. (c) 2004 Published by Elsevier B.V.

关键词： multiobjective programming symmetric duality generalized (F, rho) invexity

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INTERACTIVE WEIGHT ASSESSMENT IN MULTIPLE ATTRIBUTE DECISION-MAKING

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1985年第1期22卷 19-25页

作者： MOND, B ROSINGER, EE UNIV PRETORIA DEPT MATHPRETORIA 0002SOUTH AFRICA CSIR NATL RES INST MATH SCIPRETORIASOUTH AFRICA

A weight assessing method is given for solving a multiple attribute decision problem involving one decision maker. The method provides significant freedom to the decision maker who is asked only to specify certain groups of attributes and the corresponding joint weights. The method then provides a sophisticated interaction between various levels of the attributes involved. Furthermore, if the decision maker wishes to give additional information of the above-mentioned kind, he establishes an interaction on the level of the solution process. This can compensate for the inherent limitations of any method based on scalar utility functions by allowing a certain intransitivity and incomparability of preferences, which are natural in multiple attribute situations.

关键词： Interactive weight assessment multiobjective programming one decision maker

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Expected value multiobjective portfolio rebalancing model with fuzzy parameters

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INSURANCE MATHEMATICS & ECONOMICS 2013年第2期52卷 190-203页

作者： Gupta, Pankaj Mittal, Garima Mehlawat, Mukesh Kumar Univ Delhi Dept Operat Res Delhi 110007 India Apeejay Sch Management Dept Decis Sci New Delhi India

In this paper we develop a multicriteria credibilistic framework for portfolio rebalancing. We use an expected value model with fuzzy parameters considering return, risk and liquidity as key financial criteria. The transaction costs are assumed to be paid on the basis of incremental discounts and are adjusted in the net return of the portfolio. A solution procedure based on fuzzy goal programming and a hybrid intelligent algorithm that combines fuzzy simulation with a real-coded genetic algorithm is presented to solve the portfolio rebalancing problem. The approach adopted here has the advantage of handling the multicriteria portfolio rebalancing problem where the fuzzy parameters are characterized by general functional forms. An empirical study is included to demonstrate the effectiveness of the solution approach and efficiency of the model in practical applications of rebalancing an existing portfolio. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Fuzzy portfolio rebalancing Transaction costs Expected value model multiobjective programming Real-coded genetic algorithm

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Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory

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INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2018年第3期17卷 941-968页

作者： Liu, Yong-Jun Zhang, Wei-Guo South China Univ Technol Sch Business Adm Guangzhou 510641 Guangdong Peoples R China

Using the central value operator and the semi-dispersion measure of fuzzy number, this paper proposes the definitions of the lower and upper semi-variances. A general multiperiod fuzzy portfolio optimization model with return demand on the portfolio at each period is proposed with the objectives of maximizing both terminal wealth and the cumulative diversification degree of portfolios over the whole investment horizon, and minimizing terminal risk. A fuzzy multiobjective nonlinear programming technique is applied to convert the proposed model into a single-objective model. A genetic algorithm (GA) is given to solve it. Besides, a numerical example is given to illustrate the application of the proposed model and the effectiveness of the designed algorithm.

关键词： Multiperiod portfolio selection possibility theory central value operator entropy multiobjective programming

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Mixed type duality for multiobjective variational problems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2000年第2期252卷 571-586页

作者： Mukherjee, RN Rao, CP Banaras Hindu Univ Inst Technol Dept Appl Math Varanasi 221005 Uttar Pradesh India

The concept of mixed-type duality has been extended to the class of multiobjective variational problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained for rho -convex (generalized rho -convex) functions. These studies have been generalized to the case of rho -invex (generalized rho -invex) functions. Our results apparently generalize a fairly large number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions. (C) 2000 Academic Press.

关键词： mixed-type dual efficient solution p-convex p-invex multiobjective programming

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multiobjective optimal control of the linear wave equation

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AIN SHAMS ENGINEERING JOURNAL 2014年第4期5卷 1299-1305页

作者： Zarei, Hassan Bahrmand, Mehdi Rezai Payame Noor Univ Dept Math Tehran Iran

In this paper, we propose a method for the solution of a multiobjective optimal control problem (MOOCP) in a linear distributed-parameter system governed by a wave equation. An explicit solution for the wave equation is derived and the control problem of this distributedparameter system is reduced to an approximate multiobjective programming problem. The fuzzy goals are incorporated for objectives and the equilibrium problem in terms of maximization of the degree of attainment for the aggregated fuzzy goals is considered. The solution of the equilibrium optimization problem is a Pareto optimal solution with the best satisfaction performance which is achieved by using a metaheuristic algorithm such as the simulated annealing (SA) together with the simplex method of linear programming (LP) problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method and the capability of the SA in finding optimal solution compared with two popular metaheurestics. (C) 2014 Production and hosting by Elsevier B. V. on behalf of Ain Shams University.

关键词： Linear distributed-parameter systems multiobjective optimal control multiobjective programming Fuzzy programming Fuzzy goals Metaheuristic algorithms

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A multiobjective APPROACH TO VENDOR SELECTION

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1993年第2期68卷 173-184页

作者： WEBER, CA CURRENT, JR OHIO STATE UNIV FAC MANAGEMENT SCICOLUMBUSOH 43210

Purchases from vendors involve significant costs for many firms. Decisions related to these purchases include the selection of vendors and the determination of order quantities to be placed with the selected vendors. Such decisions are frequently multiobjective in nature. That is, they are evaluated by more than one criterion. At least 23 criteria for various vendor selection problems have been identified. In this article, we present a multiobjective approach to systematically analyze the inherent tradeoffs involved in multicriteria vendor selection problems. The approach is motivated by, and demonstrated with, an actual purchasing problem facing a division of a Fortune 500 company.

关键词： multiobjective programming PURCHASING VENDOR SELECTION DECISION SUPPORT SYSTEM

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FUZZY COORDINATION OF multiobjectiveS REFLECTING THE OPERATORS INTENTION FOR DYNAMIC GENERATION RESCHEDULING

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 1992年第5期14卷 314-320页

作者： MAEKAWA, T YASUDA, K YOKOYAMA, R OHTSUKI, H MIZUKAMI, Y Department of Electric Engineering Tokyo Metropolitan University 1-1 Minami-Osawa Hachioji-City Tokyo 192-03 Japan Kansai Electric Power Co. Inc. 3-3-22 Nakanoshima Kita-ku Osaka 530 Japan

This paper proposes a novel and efficient algorithm to obtain the optimal generation dispatch reflecting the operator's intention in power system rescheduling by solving a multi-objective optimization problem. In deciding the optimal system operation, various objectives, such as economy, quality and transmission security, should be attained simultaneously. However, these objectives are contradictory to each other and are in trade-off relations, thus making it difficult to handle this class of problems by conventional approaches. In the proposed algorithm, the optimal generation dispatch problem is formulated as a multi-objective optimization problem. Fuzzy coordination technique based on fuzzy set theory is used to obtain an optimal solution. Evaluation indices composed of fuel cost, transmission line overload and AFC regulation capacity margin are measured by the membership functions, and multi-objective optimization is solved by maximizing the composite performance index, namely, the fuzzy decision-making The proposed algorithm has made it possible to treat optimal dispatch problems with multiple objectives and to grasp trade-off relations between selected indices. The effect of uncertain factors pertaining to power systems can also be taken into account. The choice of membership function parameters, reflecting the operator's preference of one of the objectives, influences the overall performance of the optimization procedure. Such an approach allows system operators to decide on different preferences according to system operating conditions, thus resulting in a more flexible operation. The validity and effectiveness of the proposed approach are verified through numerical examples on the 10 mode, 5 generator system.

关键词： FUZZY SET THEORY GENERATION CONTROL ECONOMIC DISPATCH AFC REGULATION CAPACITY LINE SECURITY multiobjective programming

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A Revised Pascoletti-Serafini Scalarization Method for multiobjective Optimization Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2018年第2期178卷 560-590页

作者： Akbari, Fereshteh Ghaznavi, Mehrdad Khorram, Esmaile Amirkabir Univ Technol Fac Math & Comp Sci Hafez Ave Tehran Iran Shahrood Univ Technol Fac Math Sci Shahrood Iran

The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti-Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti-Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti-Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples.

关键词： multiobjective programming Scalarization technique Pascoletti-Serafini method Properly efficient solution

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A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期238卷 475-496页

作者： Petridis, Konstantinos Chatzigeorgiou, Alexander Stiakakis, Emmanouil Aston Univ Aston Business Sch Birmingham B4 7ET W Midlands England Univ Macedonia Dept Appl Informat Thessaloniki 54006 Greece

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA (S-T DEA) approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a multiobjective Mixed Integer Linear programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

关键词： Data Envelopment Analysis Efficiency OR in software multiobjective programming Linear programming

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