• Title/Summary/Keyword: Multiobjective Programming

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MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

  • Kim, Moon-Hee
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.179-196
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    • 2004
  • Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

Interactive Fuzzy Multiobjective Decision-Making with Imprecise Goals (모호한 목표를 가진 대화형 퍼지 다목적 의사결정)

  • ;;Hong, S. L.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.17 no.3
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    • pp.67-78
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    • 1992
  • MODM (multiobjective decision-making) problem is very complex system for the analyst. The problem is more complex if the goals of each of the objective functions are expressed imprecisely. It requires suitable MODM method to deal with imprecisions. Therefore, we present a new interactive fuzzy decision making method for solving multiobjective nonlinear programming problems by assuming that the decision maker (DM) has imprecise goals that assume fuzzy linguistic variable for each of the objective functions. The imprecise goals of the DM are quantified by eliciting corresponding membership functions through the interactive with the DM out of six membership functions. After determining membership functions, in order to generate the compromise or satisficing solution which is .lambda.-pareto optimal, .lambda.-max problem is solved. The higher degree of membership is chosen to satisfy imprecise goals of all objective functions by combining the membership functions. Then, the values are the compromise or satisficing solution. On the basis of the proposed method, and interactive computer programming is written to implement man-machine interactive procedures. Our programming is a revised version of sequential unconstrained minimization technique. Finally, a numerical example illustrates various aspects of the results developed in this paper.

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Multiobjective Optimization of Three-Stage Spur Gear Reduction Units Using Interactive Physical Programming

  • Huang Hong Zhong;Tian Zhi Gang;Zuo Ming J.
    • Journal of Mechanical Science and Technology
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    • v.19 no.5
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    • pp.1080-1086
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    • 2005
  • The preliminary design optimization of multi-stage spur gear reduction units has been a subject of considerable interest, since many high-performance power transmission applications (e.g., automotive and aerospace) require high-performance gear reduction units. There are multiple objectives in the optimal design of multi-stage spur gear reduction unit, such as minimizing the volume and maximizing the surface fatigue life. It is reasonable to formulate the design of spur gear reduction unit as a multi-objective optimization problem, and find an appropriate approach to solve it. In this paper an interactive physical programming approach is developed to place physical programming into an interactive framework in a natural way. Class functions, which are used to represent the designer's preferences on design objectives, are fixed during the interactive physical programming procedure. After a Pareto solution is generated, a preference offset is added into the class function of each objective based on whether the designer would like to improve this objective or sacrifice the objective so as to improve other objectives. The preference offsets are adjusted during the interactive physical programming procedure, and an optimal solution that satisfies the designer's preferences is supposed to be obtained by the end of the procedure. An optimization problem of three-stage spur gear reduction unit is given to illustrate the effectiveness of the proposed approach.

SECOND ORDER NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEM INVOLVING SUPPORT FUNCTIONS

  • Kharbanda, Pallavi;Agarwal, Divya;Sinha, Deepa
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.835-852
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    • 2013
  • In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

Interval Valued Solution of Multiobjective Problem with Interval Cost, Source and Destination Parameters

  • Hong, Dug-Hun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.1
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    • pp.42-46
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    • 2009
  • Das et al. [EJOR 117(1999) 100-112] discussed the real valued solution procedure of the multiobjective transportation problem(MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. In this note, we consider the interval valued solution procedure of the same problem. This problem has been transformed into a classical multiobjective transportation problem where the constraints with interval source and destination parameters have been converted into deterministic ones. Numerical examples have been provided to illustrate the solution procedure for this case.

Multiobjective R&D Investment Planning under Uncertainty (불확실한 상황하에서의 다복적 R & D 투자계획수립에 관한 연구-최적화 기법과 계층화 분석과정의 통합접 접근방안을 중심으로-)

  • 이영찬;민재형
    • Journal of the Korean Operations Research and Management Science Society
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    • v.20 no.2
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    • pp.39-60
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    • 1995
  • In this paper, an integration of stochastic dynamic programming (SDP), integer goal programming (IGP) and analytic hierarchy process (AHP) is proposed to handle multiobjective-multicriteria sequential decision making problems under uncertainty inherent in R & D investment planning. SDP has its capability to handle problems which are sequential and stochastic. In the SDP model, the probabilities of the funding levels in any time period are generated using a subjective model which employs functional relationships among interrelated parameters, scenarios of future budget availability and subjective inputs elicited from a group of decision makers. The SDP model primarily yields an optimal investment planning policy considering the possibility that actual funding received may be less than anticipated one and thus the projects being selected under the anticipated budget would be interrupted. IGP is used to handle the multiobjective issues such as tradoff between economic benefit and technology accumulation level. Other managerial concerns related to the determination of the optimal project portifolio within each stage of the SDP model. including project selection, project scheduling and annual budget allocation are also determined by the IGP. AHP is proposed for generating scenario-based transformation probabilities under budgetary uncertainty and for quantifying the environmental risk to be considered.

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A Study on IFGP Model for Solving Multiobjective Quality Management under Fuzzy Condition

  • Cheong, Jong Shik;Pak, Pyong Ki
    • Journal of Korean Society for Quality Management
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    • v.21 no.2
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    • pp.194-214
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    • 1993
  • This paper purports to study on interactive fuzzy goal programming model which leads to the compromise solution which the decision maker satisfies through the interactive approach. We also attempted to calculate local proxy preference function from utility function of sum-of-logarithms in connection with marginal rate of substitution and interactive approach for the purpose of applying weight of multiobjective function. In an attempt to grasp compromise solution from fuzzy efficient solution, we decided to take the interactive method and presented stopping rule for this.

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MULTIOBJECTIVE SECOND-ORDER NONDIFFERENTIABLE SYMMETRIC DUALITY INVOLVING (F, $\alpha$, $\rho$, d)-CONVEX FUNCTIONS

  • Gupta, S.K.;Kailey, N.;Sharma, M.K.
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1395-1408
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    • 2010
  • In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.