• Title/Summary/Keyword: Multiobjective Programming

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ON SUFFICIENCY AND DUALITY IN MULTIOBJECTIVE SUBSET PROGRAMMING PROBLEMS INVOLVING GENERALIZED $d$-TYPE I UNIVEX FUNCTIONS

  • Jayswal, Anurag;Stancu-Minasian, I.M.
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.111-125
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    • 2012
  • In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

Cell Formation Using Fuzzy Multiobjective Nonlinear Mixed-integer Programming (다목적 비선형 혼합정수계획법을 이용한 셀 형성)

  • 오명진
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.23 no.61
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    • pp.41-50
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    • 2000
  • Cell formation(CF) Is to group parts with similar geometry, function, material and process into part families, and the corresponding machines into machine cells. Cell formation solutions often contain exceptional elements(EEs). Also, the following objective functions - minimizing the total costs of dealing with exceptional elements and maximizing total similarity coefficients between parts - have been used in CF modeling. Thus, multiobjective programming approach can be developed to model cell formation problems with two conflicting objective functions. This paper presents an effective cell formation method with fuzzy multiobjective nonlinear mixed-integer programming simultaneously to form machine cells and to minimize the cost of eliminating EEs.

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SECOND-ORDER UNIVEX FUNCTIONS AND GENERALIZED DUALITY MODELS FOR MULTIOBJECTIVE PROGRAMMING PROBLEMS CONTAINING ARBITRARY NORMS

  • Zalmai, G.J.
    • Journal of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.727-753
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    • 2013
  • In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.

Constrained Integer Multiobjective Linear Fractional Programming Problem

  • Thirwani, Deepa;Arora, S.R.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.21 no.3
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    • pp.227-236
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    • 1996
  • In this paper an algorithm based on cutting plane approach is developed which constructs all the efficient p-tuples of multiobjective integer linear fractional programming problem. The integer solution is constrained to satisfy and h out of n additional constraint sets. A numerical illustration in support of the proposed algorithm is developed.

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A Multiobjective Dynamic Programming Model for Sequenetial Testing Strategy Selection (축차검사전략의 선정을 위한 다목적. 동적계획 모형)

  • 최병돈
    • Journal of the Korean Operations Research and Management Science Society
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    • v.18 no.1
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    • pp.55-69
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    • 1993
  • The tests in a battery can be performed in different sequences, and different sequential testing strategies will have exactly the same overall performances for that battery, but at different expected total costs and expected time consumptions. By using a multiobjective dynamic programming model, we are able to find all noninferior testing strategies for a given battery of tests and a stopping rule.

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FENCHEL DUALITY THEOREM IN MULTIOBJECTIVE PROGRAMMING PROBLEMS WITH SET FUNCTIONS

  • Liu, Sanming;Feng, Enmin
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.139-152
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    • 2003
  • In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

Decision of Compensatory Aggregation Operator in Interactive Fuzzy Multiobjective Nonlinear Programming (퍼지 대화형 다목적 비선형계획에서의 절충된 통합연산자의 결정)

  • 윤연근;남현우;이상완
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.19 no.39
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    • pp.75-80
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    • 1996
  • Fuzzy approaches used to solve MONLP(Multiobjective Nonlinear Programming Problem) are based on the max-min method of fuzzy sets theory However, since the min operator noncompensatory, these approaches can not guarentee an efficient solution to the problem. In this paper, we presents an algorithm for finding the aggregation operator to find efficient solution. In particular, our presented algorithm is guarentee an efficient solution. On the basis of proposed algorithm, an illustrative numerical example is presented.

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OPTIMALITY CRITERIA AND DUALITY FOR MULTIOBJECTIVE VARIATIONAL PROBLEMS INVOLVING HIGHER ORDER DERIVATIVES

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.123-137
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    • 2009
  • A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

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Two-Phase Approach to Solve Multiobjective Nonlinear Programming Problem (다목적 비선형계획문제의 해결을 위한 2단계 접근법)

  • 이상완;남현우
    • Journal of the Korean Society of Safety
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    • v.12 no.1
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    • pp.122-128
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    • 1997
  • A new approach, called "two-phase approach", has been proposed In this study. Using this approach to solve MONLP(multiobjective nonlinear programming problem), the solution process is divied into two phase. In the first phase, the min-operator is used to aggregate the membership degree of fuzzy goals and constraints. In the second phase, the $\gamma$-operator is used to test and find an efficient solution in the sense of nondominated. It has been shown that no matter what the solution of the problem is unique or not, an efficient solution can be always obtained at the second phase. The proposed approach can be applied to industrial safety problem with multiobjective problems. On the basis of proposed approach, an illustrative numerical example is presented.presented.

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Multiobjective Nonlinear Decision Making with Fuzzy Parameters and Fuzzy Equal Goals (퍼지모수들과 퍼지항등목표들을 가지는 다목적 비선형 의사결정)

  • 윤연근;남현우;이상완
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.20 no.41
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    • pp.41-50
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    • 1997
  • In this paper, we presents the method for finding the compensatory solution for fuzzy multiobjective nonlinear programming problem with fuzzy parameters involved in the problem-formulation process and fuzzy equal goals of the decision maker for each of the objective functions. The fuzzy parameters in the objective functions and the constraints characterized by fuzzy numbers. The proposed method can be applied to case with multiobjective problems and guarantee an efficient solution. An illustrative numerical example is presented.

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