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Stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints

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INFORMATION SCIENCES 2008年第6期178卷 1663-1679页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

The aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent, in addition, the related dual problems for which the set of feasible parameters and the solvability set are studied. These fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers. The existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of alpha-Pareto optimality. An illustrative example is given to clarify the obtained results. (c) 2007 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming parametric programming stability fuzzy parameters fuzzy numbers alpha-Pareto optimality

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IT-CEMOP: An iterative co-evolutionary algorithm for multiobjective optimization problem with nonlinear constraints

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期183卷 373-389页

作者： Osman, M. S. Abo-Sinna, Mahmoud A. Mousa, A. A. Menoufia Univ Fac Engn Dept Basic Engn Sci Shibin Al Kawm Egypt High Inst Technol Ramadan Egypt

Over the past few years, researchers have developed a number of multiobjective evolutionary algorithms (MOEAs). Although most studies concentrate on solving unconstrained optimization problems, there exit a few studies where MOEAs have been extended to solve constrained optimization problems. Most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms. However the performance of these methods is highly problem-dependent, many methods require additional tuning of several parameters. In this paper, we present a new optimization algorithm, which is based on concept of co-evolution and repair algorithm for handling nonlinear constraints. The algorithm maintains a finite-sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of epsilon-dominance. The use of epsilon-dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation by choosing an appropriate e value, which guarantees convergence and diversity. The results, provided by the proposed algorithm for six benchmark problems, are promising when compared with exiting well-known algorithms. Also, our results suggest that our algorithm is better applicable for solving real-world application problems. (c) 2006 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming multiobjective evolutionary algorithms genetic algorithms epsilon-dominance

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An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第2期69卷 267-296页

作者： Cocchi, G. Liuzzi, G. Papini, A. Sciandrone, M. Univ Firenze Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy Univ Firenze Dipartimento Ingn Ind Viale Morgagni 40-44 I-50134 Florence Italy

This paper is concerned with the definition of new derivative-free methods for box constrained multiobjective optimization. The method that we propose is a non-trivial extension of the well-known implicit filtering algorithm to the multiobjective case. Global convergence results are stated under smooth assumptions on the objective functions. We also show how the proposed method can be used as a tool to enhance the performance of the Direct MultiSearch (DMS) algorithm. Numerical results on a set of test problems show the efficiency of the implicit filtering algorithm when used to find a single Pareto solution of the problem. Furthermore, we also show through numerical experience that the proposed algorithm improves the performance of DMS alone when used to reconstruct the entire Pareto front.

关键词： multiobjective nonlinear programming Derivative-free optimization Implicit filtering

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Interactive goal programming algorithm with Taylor series and interval type 2 fuzzy numbers

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2019年第6期10卷 1563-1579页

作者： Dalman, Hasan Bayram, Mustafa Istanbul Gelisim Univ Dept Comp Engn Istanbul Turkey

This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming Problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered fuzzy problem is first transformed into an equivalent crisp MONLPP, and then the MONLPP is converted into an equivalent multiobjective linear programming problem (MOLPP). By using an algorithm based on Taylor series, this problem is also reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by a numerical example.

关键词： Fuzzy goals Taylor series Interval type 2 fuzzy sets multiobjective nonlinear programming Interactive mechanism

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Stability of multiciteria nonlinear programming problems using fuzziness

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FUZZY SETS AND SYSTEMS 2002年第3期125卷 343-354页

作者： Badra, NM Ain Shams Univ Fac Engn Dept Engn Math Cairo Egypt

This paper presents a generalized fuzzy approach for determining the stability of multicriteria nonlinear programming problems. The proposed approach refers to an ideal, equivalent, single objective representation for the whole objectives. The membership functions for each objective function are constructed and, by the proposed formulation, the multicriteria programming problem will be transformed to an ideal equivalent single problem. By the proposed approach, the crisp intervals for the stability could be determined for the multicriteria nonlinear programming problems after solving two single nonlinear problems. Two illustrative examples are presented to verify the idea of the proposed stability approach. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multiobjective nonlinear programming decision making membership functions pareto-optimal solutions stability set

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Symmetric and self duality in vector optimization problem

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期183卷 1121-1126页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we present the first-order symmetric and self duality programs in multiobjective nonlinear programming problems. For these first-order symmetric and dual programs, we introduce the weak, strong, and converse duality theorems under convexity and concavity conditions, where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in [D.S. Kim, Y.B. Yun, H. Kuk, Second-order symmetric and self duality in multiobjective programming. Appl. Math. Lett. 10(2) (1997) 17-22]. Also, we prove the self duality theorem for these first-order self dual programs and illustrate its example. (c) 2006 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming first-order symmetric duality self duality Pareto optimal solution

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Study on multi-objective nonlinear programming problem with rough parameters

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022年第4期42卷 3591-3604页

作者： Garg, Harish Alodhaibi, Sultan S. Khalifa, Hamiden Abd El-Wahed Deemed Univ Sch Math Thapar Inst Engn & Technol Patiala 147004 Punjab India Qassim Univ Coll Sci & Arts Dept Math Arrass Saudi Arabia Cairo Univ Giza Fac Grad Studies Stat Res Dept Operat Res Giza Egypt Qassim Univ Coll Sci & Arts Dept Math Al Badayaa Saudi Arabia

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the epsilon-constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker's optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameters are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

关键词： multiobjective nonlinear programming rough set lower approximation programming problem upper approximation programming problem weighting method epsilon-constraints method parametric analysis

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Integer compromise allocation in multivariate stratified surveys

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ANNALS OF OPERATIONS RESEARCH 2015年第1期226卷 659-668页

作者： Varshney, Rahul Khan, M. G. M. Fatima, Ummatul Ahsan, M. J. Amity Univ Dept Stat Noida India Univ S Pacific Sch Comp Informat & Math Sci Suva Fiji Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

In multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. To resolve this problem, a compromise criterion is needed to work out a usable allocation. In this manuscript, a compromise criterion is discussed and integer compromise allocations are obtained by using goal programming technique. A numerical example is presented to illustrate the computational details, which reveals that the proposed criterion is suitable for working out a usable compromise allocation for multivariate stratified surveys.

关键词： Compromise allocation Goal programming multiobjective nonlinear programming Multivariate stratified sampling

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A parametric study of multiobjective NLP problems with fuzzy parameters in the objective functions

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FUZZY SETS AND SYSTEMS 1996年第2期80卷 187-196页

作者： Kassem, MAE Ammar, EE TANTA UNIV FAC SCIDEPT MATHTANTAEGYPT

This paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first kind and of the second kind) in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of alpha-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding alpha-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.

关键词： multiobjective nonlinear programming parametric analysis stability fuzzy programming fuzzy numbers

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An optimum multivariate-multiobjective stratified sampling design

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METRON-INTERNATIONAL JOURNAL OF STATISTICS 2011年第3期69卷 227-250页

作者： Ansari, Athar Varshney, Rahul Najmussehar Ahsan, Mohammad Kejriwal Inst Management & Dev Studies Ranchi Bihar India Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

It is well known that in stratified sampling design when the measurement cost does not vary from stratum to stratum, an estimate of population mean or total constructed from a sample selected according to Neyman allocation is the most precise estimate. But unfortunately the practical use of Neyman allocation suffers from a number of limitations. The most serious of all is the absence of the true values of the stratum standard deviations. When the strata standard deviations are unknown but we have additional information about the equality of standard deviations between some of the strata, we can use this information to increase the precision of the estimate by pooling the strata with equal standard deviations as a single stratum and using Neyman and proportional allocations together. This paper studies the case of multiple pooling of the standard deviations in a multivariate stratified sampling when the number of strata is more than three. The problem is formulated as a multiobjective nonlinear programming Problem. A solution procedure is developed using Goal programming approach. For computation purpose, the software LINGO is used.

关键词： Multivariate stratified sampling Compromise allocation Pooled standard deviations Multiple pooling multiobjective nonlinear programming Goal programming

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