Branch and bound computational method for multi-objective linear fractional optimization problem

Bhati, Deepak; Singh, Pitam

doi:10.1007/s00521-016-2243-6

Cited by 16 publications

(3 citation statements)

References 41 publications

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“…Bhati and Singh [5] developed a branch and bound approach to derive solution of a multi-objective FPP. In their method, there exist several steps such as transforming maximization problem to minimization problem, converting multi-objective problem into single objective problem, calculating lower and upper bounds of the each objective function and others which lead more computational burden than our suggested FCRA technique to extract optimal solution from multi-objective FPP.…”

Section: Deficiencies Of Existing Methodsmentioning

confidence: 99%

“…Mahmoodirad et al [25] designed a linear fractional TP under uncertain environment. In recent years, many researchers have studied on FPP/FTP by considering the parameters of FTP as either a crisp or an interval or a fuzzy value, such as Chang [8], Bhati & Singh [5], Das et al [9], Ebrahimnejad et al [11], Sivri et al [43] and Arya et al [3]. In the last few decades, many researchers have shown significant interest in uncertain environment to tackle uncertainty in FTP and FCTP.…”

Section: Literature Surveymentioning

confidence: 99%

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Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

2021

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This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.

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Section: Deficiencies Of Existing Methodsmentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

2021

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“…The fractional optimization problem is one of the most difficult problems in the field of optimization. Optimization of the ratio of two functions is called fractional programming (ratio optimization) problem [13]. Indeed, in such situations, it is often a question of optimizing a ratio of output/employee, profit/cost, inventory/sales, student/cost, doctor/patient, and so on subject to some constraints [14,15].…”

Section: Introductionmentioning

confidence: 99%

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

Osman

Emam

Sayed

2017

ARJOM

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The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the-cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

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Duality-based branch–bound computational algorithm for sum-of-linear-fractional multi-objective optimization problem

et al. 2018

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Branch and bound computational method for multi-objective linear fractional optimization problem

Cited by 16 publications

References 41 publications

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

Duality-based branch–bound computational algorithm for sum-of-linear-fractional multi-objective optimization problem

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