Parametric Solution Algorithms for Large-Scale Mixed-Integer Fractional Programming Problems and Applications in Process Systems Engineering

Zhong, Zhixia; You, Fengqi

doi:10.1016/b978-0-444-63456-6.50044-2

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…Miettinen [32] clarified several methods to solve multiobjective optimization problems [17]. The mixed integer fractional programming problems were solved by Zhixia and Fengqi [33]. The fuzzy linear fractional programming problems were considered by Das et al [34] and by Chinnadurai and Muthukumar [35].…”

Section: Introductionmentioning

confidence: 99%

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Saad

Taha

2023

Arab Journal of Nuclear Sciences and Applications

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This paper presents the use of a Taylor series for multiobjective integer linear fractional programming problem having grey parameters in the right-side of the constraints (GMOILFP). To deal with the grey parameters in the right-side of the constraints the positioned programming should be used. An equivalent grey multiobjective linear fractional programming problem (GMOLFP) is formulated using Gomory's cutting plane method. The Taylor series, which is a series expansion that a representation of a function, is applied to convert the fractional functions into polynomials. In the proposed approach a white value of each grey parameter is determined, Taylor series is applied and the functions are unified by using the nonnegative weighted sum method. Thus, the problem is reduced to a single linear objective with grey parameter in the right side of the constrains. An algorithm for solving GMOILGP problem with grey interval coefficients using positioned programming and Taylor series polynomials is proposed. A numerical example is provided to demonstrate the efficiency and feasibility of the proposed approach. A special case study for handling the environmental economic energy dispatch problem also is included in this paper, the main goal of this problem is how to schedule committed generators to meet the load required to minimize the pollution emissions and fuel cost. The model formulation for a special case study problem is presented, the mathematical model will be considered as (GMOLFP) and the problem is solved according to the proposed solution algorithm.

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Section: Introductionmentioning

confidence: 99%

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Saad

Taha

2023

Arab Journal of Nuclear Sciences and Applications

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“…Miettinen (2012) showed numerous approaches to solving multi-objective optimization problems. Zhong and You (2014) suggested a parametric approach to solving mixed integer linear and non-linear fractional programming problems by converting them into the equivalent parametric formulation.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

Solomon¹,

Zaher²,

Saied³

2023

Int. j. adv. appl. sci.

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An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development of the proposed algorithm is based on the principle of optimal decision set achieved by the intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Additionally, as the intuitionistic fuzzy optimization method utilizes the degree of belonging and degree of non-belonging, we used the linear membership function for belonging and non-belonging to see its impact on optimization and to get insight into such an optimization process. The proposed approaches have been illustrated with numerical examples.

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Solution approach to multi-objective linear fractional programming problem using parametric functions

Nayak

Ojha

2019

OPSEARCH

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Parametric Solution Algorithms for Large-Scale Mixed-Integer Fractional Programming Problems and Applications in Process Systems Engineering

Cited by 4 publications

References 10 publications

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

Solution approach to multi-objective linear fractional programming problem using parametric functions

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