Stochastic simulation-based genetic algorithm for chance constrained fractional programming problem

Udhayakumar, A.; Charles, Vincent; Uthariaraj, V. Rhymend

doi:10.1504/ijor.2010.034359

Cited by 11 publications

(4 citation statements)

References 30 publications

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“…[ 14 ] showed the application of probabilistic fractional goal programming involving multiple-objectives for the distribution of water resource in industries. GA is proposed to find chance constraint fractional programming by handling the probabilistic limitations using stochastic simulation [ 15 – 17 ]. In some real life circumstances, all or some data of the probabilistic programming problem are expressed by discrete random variables.…”

Section: Literature Surveymentioning

confidence: 99%

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Belay

Gessesse

2022

PLoS ONE

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This manuscript presents a technique for solving a multiple-objective probabilistic fractional programming problem with discrete random variables. A multiple-objective probabilistic mathematical model is constructed with fractional objectives. In the model, some parameters of coefficients and right hand side parameters of restrictions are assumed as random variables having Pascal and Hyper geometric distributions. The feasibility of probabilistic constraints is checked by means of stochastic simulation. Genetic algorithm approach method is used to obtain the Pareto optimal solution of the proposed model without finding the deterministic model. Genetic algorithm parameters are fixed in all generation. The proposed method is coded by C++ programming language. To illustrate the method, a numerical example and practical example on the case of supply chain management are presented. The result shows that the values of the objective functions are conflicting each other.

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Section: Literature Surveymentioning

confidence: 99%

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Belay

Gessesse

2022

PLoS ONE

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“…Bibliography on fractional mathematical programming has been presented by Stancu [22,23]. Udhayakumar et al [25] solved probabilistic fractional programming problems using stochastic simulation based genetic algorithm, where random variables follow any continuous distribution. Charles and Dutta [5] obtained the efficient solution of multi-objective stochastic fractional mathematical programming problems when the continuous random variables involved in the objective functions and constraints.…”

Section: Literature Surveymentioning

confidence: 99%

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Acharya

Belay

Mishra

2019

Mathematical Modelling and Analysis

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The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In ﬁrst step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to ﬁnd the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

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“…In all the above methods the deterministic of programming problems is required, which is difficult to find the deterministic equivalent. Udhayakumar et al [22] presented a stochastic simulation-based genetic GA for probabilistic fractional programming. They combined the parametric method developed by Charles and Dutta [23] and stochastic simulation GA to solve single-objective probabilistic linear fractional programming problem.…”

Section: Literature Surveymentioning

confidence: 99%

Solving multi-objective probabilistic factional programming problem

Belay¹,

Acharya²,

Mishra³

2019

IJEAT

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This paper presents the solution methodology of a multiobjective probabilistic fractional programming problem. In the proposed model the parameters in the constraints coefficient and the right-hand sides of the constraints follow continuous random variables having known distribution. Since the programming problem consists of random variables, multi-objective function and fractional objective function, it is lengthy, time-consuming and clumsy to solve the proposed programming problem using analytical methods. Stochastic simulation-based genetic algorithm approach is directly applied to solve multi-objective probabilistic non-linear fractional programming problem involving beta distribution and chi-square distribution. In the proposed method, it is not necessary to find the deterministic equivalent of a probabilistic programming problem and applying any traditional methods of fractional programming problem. The stochastic simulation-based genetic algorithm is coded by Code block C++ 16.01 compiler. A set of Pareto optimal solutions are generated for a multi objective probabilistic non-linear fractional programming problem. A numerical example and case study on inventory problem are presented to validate the proposed method.

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Stochastic simulation-based genetic algorithm for chance constrained fractional programming problem

Cited by 11 publications

References 30 publications

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Solving multi-objective probabilistic factional programming problem

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