Abstract
This paper investigated solving Fractional Programming Problems under Uncertainty (FPPU) using Sperm Motility Algorithm. Sperm Motility Algorithm (SMA) is a novel metaheuristic algorithm inspired by fertilization process in human, was proposed for solving optimization problems by Osama and Hezam [1]. The uncertainty in the Fractional Programming Problem (FPP) could be found in the objective function coefficients and/or the coefficients of the constraints. The uncertainty in the coefficients can be characterised by two methods. The first method is fuzzy logic-based alpha-cut analysis in which uncertain parameters are treated as fuzzy numbers leading to Fuzzy Fractional Programming Problems (FFPP). The second is Monte Carlo simulation (MCS) in which parameters are treated as random variables bound to a given probability distribution leading to Probabilistic Fractional Programming Problems (PFPP). The two different methods are used to revise the trustiness in the transformation to the deterministic domain. A comparative study of the obtained result using SMA with genetic algorithm and the two SI algorithms on a selected benchmark examples is carried out. A detailed comparison is induced giving a ranked recommendation for algorithms and methods proper for solving FPPU.
Highlights
In real life decision-making situations, the decision makers often face problems in making decision from linear/non-linear fractional programming problems (FPPs); the objectives are generally conflicted, non-commensurable and fuzzy in nature and many considerations of the vague nature of uncertainty should be taken in the formulation of the problem
Procedure II: Sperm Motility Algorithm for Probabilistic Fractional Programming Problems (PFPP) based on Monte Carlo Method: Step 1: Define the objective function and the constraints
Two different methods were used to characterise the uncertainty in the coefficients of the objective function and/or the constraints
Summary
In real life decision-making situations, the decision makers often face problems in making decision from linear/non-linear fractional programming problems (FPPs); the objectives are generally conflicted, non-commensurable and fuzzy in nature and many considerations of the vague nature of uncertainty should be taken in the formulation of the problem. There are many different algorithms to solve fuzzy fractional programming problem Many of these approaches are based upon traditional optimization or classical methods. That is, it is still inefficient and lack universality, especially for non-linear and non-differentiable fractional objective functions. L., et al [4] proposed and analysed fuzzy form of the bi-level programming by using the interactive method and by imposing the improved PSO algorithm. A. et al [10] presented a comparison between Monte Carlo simulation (MCS) and fuzzy logic-based α-level cut analysis. W.C. et al [13] proposed Particle Swarm Optimization (PSO) based on Monte Carlo simulation (MCS), to solve complex network reliability optimization problems. A stepwise interactive algorithm based on the idea of the design of the www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol 8, No 5, 2017 experiment is introduced to solve the generalised fuzzy
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