Sperm Motility Algorithm for Solving Fractional Programming Problems under Uncertainty

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. Keywords—Sperm Motility Algorithm; Fractional Programming; Uncertainty; Fuzzy Programming; Monte Carlo Method