Ibrahim M. Hezam

A hybrid flower pollination algorithm for solving ill-conditioned set of equations

In this paper, we propose a novel technique to solve the ill-conditioned system of linear and nonlinear equations. The aim of hybridisation is to combine the feature of flower pollination algorithm FPA and conjugate direction CD method. Flower pollination algorithm is employed for fast convergence and finds more than one root as well as CD method is used to increase the accuracy of the final results and avoids falling into local minima. Conjugate direction flower pollination algorithm CDFPA will be used to solve system of linear equations. The proposed algorithm retained the global search capability with more accurate and faster convergence. Numerical simulation results of all tested problems show that the proposed algorithm proved to be superior in convergence efficiency, and computational accuracy.

Stellar population analysis of galaxies based on improved flower pollination algorithm

When numerical simulations are used for determining the age and contribution of different stellar populations in the integrated colour of a galaxy some problems were encountered. In this paper, a modified flower pollination algorithm (MFPA) is proposed for determining the age and relative contribution of different stellar populations of galaxies. The results show that the proposed algorithm can search efficiently through the very large space of the possible ages for the different integrated colour of galaxies. The proposed algorithm will be applied to an integrated colour of galaxy NGC 3384. The numerical results and statistical analysis show that the proposed algorithm performs significantly better than a previously used genetic algorithm (Attia et al., 2005) and cuckoo search (Abdel-Baset et al., 2015). The study revealed that the proposed algorithm can successfully be applied to a wide range of stellar population and space optimisation problems.

Sperm motility algorithm: a novel metaheuristic approach for global optimisation

This paper proposes a new metaheuristic approach, namely, sperm motility algorithm (SMA), inspired by the fertilisation process in humans. Sperms are randomly diffused inside the female vagina to start searching for ovum. Investigation considering the modelling process of the sperm flow typical movement is carried out leading to selection of Stokes equations as mathematical model. A heuristic mechanism of sperms guided by chemoattractant secreted by ovum is to guarantee the progressing towards the goal. When the chemoattractant concentration increases the sperms are more likely to approach the ovum. Through the mimicking of the whole fertilisation process, a search approach to find a global optimisation algorithm is achieved. The proposed algorithm is tested using several standard benchmark functions as well as two engineering problems. A comparative study of the results with those obtained using well-known swarm intelligence algorithms is to validate and verify the efficiency of SMA. Getting the benefit of fertilisation chemoattractant, the proposed algorithm managed to solve unbounded constraint optimisation problems. A global optimal solution was reached in the solution of all benchmark problems proving the capability of the new algorithm to escape from local optimum.

Solving systems of nonlinear equations via conjugate direction flower pollination algorithm

In this paper, we propose a new hybrid algorithm for solving system of nonlinear equations. The aim of hybridisation is to utilise the feature of flower pollination algorithm (FPA) and conjugate direction method (CD). Conjugate direction flower pollination algorithm (CDFPA) combines the advantages of CD and FPA. The problem of solving nonlinear equations is equivalently changed to the problem of function optimisation and then a solution is obtained by CDFPA. The results show the proposed algorithm has high convergence speed and accuracy for solving nonlinear equations.

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.