An Improved Flower Pollination Algorithm with Chaos

Abstract

Flower pollination algorithm is a new nature-inspired algorithm, based on the characteristics of flowering plants. In this paper, a new method is developed based on the flower pollination algorithm combined with chaos theory (IFPCH) to solve definite integral. The definite integral has wide ranging applications in operation research, computer science, mathematics, mechanics, physics, and civil and mechanical engineering. Definite integral has always been useful in biostatistics to evaluate distribution functions and other quantities. Numerical simulation results show that the algorithm offers an effective way to calculate numerical value of definite integrals, and it has a high convergence rate, high accuracy and robustness.

On the performances of the flower pollination algorithm – Qualitative and quantitative analyses

“…The authors compare the FPA variant they devise to the basic harmony search algorithm and one of its variants, but the parameters of these algorithms and the criteria of comparison (total number of function evaluations) are missing. Publication 12 [33]: Abdel-Raouf et al [33] extend in this work the basic FPA by including chaotic search. They apply this algorithm to the definite integral problem.…”

“…We categorise them into 4 classes: (1) The works proposed by Yang and his co-authors [18,[22][23][24][25], (2) the works just applying the FPA for solving optimisation problems [27][28][29][30], (3) FPA extensions [31][32][33][34][35] and (4) the works analysing the FPA performances [36][37][38]. These contributions are analysed with greater detail in the next section.…”

On the efficiency of the binary flower pollination algorithm: Application on the antenna positioning problem

“…In [52], the FPA was hybridised with the particle swarm optimisation algorithm to solve the active power loss. A chaotic FPA was introduced in [40,65]. The FPA was also used in [59] for wireless sensor network optimisation.…”

A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming Problems

“…Moreover, it depends on its initial condition and parameters [32][33][34]. Applications of chaos has several disciplines including operations research, physics, engineering, economics, biology, philosophy and computer science [35][36][37]. Recently chaos has been extended to various optimization areas because it can more easily escape from local minima and improve global convergence in comparison with other stochastic optimization algorithms [34][35][36][37][38].…”