Fick's Law Algorithm: a physical law-based algorithm for numerical optimization

Fatma A. Hashim, Reham R. Mostafa, Abdelazim G. Hussien, Seyedali Mirjalili, Karam M. Sallam

Research output: Contribution to journalArticlepeer-review

94 Citations (Scopus)


Recently, many metaheuristic optimization algorithms have been developed to address real-world issues. In this study, a new physics-based metaheuristic called Fick's law optimization (FLA) is presented, in which Fick's first rule of diffusion is utilized. According to Fick's law of diffusion, molecules tend to diffuse from higher to lower concentration areas. Many experimental series are done to test FLA's performance and ability in solving different optimization problems. Firstly, FLA is tested using twenty well-known benchmark functions and thirty CEC2017 test functions. Secondly, five real-world engineering problems are utilized to demonstrate the feasibility of the proposed FLA. The findings are compared with 12 well-known and powerful optimizers. A Wilcoxon rank-sum test is carried out to evaluate the comparable statistical performance of competing algorithms. Results prove that FLA achieves competitive and promising findings, a good convergence curve rate, and a good balance between exploration and exploitation. The source code is currently available for public from:

Original languageEnglish
Article number110146
Pages (from-to)1-22
Number of pages22
JournalKnowledge-Based Systems
Publication statusPublished - 25 Jan 2023


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