Convergence analysis of flow direction algorithm in continuous search space and its improvement

The flow direction algorithm (FDA) is a new physics-based meta-heuristic optimization algorithm that is being used successfully in a variety of applications. However, FDA lacks theoretically rigorous convergency analysis and suffers from several drawbacks, such as premature convergence, lack of population diversity, and imbalance between exploitation and exploration. In this paper, the supermartingale convergence theorem is used to analyse the global convergence of FDA in a continuous search space. We first demonstrate that FDA's global convergence is determined by the accumulation of the minimum probability (Pt*) that the flow swarm fall into the global optimal region in each iteration. Then, an improved flow direction algorithm, namely, guided flow direction algorithm (GFDA), is proposed to increase the minimum probability by making full use of the neighbourhood information. Comprehensive experimental studies were conducted to test and validate the proposed GFDA. Twenty competitive meta-heuristic optimization algorithms, twenty-three classical benchmark functions, ten recently single objective bound constrained numerical optimization problems(CEC2020), and four constrained engineering problems were used. Finally, the experimental results and statistical tests (Friedman test and Wilcoxon test) demonstrate the superiority of GFDA compared to other algorithms.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

The flow direction algorithm (FDA) is a physics-based meta-heuristic optimization algorithm that has been successfully applied in various fields. However, FDA lacks rigorous convergency analysis and faces issues such as premature convergence, lack of diversity, and imbalance between exploitation and exploration. This paper introduces the supermartingale convergence theorem to analyze FDA's global convergence and proposes an improved version called guided flow direction algorithm (GFDA) to enhance diversity and exploration. Experimental studies demonstrate the superiority of GFDA over other algorithms using multiple benchmark functions and constrained optimization problems.