Application of a novel metaheuristic algorithm inspired by Adam gradient descent in distributed permutation flow shop scheduling problem and continuous engineering problems.

Over the past few years, numerous swarm intelligence-based metaheuristic algorithms have been introduced and extensively applied. Although these algorithms draw on biological behaviors, their similar heuristic paradigms and modular designs lead to unbalanced exploration and exploitation in complex optimization problems. Metaheuristic algorithms that combine mathematical properties with stochastic search processes can help break through the traditional evolutionary paradigm and enhance individual optimization. In pursuit of this goal, this study introduces an innovative meta-heuristic algorithm grounded in mathematics, called the Adam Gradient Descent Optimizer (AGDO), designed for addressing continuous optimization and engineering challenges. AGDO is inspired by the Adam optimizer and explores the entire search process using three rules: progressive gradient momentum integration, dynamic gradient interaction system, and system optimization operator. The progressive gradient momentum integration and dynamic gradient interaction system balance exploration and exploitation well, while the system optimization operator refines the exploitation aspect. AGDO's performance, in conjunction with several well-known and newly introduced metaheuristics, is assessed on the CEC2017 benchmarks across various dimensions and six practical engineering challenges. The Wilcoxon rank-sum test confirms its efficacy. The findings from the experiment indicate that AGDO demonstrates strong performance across four dimensions-10, 30, 50, and 100-when compared to 19 other algorithms, and it achieves the highest Wilcoxon rank-sum test scores in three of these dimensions. AGDO is also compared to six SOTA algorithms, the findings show that the algorithm maintains an excellent equilibrium between exploration and exploitation, converges rapidly, and successfully evades local optima, highlighting superior optimization performance. Moreover, AGDO demonstrates significant effectiveness and excellence in addressing intricate real-life challenges. Notably, AGDO demonstrated extreme strengths in Distributed Permutation Flow Shop Scheduling Problem (DPFSP). Source codes of AGDO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/180348-agdo .