Raindrop optimizer: a novel nature-inspired metaheuristic algorithm for artificial intelligence and engineering optimization.

This paper presents a novel meta-heuristic optimization method, the Raindrop Algorithm (RD), inspired by natural raindrop phenomena, and explores its applications in artificial intelligence. The raindrop algorithm comprises two primary phases: exploration and exploitation. During the exploration phase, mechanisms including splash, diversion, and evaporation are employed to enhance global search capabilities. In the exploitation phase, raindrop convergence and overflow behaviors are simulated to improve local search performance. The algorithm demonstrates rapid convergence characteristics, typically achieving optimal solutions within 500 iterations while maintaining computational efficiency. The effectiveness and competitiveness of the raindrop algorithm have been validated on 23 benchmark functions and the CEC-BC-2020 benchmark suite, achieving first-place rankings in 76% of test cases. Specifically, on the CEC-BC-2020 benchmark, Wilcoxon rank-sum tests ([Formula: see text]) demonstrate statistically significant superiority in 94.55% of comparative cases. The raindrop algorithm has been successfully applied to optimize state estimation filters and controller parameters in robotic engineering problems, achieving an 18.5% reduction in position estimation error and a 7.1% improvement in overall filtering accuracy compared to conventional methods. Experimental results across five distinct engineering scenarios confirm the competitiveness and versatility of the raindrop algorithm, consistently maintaining top-three rankings in complex, nonlinear, and constrained optimization problems, thereby providing a promising solution for challenging optimization tasks in artificial intelligence-driven engineering environments.