Euler optimizer: a novel metaheuristic algorithm for 3D UAV path planning and engineering design problems

Abstract Three-dimensional (3D) path planning for unmanned aerial vehicles (UAVs) and real-world engineering design problems has been a hot research issue. Traditional methods show limitations in dealing with these complex nonlinear models. To overcome these challenges, this paper proposes a new metaheuristic method, Euler optimizer (ELO), inspired by Euler’s method for the numerical solution of differential equations.ELO simulates Euler’s method to predict the position of the next point by the derivative and step size of the current point to perform the position updating, and sets the exploration weighting factor and the exploration factors that are used to tune the exploration and exploitation capabilities of the algorithm. We compared ELO with 11 representative state-of-the-art algorithms using the CEC2017 and CEC2022 benchmark suites, and performed the Wilcoxon rank sum test and Friedman’s test. The results show that ELO outperforms the other comparative algorithms by 90%, 96%, 99%, and 84% on CEC2017 (30/50/100 dimensions) and CEC2022 (20 dimensions), respectively. Finally, ELO is applied to UAV 3D path planning and five real-world engineering design problems. The experimental results show that ELO achieves the best compared to all 11 comparison algorithms, demonstrating ELO’s effectiveness and extensiveness in engineering optimization problems.