A Metropolis-Based Ant Colony Optimization Algorithm with Dynamic Exploration for UAV 3D Path Planning

Abstract

Traditional Ant Colony Optimization (ACO) suffers from premature convergence, slow convergence speed, and insufficient path smoothness in three-dimensional (3D) unmanned aerial vehicle (UAV) path planning. This paper proposes a Metropolis-based dynamic exploration ACO algorithm (MACO) that introduces four complementary mechanisms: (1) probabilistic acceptance of inferior solutions via the Metropolis criterion to escape local optima; (2) a linearly decaying dynamic exploration rate to balance global exploration and local exploitation; (3) adaptive step size adjustment to improve late-stage search precision; and (4) adaptive pheromone evaporation (0.7 to 0.3) to regulate convergence. Comparative experiments are conducted in a 250× 250 continuous 3D environment with six algorithms over 30 independent runs. Results show that MACO achieves the best mean fitness of $367.80 \pm 3.12$ and the shortest path length of 338.42m with a 100% collision-free rate. The Wilcoxon rank-sum test confirms MACO's statistically significant superiority $(p<0.001)$.