Multi-UAV Path Planning Based on Cooperative Co-Evolutionary Algorithms with Adaptive Decision Variable Selection

When dealing with UAV path planning problems, evolutionary algorithms demonstrate strong flexibility and global search capabilities. However, as the number of UAVs increases, the scale of the path planning problem grows exponentially, leading to a significant rise in computational complexity. The Cooperative Co-Evolutionary Algorithm (CCEA) effectively addresses this issue through its divide-and-conquer strategy. Nonetheless, the CCEA needs to find a balance between computational efficiency and algorithmic performance while also resolving convergence difficulties arising from the increased number of decision variables. Moreover, the complex interrelationships between the decision variables of each UAV add to the challenge of selecting appropriate decision variables. To tackle this problem, we propose a novel collaborative algorithm called CCEA-ADVS. This algorithm reduces the difficulty of the problem by decomposing high-dimensional variables into sub-variables for collaborative optimization. To improve the efficiency of decision variable selection in the collaborative algorithm and to accelerate the convergence speed, an adaptive decision variable selection strategy is introduced. This strategy selects decision variables according to the order of solving single-UAV constraints and multi-UAV constraints, reducing the cost of the optimization objective. Furthermore, to improve computational efficiency, a two-stage evolutionary optimization process from coarse to fine is adopted. Specifically, the Adaptive Differential Evolution with Optional External Archive algorithm (JADE) is first used to optimize the waypoints of the UAVs to generate a basic path, and then, the Dubins algorithm is combined to optimize the trajectory, yielding the final flight path. The experimental results show that in four different scenarios involving 40 UAVs, the CCEA-ADVS algorithm significantly outperforms the Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and JADE algorithms in terms of path performance, running time, computational efficiency, and convergence speed. In addition, in large-scale experiments involving 500 UAVs, the algorithm also demonstrates good adaptability, stability, and scalability.