Abstract: Aiming at the multi-depot vehicle routing problem with time windows, we constructed a model with the goal of minimizing total cost,  proposed an improved dung beetle optimizer algorithm based on multi-strategy, and solved it. By introducing a hierarchical system to update rolling dung beetles, it established communication with top-tier beetles to enhance the algorithm’s search capability. Differential variation was designed to perturb the positions of reproductive dung beetles and  reduce the likelihood of getting stuck in local optima. Probability-driven random foraging behavior was devised for foraging dung beetles, enabling them to randomly explore broader search spaces to find potential optimal solutions. Adversarial learning was using to generate reverse 
solutions for thief dung beetles, increasing the probability of finding better candidate solutions and strengthening the algorithm’s optimization capability. This algorithm was using to solve the multi-depot vehicle routing  problem with time windows. Comparative experiments with six other intelligent algorithms on the Solomon dataset show that the proposed algorithm is superior to other comparative algorithms and has good  search capabilities and application value.

Key words: dung beetle optimizer algorithm, multi-depot vehicle routing problem, differential variation, social hierarchy, adversarial learning