Research on Algorithm for Multi-Objective Symmetric Collaborative Optimization Vehicle Routing Problem with Time Windows

This paper proposes a collaborative optimization method that combines the multi-objective grey wolf optimizer (MOGWO) and the dual-thread ant colony optimization (DTACO) algorithm to solve the vehicle routing problem with time windows (VRPTW). The aim is to simultaneously optimize two often conflicting objectives: minimizing the number of vehicles and travel costs. Traditional methods usually optimize the number of vehicles or travel costs separately, making it difficult to balance the two and leading to insufficient resource utilization or excessively high travel costs in practical applications. To address this issue, this paper presents a symmetrical collaborative framework that integrates multi-objective grey wolf optimization with the dual-thread ant colony system to achieve synchronous and balanced optimization of multiple objectives. Moreover, to solve the problem of premature convergence of the algorithm, a backtracking mechanism is proposed, and its effectiveness is verified through ablation experiments. Experimental results show that this method significantly outperforms single-objective optimization algorithms on the Solomon dataset. Compared with the best known solutions (BKSs), this paper finds better solutions in some datasets, and the performance on the remaining datasets is also close to BKSs. For example, in C204-50, the lowest cost is reduced by 0.48%, in R102-50, the lowest cost is reduced by 1.29% and the number of vehicles is reduced by 1, and in RC106-50, the lowest cost is reduced by 8.48% and the number of vehicles is also reduced by 1. Therefore, the proposed algorithm provides an efficient meta-heuristic framework for VRPTW, effectively balancing the dual objectives and highlighting the value of symmetrical collaboration in multi-objective optimization.