The well-known Vehicle Routing Problem with Time Windows (VRPTW) aims to reduce the cost of moving goods between several destinations while accommodating constraints like set time windows for certain locations and vehicle capacity. Applications of the VRPTW problem in the real world include Supply Chain Management (SCM) and logistic dispatching, both of which are crucial to the economy and are expanding quickly as work habits change. Therefore, to solve the VRPTW problem, metaheuristic algorithms i.e. Particle Swarm Optimization (PSO) have been found to work effectively, however, they can experience premature convergence. To lower the risk of PSO's premature convergence, the authors have solved VRPTW in this paper utilising a novel form of the PSO methodology that uses the Roulette Wheel Method (RWPSO). Computing experiments using the Solomon VRPTW benchmark datasets on the RWPSO demonstrate that RWPSO is competitive with other state-of-the-art algorithms from the literature. Also, comparisons with two cutting-edge algorithms from the literature show how competitive the suggested algorithm is.

翻译：著名的带时间窗的车辆路径问题（VRPTW）旨在降低多个目的地之间货物运输的成本，同时满足诸如特定地点设定时间窗和车辆容量等约束条件。VRPTW问题在现实世界中的应用包括供应链管理（SCM）和物流调度，这两者对经济至关重要，并且随着工作习惯的改变而迅速扩展。因此，在求解VRPTW问题时，元启发式算法（如粒子群优化算法PSO）已被证明是有效的，然而这些算法可能会出现早熟收敛。为了降低PSO算法早熟收敛的风险，作者在本文中采用了一种新颖的PSO方法形式——轮盘赌方法（RWPSO）来求解VRPTW问题。使用Solomon VRPTW基准数据集对RWPSO进行的计算实验表明，RWPSO与文献中其他最先进的算法相比具有竞争力。此外，与文献中两种前沿算法的比较结果进一步证明了所提算法的竞争力。