The paper explores the Biased Random-Key Genetic Algorithm (BRKGA) in the domain of logistics and vehicle routing. Specifically, the application of the algorithm is contextualized within the framework of the Vehicle Routing Problem with Occasional Drivers and Time Window (VRPODTW) that represents a critical challenge in contemporary delivery systems. Within this context, BRKGA emerges as an innovative solution approach to optimize routing plans, balancing cost-efficiency with operational constraints. This research introduces a new BRKGA, characterized by a variable mutant population which can vary from generation to generation, named BRKGA-VM. This novel variant was tested to solve a VRPODTW. For this purpose, an innovative specific decoder procedure was proposed and implemented. Furthermore, a hybridization of the algorithm with a Variable Neighborhood Descent (VND) algorithm has also been considered, showing an improvement of problem-solving capabilities. Computational results show a better performances in term of effectiveness over a previous version of BRKGA, denoted as MP. The improved performance of BRKGA-VM is evident from its ability to optimize solutions across a wide range of scenarios, with significant improvements observed for each type of instance considered. The analysis also reveals that VM achieves preset goals more quickly compared to MP, thanks to the increased variability induced in the mutant population which facilitates the exploration of new regions of the solution space. Furthermore, the integration of VND has shown an additional positive impact on the quality of the solutions found.

翻译：本文探讨了有偏随机密钥遗传算法（BRKGA）在物流与车辆路径领域中的应用。具体而言，该算法被应用于带临时司机及时间窗的车辆路径问题（VRPODTW）框架下，这一问题对现代配送系统构成了关键挑战。在此背景下，BRKGA作为一种创新性求解方法，能够在平衡成本效率与运营约束的同时优化路径规划方案。本研究提出了一种新型BRKGA变体——BRKGA-VM，其核心特征在于变异种群规模可在代际间动态变化。通过设计并实现一种专用的解码器程序，该变体被应用于求解VRPODTW。此外，本文还探索了算法与变邻域下降（VND）算法的混合策略，结果表明该混合方法显著提升了问题求解能力。计算实验显示，相较于先前版本（记为MP），BRKGA-VM在有效性方面表现更优。这种性能提升体现在其能在广泛场景中优化求解质量，且对各类测试实例均取得显著改进。分析进一步表明，由于变异种群引入的变异性增强，BRKGA-VM与MP相比能更快达成预设目标——这种变异性有效促进了算法对解空间新区域的探索。同时，VND的集成对解质量的提升产生了额外正向影响。