Fragment-Based Knowledge Transfer for Multi-Task Capacitated Vehicle Routing

In a capacitated vehicle routing problem (CVRP), multiple vehicles are planned to travel for serving customers so as to reduce transportation costs in logistics. Taking each CVRP as a task, multiple CVRPs can form a multi-task optimization problem. Based on the similarity between tasks, knowledge transfer methods are developed to improve optimization performance by utilizing the search experience of related tasks. However, existing methods tend to use one task only for knowledge transfer. Indeed, in a target task, the different parts of customer distributions are similar to that of multiple related tasks. The information of multiple source tasks can be fused to assist the optimization of target tasks. Thus, this paper proposes a genetic algorithm with fragment-based knowledge transfer (FKT-GA), which fuses route fragments from multiple related tasks to assist the optimization of target tasks. In FKT-GA, multiple source tasks are selected for each target task based on distribution features that are invariant to rotation, shift, and scaling. Solutions of source tasks are aligned to target spaces for sampling route fragments, which are integrated to construct high-quality solutions for target tasks. In addition, mutation and crossover operators are developed to enhance solution diversity. Experimental results on fifteen 6-task instances show that FKT-GA outperforms state-of-the-art algorithms in terms of solution optimality. The proposed FKT can improve algorithm performance.