The Clustered Team Orienteering Problem (CluTOP) extends the classic Clustered Orienteering Problem by considering the use of multiple vehicles. The problem is known to be NP-hard and can be used to formulate many real-life applications. This work presents a highly effective multi-level memetic search for CluTOP that combines a backbone-based edge assembly crossover to generate promising offspring solutions with an effective bilevel synergistic local search procedure at both cluster and customer levels to improve offspring solutions. Other novel features of the proposed approach include a joint use of three specific hash functions to identify the tabu status of candidate solutions at the cluster level, a multi-neighborhood search with inter-route and intra-route optimization at the customer level, a pre-processing neighborhood reduction strategy to avoid examining non-promising candidate solutions, and a strategy for controlled exploration of infeasible solutions. Extensive experimental results on 1848 benchmark instances convincingly demonstrate high competitiveness of the approach in terms of both solution quality and computational time, compared to the state-of-the-art heuristics from the literature. In particular, the proposed algorithm improves upon the existing best-known solutions for 294 instances, while matching the previous best-known results for all but 3 of the remaining instances. To gain further insights into the algorithm’s performance, additional experiments are conducted to analyze its main components.

中文翻译：

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针对集群团队定向运动问题的邻域缩减的有效多级模因搜索


集群团队定向问题 (CluTOP) 通过考虑使用多辆车来扩展经典的集群定向问题。该问题被认为是 NP 难题，可用于制定许多现实生活中的应用。这项工作为 CluTOP 提供了一种高效的多级模因搜索，它结合了基于主干的边缘组装交叉来生成有前途的后代解决方案，并在集群和客户级别上使用有效的双层协同局部搜索程序来改进后代解决方案。该方法的其他新颖特征包括联合使用三个特定的哈希函数来识别集群级别候选解决方案的禁忌状态、在客户级别进行具有路由间和路由内优化的多邻域搜索、预-处理邻域缩减策略以避免检查无希望的候选解决方案，以及对不可行解决方案进行受控探索的策略。与文献中最先进的启发式方法相比，1848 个基准实​​例的大量实验结果令人信服地证明了该方法在解决方案质量和计算时间方面的高竞争力。特别是，所提出的算法改进了 294 个实例的现有最著名解决方案，同时匹配除 3 个其余实例之外的所有实例的先前最著名结果。为了进一步了解该算法的性能，进行了额外的实验来分析其主要组成部分。