Covering salesman problem (CSP) is an extension of the popular traveling salesman problem (TSP) arising from a number of real-life applications. Given a set of vertices and a predetermined coverage radius associated with each vertex, the goal of CSP is to find a minimum cost Hamiltonian cycle across a subset of vertices, such that each unvisited vertex must be within the coverage radius of at least one vertex included in the tour. For this NP-hard problem, we present a highly effective hybrid evolutionary algorithm (HEA) that integrates a crossover operator based on solution reconstruction, a destroy-and-repair mutation operator to generate multiple distinct offspring solutions, and a two-phase tabu search procedure to seek for high-quality local optima. Another distinguishing feature of HEA is the use of the Lin–Kernighan TSP heuristic to find an improved node sequence of a CSP tour during multiple stages of HEA. Extensive experiments on a large set of benchmark instances show that the proposed approach is able to surpass the current best-performing CSP heuristics. In particular, it reports new upper bound (improved best-known solution) for 21 out of the 27 large instances, while matching the best-known result for the remaining small and medium instances. In addition to CSP, the proposed HEA is adapted to solve the generalized covering traveling salesman problem (GCTSP). Extensive experimental results on the GCTSP benchmark disclose that the proposed adaptation of HEA outperforms all the existing GCTSP heuristics from the literature.

涵盖销售员问题（CSP）是由许多实际应用引起的流行旅行销售员问题（TSP）的扩展。给定一组顶点和与每个顶点关联的预定覆盖范围半径，CSP的目标是找到整个顶点子集的最小成本汉密尔顿周期，以使每个未访问的顶点必须在包含的至少一个顶点的覆盖范围内在旅行中。针对此NP难题，我们提出了一种高效的混合进化算法（HEA），该算法基于解决方案重构，销毁与修复功能集成了交叉算子变异算子，以生成多个不同的后代解，以及两阶段禁忌搜索程序，以寻求高质量的局部最优。HEA的另一个显着特征是使用Lin–Kernighan TSP启发式算法在HEA的多个阶段中找到CSP巡视的改进节点序列。在大量基准实例上进行的大量实验表明，该方法能够超越当前性能最佳的CSP启发式算法。特别是，它报告了27个大型实例中21个的新上限（改进的最佳解决方案），同时匹配了其余中小型实例的最佳结果。除了CSP，拟议的HEA还适用于解决广义的覆盖旅行商问题（GCTSP）。