The Traveling Purchaser Problem (TPP) is a generalization of the TSP that consists in choosing which nodes (markets) to visit to create a tour that allows to buy a set of products at minimum transportation and purchasing cost. The TPP has gained attention due to the computational challenges it poses and the potential applications it can support in today's technology-driven industry. This paper presents a GRASP-based methodology for the TPP based on three constructive procedures (route-first, purchase-first, and purchase-and-route) and two local search operators (insert and remove). The methodology is strengthened with a Path Relinking strategy to improve the GRASP performance by re-combining a set of elite solutions and with a Filtering strategy to improve the algorithm's efficiency by avoiding local search operations on the least promising solutions. The algorithm is tested with 855 instances of the asymmetric TPP and 190 instances of the symmetric TPP. Computational results prove the benefit of including the Path Relinking and Filtering strategies and suggest that the purchase-first constructive procedure is the most competitive in terms of objective function value with little extra effort in execution time with respect to the other constructive procedures. Our results outperform published results for the asymmetric TPP in a statistically significant way and show competitive performance for the symmetric TPP.

中文翻译：

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旅行购买者问题的 GRASP/Path-Relinking 算法

旅行购买者问题 (TPP) 是 TSP 的概括，包括选择访问哪些节点（市场）以创建允许以最低运输和购买成本购买一组产品的旅行。TPP 因其带来的计算挑战以及它在当今技术驱动的行业中可以支持的潜在应用而受到关注。本文提出了一种基于 GRASP 的 TPP 方法，该方法基于三个建设性程序（路由优先、购买优先和购买和路由）和两个本地搜索算子（插入和删除））。该方法通过路径重新链接策略得到加强，通过重新组合一组精英解决方案来提高 GRASP 性能，并使用过滤策略通过避免对最没有希望的解决方案进行局部搜索操作来提高算法的效率。该算法使用 855 个非对称 TPP 实例和 190 个对称 TPP 实例进行了测试。计算结果证明了包含路径重新链接和过滤策略的好处，并表明购买优先的建设性程序在目标函数价值方面最具竞争力，相对于其他建设性程序在执行时间上几乎没有额外的努力。我们的结果在统计上显着优于非对称 TPP 的已发布结果，并显示出对称 TPP 的竞争性能。