{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-min-cost-traveling-salesman-problem","title":"On the Min-cost Traveling Salesman Problem with Drone","arxiv_id":"1509.08764","date":"2015-09-29","proceeding":null,"authors":["Quang Minh Ha","Yves Deville","Quang Dung Pham","Minh Hoàng Hà"],"abstract":"Over the past few years, unmanned aerial vehicles (UAV), also known as\ndrones, have been adopted as part of a new logistic method in the commercial\nsector called \"last-mile delivery\". In this novel approach, they are deployed\nalongside trucks to deliver goods to customers to improve the quality of\nservice and reduce the transportation cost. This approach gives rise to a new\nvariant of the traveling salesman problem (TSP), called TSP with drone (TSP-D).\nA variant of this problem that aims to minimize the time at which truck and\ndrone finish the service (or, in other words, to maximize the quality of\nservice) was studied in the work of Murray and Chu (2015). In contrast, this\npaper considers a new variant of TSP-D in which the objective is to minimize\noperational costs including total transportation cost and one created by waste\ntime a vehicle has to wait for the other. The problem is first formulated\nmathematically. Then, two algorithms are proposed for the solution. The first\nalgorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu\n(2015), in which an optimal TSP solution is converted to a feasible TSP-D\nsolution by local searches. The second algorithm, a Greedy Randomized Adaptive\nSearch Procedure (GRASP), is based on a new split procedure that optimally\nsplits any TSP tour into a TSP-D solution. After a TSP-D solution has been\ngenerated, it is then improved through local search operators. Numerical\nresults obtained on various instances of both objective functions with\ndifferent sizes and characteristics are presented. The results show that GRASP\noutperforms TSP-LS in terms of solution quality under an acceptable running\ntime.","url_abs":"http://arxiv.org/abs/1509.08764v3","url_pdf":"http://arxiv.org/pdf/1509.08764v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-the-min-cost-traveling-salesman-problem","repo_url":"https://github.com/ovidiuchile/AEA2019","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"traveling-salesman-problem","task_name":"Traveling Salesman Problem"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}