ROAR: Restricted 2-Opt And Ruin-and-recreate Heuristic for Large and Extreme Scale Traveling Repairman Problem

The Traveling Repairman Problem minimizes cumulative arrival times rather than the total route length, as in the classical Traveling Salesman Problem. The literature contains several legacy metaheuristics for the TRP; however, most are evaluated on small- and medium-scale instances and show limited scalability for large and extreme datasets. GILS-RVND, the current gold standard in metaheuristic algorithms, performs well on small and medium instances but struggles to scale due to the exhaustive neighborhood search in the RVND phase. To address this limitation, we introduce Restricted 2-Opt And Ruin-and-recreate (ROAR), a Large Neighborhood Search-based method that integrates ruin-and-recreate with greedy insertion and a restricted, insertion-anchored 2-opt operator. Computational experiments demonstrate that ROAR produces high-quality solutions for large-scale instances and outperforms existing methods under strict time limits. We further introduce an O(1)-time, O(1)-space algorithm for evaluating 2-opt moves during a contiguous systematic sweep, which, to the best of our knowledge, is unprecedented. Finally, we evaluate ROAR on instances with up to 200,000 nodes, substantially exceeding the largest instances previously reported in the literature (11,849 nodes).