A multi-population multi-tasking Tabu Search with Variable Neighborhood Search algorithm to solve post-disaster clustered repairman problem with priorities

The Clustered Traveling Repairman Problem (cTRP) is an extended variant of the Traveling Repairman Problem (TRP), where customers are grouped into clusters that must be visited contiguously. However, the problem in post-disaster contexts has not yet been considered under the following constraints. First, the repairman requires additional time to remove debris, which adds debris removal time to the travel cost. Second, vertices in each cluster have varying priorities depending on their importance, with higher-priority vertices offering greater benefits when reached. This paper addresses these challenges by first defining the problem in post-disaster scenarios and then introducing a novel metaheuristic, TS-MMP, based on Multitasking Multipopulation Optimization (MMPO). This approach enables concurrent and independent task execution by integrating Randomized Neighborhood Search (RNVS), Tabu Search (TS), and dynamic knowledge sharing to improve problem-solving efficiency. In TS-MMP, the dynamic knowledge transfer mechanism ensures diversification, while TS and RNVS enhance intensification capabilities. Tabu lists prevent the search process from revisiting previously explored solution spaces. As a result, TS-MMP achieves superior solutions compared to other algorithms. Empirical results demonstrate that optimal solutions for instances with up to 30 vertices can be solved exactly using both the proposed formulation and TS-VNS-MMP. Moreover, TS-VNS-MMP provides high-quality solutions within a reasonable time for larger instances, confirming its impressive efficiency.