A grasp+VND algorithm for the multiple traveling repairmen problem with distance constraints

Abstract

Multiple Traveling Repairmen Problem (MTRP) is a class of NP-hard combinatorial optimization problems. In this paper, another variant of MTRP, also known as Multiple Traveling Repairmen Problem with Distance Constraint (MTRPD), is introduced. In MTRPD problem, a fleet of vehicles serves a set of customers. Each vehicle which starts from the depot is not allowed to travel any distance longer than a limit and each customer must be visited exactly once. The goal is to find the order of customer visits of all vehicles that minimizes the sum of all vertices’ waiting time. To the best of our knowledge, the problem has not been studied much previously, even though it is a natural and practical extension of the Traveling Repairman Problem or Multiple Traveling Repairmen Problem case. In our work, we propose a metaheuristic algorithm which is mainly based on the principles of Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Descent (VND) to solve the problem. The GRASP is used to build an initial solution which is good enough in a construction phase. In a cooperative way, the VND is employed to generate diverse neighborhoods in an improvement phase, therefore, it can help the search escape from local optimal. Extensive numerical experiments on 321 benchmark instances show that our algorithm can find the optimal solutions with up to 50 vertices in several instances. For larger instances, our algorithm obtains provably near-optimal solutions, even for large instances.