Abstract
The Capacitated Multiple Traveling Repairmen Problem (CmTRP) is an extension of the Multiple Traveling Repairmen Problem (mTRP). In the CmTRP, the number of vehicles is dispatched to serve a set of customers, while each vehicle’s capacity is limited by a predefined-value as well as each customer is visited exactly once. The goal is to find a tour that minimizes the sum of waiting times. The problem is NP-hard because it is harder than the mTRP. Even finding a feasible solution is also NP-hard problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The first phase constructs a feasible solution by combining between the Nearest Neighborhood Search (NNS) and Variable Neighborhood Search (VNS), while the optimization phase develops the feasible solution by the General Variable Neighborhood Search (GVNS). The combination maintains the balance between intensification and diversification to escape local optima. The proposed algorithm is implemented on benchmark instances from the literature. The results indicate that the developed algorithm obtains good feasible solutions in a short time, even for the cases with up to 200 vertices.
Highlights
The Capacitated Multiple Traveling Repairmen Problem (CmTRP) asks for a tour, which starts at a depot v1, visits each vertex once exactly with the waiting time of all vertices being minimized
The first phase constructs a feasible solution by combining between the Nearest Neighborhood Search (NNS) and Variable Neighborhood Search (VNS), while the optimization phase develops the feasible solution by the General Variable Neighborhood Search (GVNS)
We describe some variants of VNS [14] such as the original VNS, Variable Neighborhood Descent (VND), and GVNS, shaking technique [13], respectively
Summary
A particular variant of the CmTRP is the Multiple Traveling Repairmen Problem (mTRP) that considers multiple vehicles or travelers to find a tour minimizing the waiting time of all customers [1], [7], [9]. The goal is to find a tour such that each vertex is visited exactly once, while the capacity constraint is satisfied, and the total waiting time of overall customers is minimized. Let W (Rl) be the sum of waiting times of all vertices. The capacity of this route must satisfy the following constraint: m. The CmTRP asks for a tour, which starts at a depot v1, visits each vertex once exactly with the waiting time of all vertices being minimized
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