Abstract
The Quota-Travelling Repairman Problem (Q-TRP) tries to find a tour that minimizes the waiting time while the profit collected by a repairman is not less than a predefined value. The Q-TRP is an extended variant of the Travelling Repairman Problem (TRP). The problem is NP-hard problem; therefore, metaheuristic is a natural approach to provide near-optimal solutions for large instance sizes in a short time. Currently, several algorithms are proposed to solve the TRP. However, the quote constraint does not include, and these algorithms cannot be adapted to the Q-TRP. Therefore, developing an efficient algorithm for the Q-TRP is necessary. In this paper, we suggest a General Variable Neighborhood Search (GVNS) that combines with the perturbation and Adaptive Memory (AM) techniques to prevent the search from local optima. The algorithm is implemented with a benchmark dataset. The results demonstrate that good solutions, even the optimal solutions for the problem with 100 vertices, can be reached in a short time. Moreover, the algorithm is comparable with the other metaheuristic algorithms in accordance with the solution quality.
Highlights
The Quota-Travelling Repairman Problem (Q-TRP) in the case of Travelling Repairman Problem (TRP) has been studied in the numerous articles [1], [2], [3], [4], [5], [6], [8], [10],[14], [15]
We propose a General Variable Neighborhood Search (GVNS) [13] that combines with the perturbation and Adaptive Memory (AM) techniques [11] to prevent the search from local optima
Note that: The value of LB in the Q-TRP is the optimal solution of the TRP
Summary
The Quota-Travelling Repairman Problem (Q-TRP) in the case of Travelling Repairman Problem (TRP) has been studied in the numerous articles [1], [2], [3], [4], [5], [6], [8], [10],. The Q-TRP tries to find a tour that minimizes the waiting time while the profit collected by a repairman is not less than a predefined value of Pmin. Repairman knows the distances between cities and how many goods he could sell in his tour His objective is to travel along a tour while minimizing the waiting time and selling the required quota of goods. For NP-hard problems, some types of algorithms are applied to solve the Q-TRP. The algorithm is one of the first metaheuristics to solve this problem. Several state-of-the-art metaheuristic algorithms for the TRP is chosen to compare to the A-GVNS. The results demonstrate that good solutions, even the optimal solutions for the problem with 100 vertices, can be reached in a short time.
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