Metaheuristic for the Traveling Repairman Problem with Time Window Constraints

Traveling Repairman Problem (TRP) is a class of NP-hard combinatorial optimization problems which has many practical applications. In this paper, a general variant of TRP, also known as TRPTW is introduced. The TRPTW problem deals with finding a tour in order to serve a set of locations, each one within a specified time window. Obviously, TRPTW is more complex than TRP because it is a generation of TRP. Due to NPhard problem, metaheuristic needs to be developed to provide near-optimal solutions within a short computation time for large instance sizes. However, the main issue of metaheuristics is that they fall into local optima in some cases since the search space of the problem is combinatorial explosion. In order to overcome the drawback, we propose a metaheuristic algorithm which is mainly based on Variable Neighborhood Search (VNS) and Shaking techniques to solve the problem. The aim of VNS is to generate diverse neighborhoods by using various neighborhood searches while Shaking techniques allow it to guide the search towards an unexplored part of the solution space. The combination supports our algorithm to escape local optimal. Extensive numerical experiments on benchmark instances show that our algorithm reaches the optimal solutions for the problem with up to 50 vertices at reasonable amount of time. In addition, our algorithm is comparable with the state of the art metaheuristic algorithms in terms of solution quality and running time for larger instances.