Traveling Repairmen Problem: A Biogeography-Based Optimization

Abstract

Traveling Repairman Problem (TRP), which is also known by names cumulative traveling salesman problem, the deliveryman problem and the minimum latency problem, is a special variant of Traveling Salesman Problem (TSP). In contrast to the minimization of completion time objective of TSP, the desired objective of TRP is to minimize the cumulative latency (waiting time or delay time) of all customers. In this paper, a generalized version of TRP with multi depots and time windows, namely Multi Depot Traveling Repairman Problem with Time Windows (MDTRPTW) is considered. A group of homogeneous repairmen initiate and finish their visit tours at multiple depots. Each customer must be visited exactly by one repairman within their provided earliest end latest times. Being a challenging Nondeterministic Polynomial-hard (NP-hard) optimization problem, exact solution approaches are not expected to scale to realistic dimensions of MDTRPTW. Thus, we propose a biogeography-based optimization algorithm (BBOA) as a metaheuristic approach to solve large size MDTRPTW problems. The proposed metaheuristic is analyzed in terms of solution quality, coefficient of variation as well as computation time by solving some test problems adapted from the related literature. The efficacy of the proposed solution methodology is demonstrated by solving instances with 288 customers within seconds.