A tabu search algorithm for the min-max k-Chinese postman problem

In this paper we present a tabu search algorithm for the min-max k-Chinese postman problem (MM k-CPP). Given an undirected edge-weighted graph and a distinguished depot node, the MM k-CPP consists of finding k > 1 tours (starting and ending at the depot node) such that each edge is traversed by at least one tour and the length of the longest tour is minimized. A special emphasis is put on investigating the trade-off between running time effort and solution quality when applying different improvement procedures in the course of the neighborhood construction. Furthermore, different neighborhoods are analyzed. Extensive computational results show that the tabu search algorithm outperforms all known heuristics and improvement procedures. Scope and purpose Given a road network, the Chinese postman problem (CPP) is to find the shortest postman tour covering all the roads in the network. Applications of the CPP include road maintenance, garbage collection, mail delivery, etc. Since usually large road networks have to be serviced the work load must be distributed among k > 2 vehicles. In contrast to the usual objective to minimize the total distance traveled by the k vehicles (k-CPP), for the min-max k-Chinese postman problem (MM k-CPP) the aim is to minimize the length of the longest of the k tours. This kind of objective is preferable when customers have to be served as early as possible. Furthermore, tours will be enforced to be more balanced resulting in a fair scheduling of tours. Although the CPP and the k-CPP are polynomially solvable, the MM k-CPP is NP-hard. Hence, we must rely on heuristics producing approximate solutions. The purpose of this paper is to present a tabu search algorithm for the MM k-CPP which outperforms all known heuristics. In many cases we obtained solutions which could be proved to be near-optimal or even optimal. (c) 2005 Published by Elsevier Ltd.