Branch-and-bound algorithm for the time dependent Chinese Postman Problem

Abstract

This paper studies an extended version of the Chinese Postman Problem involving the added complexity of time dependent travel times, which is motivated from hybrid system testing. In the literature, the conventional Chinese Postman Problems defined on the Euler graph are polynomially solvable. However, we prove that the Chinese Postman Problem defined on the time dependent network is N P-Hard even if it verifies the Eulerian and First-In-First-Out properties. Furthermore, A branch-and-bound algorithm is proposed for the problem with the First-In-First-Out property. Experimental results show that the dominance relation in the branch-and-bound algorithm is more efficient when the network is not Euclidian, and that small to medium-sized instances can be solved to proven optimality.