We study a combinatorial optimization problem for conflict-free routing in a Network-on-Chip. Based on time division multiplexing and cyclic emission, the problem consists in finding a set of K shortest paths, such that packets will never conflict through the network but can use shared communication links in an efficient way. The model allows to avoid collisions and deadlocks in irregular network topologies, while minimizing latency. A time-expanded graph approach is retained for the solution process. First, we present a mixed integer linear programming model for the problem. Second, a set of shortest paths operators are combined within three iterated local search schemes able to quickly generate admissible solutions for the problem. To evaluate the method, experiments are conducted on a set of five real-life problem instances, and on many artificial unstructured random instances derived from them. We detail the problem of traffic instance generation, that also illustrates the designer’s task of flow decomposition between communicating components. Intensive simulations illustrate the accuracy of the solution method.