Beam-ACO based on stochastic sampling for makespan optimization concerning the TSP with time windows

The travelling salesman problem with time windows is a difficult optimization problem that appears, for example, in logistics. Among the possible objective functions we chose the optimization of the makespan. For solving this problem we propose a so-called Beam-ACO algorithm, which is a hybrid method that combines ant colony optimization with beam search. In general, Beam-ACO algorithms heavily rely on accurate and computationally inexpensive bounding information for differentiating between partial solutions. In this work we use stochastic sampling as an alternative to bounding information. Our results clearly demonstrate that the proposed algorithm is currently a state-of-the-art method for the tackled problem. © Springer-Verlag Berlin Heidelberg 2009.