The travelling salesman problem with time windows is a difficult optimization problem that arises, for example, in logistics. This paper deals with the minimization of the travel cost. For solving this problem, this paper proposes a 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. This work uses stochastic sampling as a useful alternative. An extensive experimental evaluation on seven benchmark sets from the literature shows that the proposed Beam-ACO algorithm is currently a state-of-the-art technique for the travelling salesman problem with time windows under travel-cost optimization.