This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling salesman problem with time windows (TSPTW). Augmenting temperature from traditional simulated annealing with the concept of pressure (analogous to the value of the penalty multiplier), compressed annealing relaxes the time window constraints by integrating a penalty method within a stochastic search procedure. Computational results validate the value of a variable penalty method versus a static penalty approach. Compressed annealing compares favorably with benchmark results in the literature, obtaining best-known results for numerous instances.

We develop a family of rollout policies based on fixed routes to obtain dynamic solutions to the vehicle routing problem with stochastic demand and duration limits (VRPSDL). In addition to a traditional one-step rollout policy, we leverage the notions of the pre-and post-decision state to distinguish two additional rollout variants. We tailor our rollout policies by developing a dynamic decomposition scheme that achieves high quality solutions to large problem instances with reasonable computational effort. Computational experiments demonstrate that our rollout policies improve upon the performance of a rolling horizon procedure and commonly employed fixed-route policies, with improvement over the latter being more substantial.

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