Abstract
We propose two variants of a known rollout algorithm for the single vehicle routing problem with stochastic demands (VRPSD) under both the a priori (AP) and restocking (RS) strategies by expanding the search space of this algorithm. To reduce the increased computational effort, we introduce a novel approach for computing the expected cost of a route when executing a rollout algorithm, which is, however, approximate in the RS case. With a sufficiently large number of customers the theoretical speed-up factor of this approach is of big-o order 1/3. On a set of instances from the literature, our rollout algorithm variants yield better routes than the known rollout algorithm, with average expected cost improvements between 1.25% and 1.89% in the AP case and 0.64% and 0.96% in the RS case. In the AP case our second variant dominates our first variant by 0.43-0.46% on average, an observation for which we provide some theoretical support. In the RS case we do not observe any such dominance. Moreover, across all the considered rollout algorithms, our expected cost evaluation approach achieves speed-up factors that range from 0.16 to 0.38 in the AP case and 0.26 and 0.34 in the RS case, with the quality of the resulting RS routes only marginally degraded. Other VRPSD heuristics can potentially benefit from the use of this approach.
Published Version
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