Amsaa: A multistep anticipatory algorithm for online stochastic combinatorial optimization

Abstract

The one-step anticipatory algorithm (1s-AA) is an online algorithm making decisions under uncertainty by ignoring future non-anticipativity constraints. It makes near-optimal decisions on a variety of online stochastic combinatorial problems in dynamic fleet management, reservation systems, and more. Here we consider applications in which 1s-AA is not as close to the optimum and propose Amsaa, an anytime multi-step anticipatory algorithm. Amsaa combines techniques from three different fields to make decisions online. It uses the sampling average approximation method from stochastic programming to approximate the problem; solves the resulting problem using a search algorithm for Markov decision processes from artificial intelligence; and uses a discrete optimization algorithm for guiding the search. Amsaa was evaluated on a stochastic project scheduling application from the pharmaceutical industry featuring endogenous observations of the uncertainty. The experimental results show that Amsaa significantly outperforms state-of-the-art algorithms on this application under various time constraints. © 2008 Springer-Verlag Berlin Heidelberg.