Rare event simulation and combinatorial optimization using cross entropy: sequence alignment by rare event simulation

We present a new stochastic method for finding the optimal alignment of DNA sequences. The method works by generating random paths through a graph (the edit graph) according to a Markov chain. Each path is assigned a score, and these scores are used to modify the transition probabilities of the Markov chain. This procedure converges to a fixed path through the graph, corresponding to the optimal (or near-optimal) sequence alignment. The rules with which to update the transition probabilities are based on Rubinstein's <i>Cross-Entropy Method</i>, a new technique for stochastic optimization. This leads to very simple and natural updating formulas. Due to its versatility, mathematical tractability and simplicity, the method has great potential for a large class of combinatorial optimization problems, in particular in biological sciences.