A comparison of physical mapping algorithms based on the maximum likehood model

Abstract

Motivation: Physical mapping of chromosomes using the maximum likelihood (ML) model is a problem of high computational complexity entailing both discrete optimization to recover the optimal probe order as well as continuous optimization to recover the optimal inter-probe spacings. In this paper, two versions of the genetic algorithm (GA) are proposed, one with heuristic crossover and deterministic replacement and the other with heuristic crossover and stochastic replacement, for the physical mapping problem under the maximum likelihood model. The genetic algorithms are compared with two other discrete optimization approaches, namely simulated annealing (SA) and large-step Markov chains (LSMC), in terms of solution quality and runtime efficiency. Results: The physical mapping algorithms based on the GA, SA and LSMC have been tested using synthetic datasets and real datasets derived from cosmid libraries of the fungus Neurospora crassa. The GA, especially the version with heuristic crossover and stochastic replacement, is shown to consistently outperform the SA-based and LSMC-based physical mapping algorithms in terms of runtime and final solution quality. Experimental results on real datasets and simulated datasets are presented. Further improvements to the GA in the context of physical mapping under the maximum likelihood model are proposed.