Algebraic, geometric, and stochastic aspects of genetic operators

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior

Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to Bayesian model selection problems. The new algorithm is tested through a change-point identification example. The numerical results indicate that the new algorithm can outperform SAMC and reversible jump MCMC significantly for the model selection problems. The new algorithm represents a general form of the stochastic approximation Markov chain Monte Carlo algorithm. It allows multiple samples to be generated at each iteration, and a bias term to be included in the parameter updating step. A rigorous proof for the convergence of the general algorithm is established under verifiable conditions. This paper also provides a framework on how to improve efficiency of Monte Carlo simulations by incorporating some nonparametric techniques.Comment: Published in at http://dx.doi.org/10.1214/07-AOS577 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimization Algorithms for Computational Systems Biology

Computational systems biology aims at integrating biology and computational methods to gain a better understating of biological phenomena. It often requires the assistance of global optimization to adequately tune its tools. This review presents three powerful methodologies for global optimization that fit the requirements of most of the computational systems biology applications, such as model tuning and biomarker identification. We include the multi-start approach for least squares methods, mostly applied for fitting experimental data. We illustrate Markov Chain Monte Carlo methods, which are stochastic techniques here applied for fitting experimental data when a model involves stochastic equations or simulations. Finally, we present Genetic Algorithms, heuristic nature-inspired methods that are applied in a broad range of optimization applications, including the ones in systems biology