The convergence to equilibrium of neutral genetic models

This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both for finite and infinite types (or alleles) models. We then analyze the decays to the equilibrium of finite populations in terms of the convergence to stationarity of their first common ancestor. We estimate the Lyapunov exponent of the distribution flows with respect to the total variation norm. We give bounds on these exponents only depending on the stability with respect to mutation of a single individual; they are inversely proportional to the population size parameter

Supervisory evolutionary optimization strategy for adaptive maintenance schedules

10.1109/ISIE.2011.5984204Proceedings - ISIE 2011: 2011 IEEE International Symposium on Industrial Electronics1137-114

System Architecture Optimization Using Hidden Genes Genetic Algorithms with Applications in Space Trajectory Optimization

In this dissertation, the concept of hidden genes genetic algorithms is developed. In system architecture optimization problems, the topology of the solution is unknown and hence, the number of design variables is variable. Hidden genes genetic algorithms are genetic algorithm based methods that are developed to handle such problems by hiding some genes in the chromosomes. The genes in the hidden genes genetic algorithms evolve through selection, mutation, and crossover operations. To determine if a gene is hidden or not, binary tags are assigned to them. The value of the tags determine the status of the genes. Different mechanisms are proposed for the evolution of the tags. Some mechanisms utilize stochastic operations while others are based on deterministic operations. All the proposed mechanisms are tested on mathematical and space trajectory optimization problems. Moreover, Markov chain models of the mechanisms are derived and their convergence is investigated analytically. The results show that the proposed concept are capable to search for the optimal solution by autonomously enabling the algorithms to assign the hidden genes

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring a large integration step to impute over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multitype branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for hematopoiesis and transposable element evolution.Comment: 18 pages, 4 figures, 2 table

Optimal System Design of In-Situ Bioremediation Using Parallel Recombinative Simulated Annealing

We present a simulation/optimization model combining optimization with BIOPLUME II simulation for optimizing in-situ bioremediation system design. In-situ bioremediation of contaminated groundwater has become widely accepted because of its cost-effective ability to achieve satisfactory cleanup. We use parallel recombinative simulated annealing to search for an optimal design and apply the BIOPLUME II model to simulate aquifer hydraulics and bioremediation. Parallel recombinative simulated annealing is a general-purpose optimization approach that has the good convergence of simulated annealing and the efficient parallelization of a genetic algorithm. This is the first time that parallel recombinative simulated annealing has been applied to groundwater management. The design goal of the in-situ bioremediation system is to minimize system installation and operation cost. System design decision variables are pumping well locations and pumping rates. The problem formulation is mixed-integer and nonlinear. The system design must satisfy constraints on pumping rates, hydraulic heads, contaminant concentration at the plume source and at downstream monitoring wells. For the posed problem, the parallel recombinative simulated annealing obtains an optimal solution that minimizes system cost, reduces contaminant concentration and prevents plume migration

Theory and practice of optimal mutation rate control in Hamming spaces of DNA sequences

We investigate the problem of optimal control of mutation by asexual self-replicating organisms represented by points in a metric space. We introduce the notion of a relatively monotonic fitness landscape and consider a generalisation of Fisher's geometric model of adaptation for such spaces. Using a Hamming space as a prime example, we derive the probability of adaptation as a function of reproduction parameters (e.g. mutation size or rate). Optimal control rules for the parameters are derived explicitly for some relatively monotonic landscapes, and then a general information-based heuristic is introduced. We then evaluate our theoretical control functions against optimal mutation functions evolved from a random population of functions using a meta genetic algorithm. Our experimental results show a close match between theory and experiment. We demonstrate this result both in artificial fitness landscapes, defined by a Hamming distance, and a natural landscape, where fitness is defined by a DNA-protein affinity. We discuss how a control of mutation rate could occur and evolve in natural organisms. We also outline future directions of this work