Elitist Schema Overlays: A Multi-Parent Genetic Operator

Genetic Algorithms are programs inspired by natural evolution used to solve difficult problems in Mathematics and Computer Science. The theoretical foundations of Genetic Algorithms, the schema theorem and the building-block hypothesis, state that the success of Genetic Algorithms stems from the propagation of fit genetic subsequences. Multi-parent operators were shown to increase the performance of Genetic Algorithms by increasing the disruptivity of genetic operations. Disruptive genetic operators help prevent suboptimal genetic sequences from propagating into future generations, which leads to an improved fitness for the population over time. In this paper we explore the use of a novel multi-parent genetic operator, the elitist schema overlay, which propagates the matching segments in the genetic sequences of the elite subpopulation to bias the global search towards the best known solutions. We investigate the parameters that drive the behavior of elitist schema overlays to determine the most successful model, and we compare this to successful multi-parent and traditional genetic operators from the literature

Tracking Stopping Times Through Noisy Observations

A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with respect to \{X_i\}_{i\geq 1}. The problem is to find a stopping time T with respect to \{Y_i\}_{i\geq 1} that optimally tracks S, in the sense that T minimizes the expected reaction delay E(T-S)^+, while keeping the false-alarm probability P(T<S) below a given threshold \alpha \in [0,1]. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control. Our results relate to the situation where the X_i's and Y_i's take values in finite alphabets and where S is bounded by some positive integer \kappa. By using elementary methods based on the analysis of the tree structure of stopping times, we exhibit an algorithm that computes the optimal average reaction delays for all \alpha \in [0,1], and constructs the associated optimal stopping times T. Under certain conditions on \{(X_i,Y_i)\}_{i\geq 1} and S, the algorithm running time is polynomial in \kappa.Comment: 19 pages, 4 figures, to appear in IEEE Transactions on Information Theor