This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of building-block fitness or so-called collateral noise is the major source of variance, and a population-sizing equation is derived to ensure that average signal-to-collateral-noise ratios are favorable to the discrimination of the best building blocks required to solve a problem of bounded deception. The sizing relation is modified to permit the inclusion of other sources of stochasticity, such as the noise of selection, the noise of genetic operators, and the explicit noise or nondeterminism of the objective function. In a test suite of five functions, the sizing relation proves to be a conservative predictor of average correct convergence, as long as all major sources of noise are considered in the sizing calculation. These results suggest how the sizing equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior. At low population sizes the GA makes many errors of decision, and the quality of convergence is largely left to the vagaries of chance or the serial fixup of flawed results through mutation or other serial injection of diversity. At large population sizes, GAs can reliably discriminate between good and bad building blocks, and parallel processing and recombination of building blocks lead to quick solution of even difficult deceptive problems. Additionally, the paper outlines a number of extensions to this work, including the development of more refined models of the relation between generational average error and ultimate convergence quality, the development of online methods for sizing populations via the estimation of population-s...

Genetic and evolutionary algorithms have been increasingly applied to solve complex, large scale search problems with mixed success. Competent genetic algorithms have been proposed to solve hard problems quickly, reliably and accurately. They have rendered problems that were difficult to solve by the earlier GAs to be solvable, requiring only a subquadratic number of function evaluations. To facilitate solving large-scale complex problems, and to further enhance the performance of competent GAs, various efficiency-enhancement techniques have been developed. This study investigates one such class of efficiency-enhancement technique called evaluation relaxation. Evaluation-relaxation schemes replace a high-cost, low-error fitness function with a low-cost, high-error fitness function. The error in fitness functions comes in two flavors: Bias and variance. The presence of bias and variance in fitness functions is considered in isolation and strategies for increasing efficiency in both cases are developed. Specifically, approaches for choosing between two fitness functions with either differing variance or differing bias values have been developed. This thesis also investigates fitness inheritance as an evaluation-

We propose a sub-structural niching method that fully exploits the problem decomposition capability of linkagelearning methods such as the estimation distribution algorithms and concentrate on maintaining diversity at the sub-structural level. The proposed method consists of three key components: (1) Problem decomposition and sub-structure identification, (2) sub-structure fitness estimation, and (3) sub-structural niche preservation. The substructural niching method is compared to restricted tournament selection (RTS)—a niching method used in hierarchical Bayesian optimization algorithm—with special emphasis on sustained preservation of multiple global solutions of a class of boundedly-difficult, additively-separable multimodal problems. The results show that sub-structural niching successfully maintains multiple global optima over large number of generations and does so with significantly less population than RTS. Additionally, the market share of each of the niche is much closer to the expected level in sub-structural niching when compared to RTS.

Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. There has been a growing interest in analyzing and understanding BB mixing and it is necessary to organize and categorize representative literature. This paper presents an exhaustive survey of studies on one or more aspects of mixing. In doing so, a classification of the literature based on the role of recombination operators assumed by those studies is developed. Such a classification not only highlights the significant results and unifies existing work, but also provides a foundation for future research in understanding mixing in genetic algorithms.

Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. This study develops facetwise models to predict the BB mixing time and the population sizing dictated by BB mixing for single-point crossover. Empirical results are used to validate these models. The population-sizing model suggests that for moderate-to-large problems, BB mixing---instead of BB decision making and BB supply---bounds the population size required to obtain a solution of constant quality. Furthermore, the population sizing for singlepoint crossover scales as O , where k is the BB size and m is the number of BBs.

In this paper, we see whether chance discovery in the form of KeyGraphs can be used to reveal deep building blocks to competent genetic algorithms, thereby speeding innovation in particularly difficult problems. On an intellectual level, showing the connection between KeyGraphs and genetic algorithms as related pieces of the innovation puzzle is both scientifically and computationally interesting. GAs represent that aspect of human innovation that tries to innovate through the exchange or cross-fertilization of notions contained in different ideas; the KeyGraph procedure represents that portion of human innovation that pays special attention to and interprets salient fortuitous events. The paper goes beyond mere conjecture and performs pilot studies that show how KeyGraphs and competent GAs can work together to solve the problem of deep building blocks; the work is promising and steps toward a practical computational combine of the two procedures are suggested.

There are two primary objectives of this dissertation. The first goal is to identify certain limits of genetic algorithms that use only fitness for learning genetic linkage. Both an ex-planatory theory and experimental results to support the theory are provided. The other goal is to propose a better design of the linkage learning genetic algorithm. After under-standing the cause of the performance barrier, the design of the linkage learning genetic algorithm is modified accordingly to improve its performance on uniformly scaled problems. This dissertation starts with presenting the background of the linkage learning genetic algorithm. Then, it introduces the use of promoters on the chromosome to improve the performance of the linkage learning genetic algorithm on uniformly scaled problems. The convergence time model is constructed by identifying the sequential behavior, developing the tightness time model, and establishing the connection in between. The use of subchro-mosome representations is to avoid the limit implied by the convergence time model. The experimental results demonstrate that the use of subchromosome representations may be a promising way to design a better linkage learning genetic algorithm.

Effective and efficient multiscale modeling is essential to advance both the science and synthesis in a wide array of fields such as physics, chemistry, materials science, biology, biotechnology and pharmacology. This study investigates the efficacy and potential of using genetic algorithms for multiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale modeling with the help of two non-trivial case studies in materials science and chemistry. The first case study explores the utility of genetic programming (GP) in multi-timescaling alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte Carlo methods to span orders-of-magnitude in simulation time. Specifically, GP is used to regress symbolically an inline barrier function from a limited set of molecular dynamics simulations to enable kinetic Monte Carlo that simulate seconds of real time. Results on a non-trivial example of vacancy-assisted migration on a surface of a face-centered cubic (fcc) Copper-Cobalt (CuxCo1−x) alloy show that GP predicts all barriers with 0.1 % error from calculations for less than 3 % of active