The paper presents an evaluation-relaxation scheme where a fitness surrogate automatically adapts to the problem structure and the partial contributions of subsolutions to the fitness of an individual are estimated efficiently and accurately. In particular, the probabilistic model built by extended compact genetic algorithm is used to infer the structural form of the surrogate and a least squares method is used to estimate the coefficients of the surrogate. Using the surrogate avoids the need for expensive fitness evaluation for some of the solutions, and thereby yields significant efficiency enhancement. Results show that a surrogate, which automatically adapts to problem knowledge mined from probabilistic models, yields substantial speedup (1.75–3.1) on a class of boundedly-difficult additively-decomposable problems with and without additive Gaussian noise. The speedup provided by the surrogate increases with the number of substructures, substructure complexity, and noise-to-signal ratio.

One benefit of using probabilistic model-building genetic algorithms is the possibility of creating cheap and accurate surrogate models. Learning classifier systems—and genetics-based machine learning in general—can greatly benefit from such surrogates which can replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness function when coupled with the probabilistic models evolved by the χ-ary extended compact classifier system (χeCCS). We present results showing how functional alignment between the probabilistic model of χeCCS and the surrogate fitness is required. We also present a transformation of populations of rules based on the dependency structure matrix genetic algorithm (DSMGA) that allows building accurate models of overlapping building blocks—a necessary condition to accurately estimate the fitness of the evolved rules. 1

Evolutionary algorithms (EAs) are particularly suited to solve problems for which there is not much information available. From this standpoint, estimation of distribution algorithms (EDAs), which guide the search by using probabilistic models of the population, have brought a new view to evolutionary computation. While solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. However, as the complexity of the used models increases, the chance of overfitting and consequently reducing model interpretability, increases as well. This paper investigates the relationship between the probabilistic models learned by the Bayesian optimization algorithm (BOA) and the underlying problem structure. The purpose of the paper is threefold. First, model building in BOA is analyzed to understand how the problem structure is learned. Second, it is shown how the selection operator can lead to model overfitting in Bayesian EDAs. Third, the scoring metric that guides the search for an adequate model structure is modified to take into account the non-uniform distribution of the mating pool generated by tournament selection. Overall, this paper makes a contribution towards

The Bayesian optimization algorithm (BOA) uses Bayesian networks to learn linkages between the decision variables of an optimization problem. This paper studies the influence of different selection and replacement methods on the accuracy of linkage learning in BOA. Results on concatenated m-k deceptive trap functions show that the model accuracy depends on a large extent on the choice of selection method and to a lesser extent on the replacement strategy used. Specifically, it is shown that linkage learning in BOA is more accurate with truncation selection than with tournament selection. The choice of replacement strategy is important when tournament selection is used, but it is not relevant when using truncation selection. On the other hand, if performance is our main concern, tournament selection and restricted tournament replacement should be preferred. These results aim to provide practitioners with useful information about the best way to tune BOA with respect to structural model accuracy and overall performance.

A wide range of niching techniques have been investigated in evolutionary and genetic algorithms. In this article, we focus on niching using crowding techniques in the context of what we call local tournament algorithms. In addition to deterministic and probabilistic crowding, the family of local tournament algorithms includes the Metropolis algorithm, simulated annealing, restricted tournament selection, and parallel recombinative simulated annealing. We describe an algorithmic and analytical framework which is applicable to a wide range of crowding algorithms. As an example of utilizing this framework, we present and analyze the probabilistic crowding niching algorithm. Like the closely related deterministic crowding approach, probabilistic crowding is fast, simple, and requires no parameters beyond those of classical genetic algorithms. In probabilistic crowding, sub-populations are maintained reliably, and we show that it is possible to analyze and predict how this maintenance takes place. We also provide novel results for deterministic crowding, show how different crowding replacement rules can be combined in portfolios, and discuss population sizing. Our analysis is backed up by experiments that further increase the understanding of probabilistic crowding.

A byproduct benefit of using probabilistic model-building genetic algorithms is the creation of cheap and accurate surrogate models. Learning classifier systems—and geneticsbased machine learning in general—can greatly benefit from such surrogates which may replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness functions when coupled with the probabilistic models evolved by the χ-ary extended compact classifier system (χeCCS). To achieve such a goal, we show the need that the probabilistic models should be able to represent all the accurate basis functions required for creating an accurate surrogate. We also introduce a procedure to transform populations of rules based into dependency structure matrices (DSMs) which allows building accurate models of overlapping building blocks—a necessary condition to accurately estimate the fitness of the evolved rules.

This paper investigates the incorporation of restricted tournament replacement (RTR) in the extended compact genetic algorithm (ECGA) for solving problems with non-stationary optima. RTR is a simple yet efficient niching method used to maintain diversity in a population of individuals. While the original version of RTR uses Hamming distance to quantify similarity between individuals, we propose an alternative substructural distance to enforce the niches. The ECGA that restarts the search after a change of environment is compared with the approach of maintaining diversity, using both versions of RTR. Results on several dynamic decomposable test problems demonstrate the usefulness of maintaining diversity throughout the run over the approach of restarting the search from scratch at each change. Furthermore, by maintaining diversity no additional mechanisms are required to detect the change of environment, which is typically a problem-dependent and non-trivial task.

This paper investigates the incorporation of restricted tournament replacement (RTR) in the extended compact genetic algorithm (ECGA) for solving problems with non-stationary optima. RTR is a simple yet efficient niching method used to maintain diversity in a population of individuals. While the original version of RTR uses Hamming distance to quantify similarity between individuals, we propose an alternative substructural distance to enforce the niches. The ECGA that restarts the search after a change of environment is compared with the approach of maintaining diversity, using both versions of RTR. Results on several dynamic decomposable test problems demonstrate the usefulness of maintaining diversity throughout the run over the approach of restarting the search from scratch at each change. Furthermore, by maintaining diversity no additional mechanisms are required to detect the change of environment, which is typically a problem-dependent and non-trivial task.

This paper reviews a competent Pittsburgh LCS that automatically mines important substructures of the underlying problems and takes problems that were intractable with firstgeneration Pittsburgh LCS and renders them tractable. Specifically, we propose a χ-ary extended compact classifier system (χeCCS) which uses (1) a competent genetic algorithm (GA) in the form of χ-ary extended compact genetic algorithm, and (2) a niching method in the form restricted tournament replacement, to evolve a set of maximally accurate and maximally general rules. Besides showing that linkage exist on the multiplexer problem, and that χeCCS scales exponentially with the number of address bits (building block size) and quadratically with the problem size, this paper also explores non-traditional rule encodings. Gene expression encodings, such as the Karva language, can also be used to build χeCCS probabilistic models. However, results show that the traditional ternary encoding 0,1, # presents a better scalability than the gene expression inspired ones. 1

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