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Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood. While…
A runtime analysis of the Univariate Marginal Distribution Algorithm (UMDA) is presented on the OneMax function for wide ranges of its parameters $\mu$ and $\lambda$. If $\mu\ge c\log n$ for some constant $c>0$ and…
Theory of evolutionary computation (EC) aims at providing mathematically founded statements about the performance of evolutionary algorithms (EAs). The predominant topic in this research domain is runtime analysis, which studies the time it…
Evolutionary algorithms rely very heavily on randomized behavior. Execution speed, therefore, depends strongly on how we implement randomness, such as our choice of pseudorandom number generator, or the algorithms used to map pseudorandom…
Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes…
It is known that the evolutionary algorithm $(1+1)$-EA with mutation rate $c/n$ optimises every monotone function efficiently if $c<1$, and needs exponential time on some monotone functions (HotTopic functions) if $c\geq 2.2$. We study the…
A Genetic Algorithm (GA) is proposed in which each member of the population can change schemata only with its neighbors according to a rule. The rule methodology and the neighborhood structure employ elements from the Cellular Automata (CA)…
Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their widespread use, a comprehensive theoretical analysis of these…
In general, we can not use algebraic or enumerative methods to optimize a quality control (QC) procedure so as to detect the critical random and systematic analytical errors with stated probabilities, while the probability for false…
It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In…
Most evolutionary algorithms (EAs) used in practice employ crossover. In contrast, only for few and mostly artificial examples a runtime advantage from crossover could be proven with mathematical means. The most convincing such result shows…
Genetic Algorithms (GAs) are used to solve search and optimization problems in which an optimal solution can be found using an iterative process with probabilistic and non-deterministic transitions. However, depending on the problem's…
The $(1 + (\lambda,\lambda))$ genetic algorithm is a younger evolutionary algorithm trying to profit also from inferior solutions. Rigorous runtime analyses on unimodal fitness functions showed that it can indeed be faster than classical…
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so…
This paper presents a genetic algorithm (GA) approach to cost-optimal task scheduling in a production line. The system consists of a set of serial processing tasks, each with a given duration, unit execution cost, and precedence…
With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is…
Unlike traditional evolutionary algorithms which produce offspring via genetic operators, Estimation of Distribution Algorithms (EDAs) sample solutions from probabilistic models which are learned from selected individuals. It is hoped that…
It is known that the $(1+(\lambda,\lambda))$~Genetic Algorithm (GA) with self-adjusting parameter choices achieves a linear expected optimization time on OneMax if its hyper-parameters are suitably chosen. However, it is not very well…
Genetic algorithms have played an important role in engineering optimization. Traditional GAs treat each gene separately. However, biophysical studies of gene regulatory networks revealed direct associations between different genes. It…
Feature selection has always been a critical step in pattern recognition, in which evolutionary algorithms, such as the genetic algorithm (GA), are most commonly used. However, the individual encoding scheme used in various GAs would either…