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Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how…
Our theoretical understanding of crossover is limited by our ability to analyze how population diversity evolves. In this study, we provide one of the first rigorous analyses of population diversity and optimization time in a setting where…
Multimodal optimization requires both exploration and exploitation. Exploration identifies promising attraction basins, while exploitation finds the best solutions within these basins. The balance between exploration and exploitation can be…
We compare the $(1,\lambda)$-EA and the $(1 + \lambda)$-EA on the recently introduced benchmark DisOM, which is the OneMax function with randomly planted local optima. Previous work showed that if all local optima have the same relative…
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions,…
In a seminal paper in 2013, Witt showed that the (1+1) Evolutionary Algorithm with standard bit mutation needs time $(1+o(1))n \ln n/p_1$ to find the optimum of any linear function, as long as the probability $p_1$ to flip exactly one bit…
Evolutionary algorithms (EAs) have been well acknowledged as a promising paradigm for solving optimisation problems with multiple conflicting objectives in the sense that they are able to locate a set of diverse approximations of Pareto…
Random constraint satisfaction problems can display a very rich structure in the space of solutions, with often an ergodicity breaking -- also known as clustering or dynamical -- transition preceding the satisfiability threshold when the…
In this article we present an Elitism Levels Traverse Mechanism that we designed to find bounds on population-based Evolutionary algorithms solving unimodal functions. We prove its efficiency theoretically and test it on OneMax function…
Evolutionary algorithms (EAs) have emerged as a predominant approach for addressing multi-objective optimization problems. However, the theoretical foundation of multi-objective EAs (MOEAs), particularly the fundamental aspects like running…
Explaining to what extent the real power of genetic algorithms lies in the ability of crossover to recombine individuals into higher quality solutions is an important problem in evolutionary computation. In this paper we show how the…
We study unbiased $(1+1)$ evolutionary algorithms on linear functions with an unknown number $n$ of bits with non-zero weight. Static algorithms achieve an optimal runtime of $O(n (\ln n)^{2+\epsilon})$, however, it remained unclear whether…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
Stochastic gradient descent is the most prevalent algorithm to train neural networks. However, other approaches such as evolutionary algorithms are also applicable to this task. Evolutionary algorithms bring unique trade-offs that are worth…
The practice of evolutionary algorithms involves the tuning of many parameters. How big should the population be? How many generations should the algorithm run? What is the (tournament selection) tournament size? What probabilities should…
Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to…
Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…
Evolutionary Learning proceeds by evolving a population of classifiers, from which it generally returns (with some notable exceptions) the single best-of-run classifier as final result. In the meanwhile, Ensemble Learning, one of the most…
Automated Machine Learning (AutoML) gained popularity due to the increased demand for Machine Learning (ML) specialists, allowing them to apply ML techniques effortlessly and quickly. AutoML implementations use optimisation methods to…
The use of Evolutionary Algorithms (EA) for solving Mathematical/Computational Optimization Problems is inspired by the biological processes of Evolution. Few of the primitives involved in the Evolutionary process/paradigm are selection of…