Related papers: All Mutation Rates $c/n$ for the $(1+1)$ Evolution…
The $(1+(\lambda,\lambda))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties. We show that its main working principle, mutation with a high rate and crossover as repair…
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…
One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a boolean function $f:\{0,1\}^n \to {\mathbb R}$. The algorithm starts with a random search point $\xi \in…
Recent works showed that simple success-based rules for self-adjusting parameters in evolutionary algorithms (EAs) can match or outperform the best fixed parameters on discrete problems. Non-elitism in a (1,$\lambda$) EA combined with a…
A deterministic mutation-selection model in the sequence space approach is investigated. Genotypes are identified with two-letter sequences. Mutation is modelled as a Markov process, fitness functions are of Hopfield type, where the fitness…
We present an evolutionary algorithm evo-SMC for the problem of Submodular Maximization under Cost constraints (SMC). Our algorithm achieves $1/2$-approximation with a high probability $1-1/n$ within $\mathcal{O}(n^2K_{\beta})$ iterations,…
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this…
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a…
Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to…
Monte Carlo Tree Search (MCTS) is a sampling best-first method to search for optimal decisions. The success of MCTS depends heavily on how the tree is built and the selection process plays a fundamental role in this. One particular…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically…
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…
We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutuation rate limit, which we model as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness…