Related papers: Fast Genetic Algorithms
For every mutation rate $p \in (0, 1)$, and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ with a unique maximum for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$ is in…
Understanding how crossover works is still one of the big challenges in evolutionary computation research, and making our understanding precise and proven by mathematical means might be an even bigger one. As one of few examples where…
This paper extends the runtime analysis of non-elitist evolutionary algorithms (EAs) with fitness-proportionate selection from the simple OneMax function to the linear functions. Not only does our analysis cover a larger class of fitness…
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…
We study evolutionary algorithms in a dynamic setting, where for each generation a different fitness function is chosen, and selection is performed with respect to the current fitness function. Specifically, we consider Dynamic BinVal, in…
Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the…
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…
The heavy-tailed mutation operator, proposed by Doerr, Le, Makhmara, and Nguyen (2017) for evolutionary algorithms, is based on the power-law assumption of mutation rate distribution. Here we generalize the power-law assumption using a…
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…
We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best fit chromosomes from one generation to the next. We argue that the genetic algorithm should operate…
The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA…
Jump functions are the {most-studied} non-unimodal benchmark in the theory of randomized search heuristics, in particular, evolutionary algorithms (EAs). They have significantly improved our understanding of how EAs escape from local…
To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the $n$-dimensional Plateau$_k$ function as natural benchmark and analyze how different variants of the $(1 +…
We study the $(1,\lambda)$-EA with mutation rate $c/n$ for $c\le 1$, where the population size is adaptively controlled with the $(1:s+1)$-success rule. Recently, Hevia Fajardo and Sudholt have shown that this setup with $c=1$ is efficient…
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 many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem…
The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use…
The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible…
We propose and analyze a self-adaptive version of the $(1,\lambda)$ evolutionary algorithm in which the current mutation rate is part of the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark…
Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous…