Related papers: Improved Runtime Analysis of a Multi-Valued Compac…
Compact Genetic Algorithms (cGAs) are condensed variants of classical Genetic Algorithms (GAs) that use a probability vector representation of the population instead of the complete population. cGAs have been shown to significantly reduce…
Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted. Continuing this research direction, we prove that the NSGA-II optimizes the OneJumpZeroJump…
NSGA-III is a prominent algorithm in evolutionary many-objective optimization. It is particularly well suited for optimizing problems with more than three objectives, distinguishing it from the classical NSGA-II. However, theoretical…
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…
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…
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…
The compact genetic algorithm (cGA) is an non-elitist estimation of distribution algorithm which has shown to be able to deal with difficult multimodal fitness landscapes that are hard to solve by elitist algorithms. In this paper, we…
Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables…
In many real-world optimization problems, the objective function evaluation is subject to noise, and we cannot obtain the exact objective value. Evolutionary algorithms (EAs), a type of general-purpose randomized optimization algorithm,…
The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has…
Estimation of distribution algorithms (EDAs) provide a distribution - based approach for optimization which adapts its probability distribution during the run of the algorithm. We contribute to the theoretical understanding of EDAs and…
Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a…
Randomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a…
In single-objective optimization, it is well known that evolutionary algorithms also without further adjustments can tolerate a certain amount of noise in the evaluation of the objective function. In contrast, this question is not at all…
The JUMP$_k$ benchmark was the first problem for which crossover was proven to give a speed-up over mutation-only evolutionary algorithms. Jansen and Wegener (2002) proved an upper bound of $O(\text{poly}(n) + 4^k/p_c)$ for the ($\mu$+1)…
Despite significant progress in the field of mathematical runtime analysis of multi-objective evolutionary algorithms (MOEAs), the performance of MOEAs on discrete many-objective problems is little understood. In particular, the few…
The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a state of the art evolutionary algorithm that leverages linkage learning to efficiently exploit problem structure. By identifying and preserving important building blocks…
The heavy-tailed mutation operator proposed in Doerr, Le, Makhmara, and Nguyen (GECCO 2017), called \emph{fast mutation} to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms.…
The running-time analysis of evolutionary combinatorial optimization is a fundamental topic in evolutionary computation. Its current research mainly focuses on specific algorithms for simplified problems due to the challenge posed by…
Runtime analysis aims at contributing to our understanding of evolutionary algorithms through mathematical analyses of their runtimes. In the context of discrete optimization problems, runtime analysis classically studies the time needed to…