Related papers: Multiplicative Drift Analysis
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…
We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with…
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…
We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using $k$-bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are…
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function $f$, but instead optimizes $N + 1$ single-objective subproblems of $f$ in a co-evolutionary manner. It…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
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…
A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann (2013). In this paper, we extend…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
Randomized search heuristics have been applied successfully to a plethora of problems. This success is complemented by a large body of theoretical results. Unfortunately, the vast majority of these results regard problems with binary or…
Hillclimbing is an essential part of any optimization algorithm. An important benchmark for hillclimbing algorithms on pseudo-Boolean functions $f: \{0,1\}^n \to \mathbb{R}$ are (strictly) montone functions, on which a surprising number of…
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current…
Recently there has been much work on selective sampling, an online active learning setting, in which algorithms work in rounds. On each round an algorithm receives an input and makes a prediction. Then, it can decide whether to query a…
Evolutionary neural architecture search (ENAS) employs evolutionary algorithms to find high-performing neural architectures automatically, and has achieved great success. However, compared to the empirical success, its rigorous theoretical…
A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a…
Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
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…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…