DeepAI AI Chat
Log In Sign Up

Better Runtime Guarantees Via Stochastic Domination

by   Benjamin Doerr, et al.

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 area. Stochastic domination allows to formulate much more informative performance guarantees than the expectation alone, it allows to decouple the algorithm analysis into the true algorithmic part of detecting a domination statement and probability theoretic part of deriving the desired probabilistic guarantees from this statement, and it allows simpler and more natural proofs. As particular results, we prove a fitness level theorem which shows that the runtime is dominated by a sum of independent geometric random variables, we prove tail bounds for several classic problems, and we give a short and natural proof for Witt's result that the runtime of any (μ,p) mutation-based algorithm on any function with unique optimum is subdominated by the runtime of a variant of the (1+1) evolutionary algorithm on the OneMax function.


page 1

page 2

page 3

page 4


On Non-Elitist Evolutionary Algorithms Optimizing Fitness Functions with a Plateau

We consider the expected runtime of non-elitist evolutionary algorithms ...

Stochastic Runtime Analysis of a Cross Entropy Algorithm for Traveling Salesman Problems

This article analyzes the stochastic runtime of a Cross-Entropy Algorith...

Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus

We propose a new method based on discrete Fourier analysis to analyze th...

A Tight Runtime Analysis for the (μ+ λ) EA

Despite significant progress in the theory of evolutionary algorithms, t...

How Well Does the Metropolis Algorithm Cope With Local Optima?

The Metropolis algorithm (MA) is a classic stochastic local search heuri...

Optimal Parameter Choices via Precise Black-Box Analysis

It has been observed that some working principles of evolutionary algori...

On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism

Clearing is a niching method inspired by the principle of assigning the ...