We reconsider a classical problem, namely how the (1+1) evolutionary algorithm optimizes the LEADINGONES function. We prove that if a mutation probability of p is used and the problem size is n, then… Expand

This book covers both classical results and the most recent theoretical developments in the field of randomized search heuristics such as runtime analysis, drift analysis and convergence.Expand

This work proposes a random mutation rate α/n, where α is chosen from a power-law distribution and proves that the (1 + 1) EA with this heavy-tailed mutation rate optimizes any Jumpm, n function in a time that is only a small polynomial factor above the one stemming from the optimal rate for this m.Expand

This work introduces multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms and demonstrates how it immediately gives natural proofs for the best known runtime bounds for the (1+1) Evolutionary Algorithm on combinatorial problems like finding minimum spanning trees, shortest paths, or Euler tours in graphs.Expand

The main result is a simple randomized algorithm called median rule that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most √n processes at any time.Expand

A few hubs with many connections share with many individuals with few connections, leading to a chain of relationships that is mutually beneficial to both parties.Expand

It is proved that if its population size is chosen according to the one-fifth success rule then the expected optimization time on OneMax is linear, better than what any static population size λ can achieve and is asymptotically optimal also among all adaptive parameter choices.Expand

This work designs a new crossover-based genetic algorithm that uses mutation with a higher-than-usual mutation probability to increase the exploration speed and crossover with the parent to repair losses incurred by the more aggressive mutation.Expand

This work studies the performance of randomized rumor spreading protocols on graphs in the preferential attachment model and proves the first time that a sublogarithmic broadcast time is proven for a natural setting.Expand

A multiplicative version of the classical drift theorem is proved, which gives natural proofs for the best known run-time bounds for the (1+1) Evolutionary Algorithm computing minimum spanning trees and shortest paths.Expand