Fast Mutation in Crossover-Based Algorithms

• Published in: Algorithmica Vol. 84; no. 6; pp. 1724 - 1761
• Main Authors: Antipov, Denis, Buzdalov, Maxim, Doerr, Benjamin
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: 2020; Algorithm Analysis and Problem Complexity; Algorithms; Asymptotic properties; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Empirical analysis; Genetic algorithms; Mathematics of Computing; Mutation; Optimization; Special Issue on Genetic and Evolutionary Computation; Theory of Computation
• ISSN: 0178-4617; 1432-0541; 1432-0541
• DOI: 10.1007/s00453-022-00957-5

The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms. There, it can relieve the algorithm designer from finding the optimal mutation rate and nevertheless obtain a performance close to the one that the optimal mutation rate gives. In this first runtime analysis of a crossover-based algorithm using a heavy-tailed choice of the mutation rate, we show an even stronger impact. For the ( 1 + ( λ , λ ) ) genetic algorithm optimizing the OneMax benchmark function, we show that with a heavy-tailed mutation rate a linear runtime can be achieved. This is asymptotically faster than what can be obtained with any static mutation rate, and is asymptotically equivalent to the runtime of the self-adjusting version of the parameters choice of the ( 1 + ( λ , λ ) ) genetic algorithm. This result is complemented by an empirical study which shows the effectiveness of the fast mutation also on random satisfiable MAX-3SAT instances.