Fast Mutation in Crossover-based Algorithms

• URL: http://arxiv.org/abs/2004.06538v4
• Date: Tue, 1 Mar 2022 11:42:05 GMT
• Title: Fast Mutation in Crossover-based Algorithms
• Authors: Denis Antipov, Maxim Buzdalov, Benjamin Doerr
• Abstract summary: Heavy-tailed mutation operator proposed in Doerr, Le, Makhmara and Nguyen (GECCO) A heavy-tailed mutation operator proposed in Doerr, Le, Makhmara and Nguyen (GECCO) An empirical study shows the effectiveness of the fast mutation also on random satisfiable Max-3SAT instances.
• Score: 8.34061303235504
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. 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 $(1+(\lambda,\lambda))$ 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 $(1+(\lambda,\lambda))$ 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.

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