Heavy-Tailed Mutation Operators in Single-Objective Combinatorial Optimization
A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a new mutation operator and analyze its performance on the (1+1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1+1) EA on classes of problems for which results on the other mutation operators are available. We present a “jump” function for which the performance of the (1+1) EA using any static uniform mutation and any restart strategy can be worse than the performance of the (1+1) EA using our mutation operator with no restarts. We show that the (1+1) EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve this problem.
Finally, we evaluate experimentally the performance of the (1+1) EA using our operator, on real-world graphs of different origins with up to \(\sim \)37 000 vertices and \(\sim \)1.6 million edges. In comparison with uniform mutation and a recently proposed dynamic scheme our operator comes out on top on these instances.
KeywordsMutation operators Minimum vertex cover problem Submodular functions maximization
The authors would like to thank Martin Krejca for giving his advice on one of the proofs, and Karen Seidel for proof-reading the paper.
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