Algorithm Performance Comparison of the (1+1) EA with Heavy-Tailed Mutators

We study variants of the (1+1) EA with heavy-tailed mutation operators in discrete optimization on an n-dimensional integer space. By combining heavy-tailed and concentrated distributions for both dimension selection and step size, we develop two novel variants: singly and doubly heavy-tailed mutators. Through experiments on integer-valued ONEMAX, integer-valued HURDLE, and a non-linear resource allocation problem, we demonstrate that these variants offer significant performance improvements. The singly heavy-tailed variant excels at escaping local optima, while the doubly heavy-tailed variant shows superior performance on complex non-linear problems.