Correlated Geometric Mutations for Integer Evolution Strategies
Ofer M. Shir, Michael Emmerich · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2025
Evolution Strategies (ESs) are effective randomized heuristics for black-box numerical optimization, known for advanced step-size adaptation and invariance to function transformations and decision space rotations. Typically used for continuous optimization, ESs have been adapted for integer and mixed-integer problems using independent multivariate or truncated continuous mutations. This study explores ESs for nonlinear integer optimization in unbounded search-spaces, based on Rudolph's 1994 convergence and unbiasedness principles, albeit with their application limited to independent Double-Geometric (DG) distributions. In this paper, we extend it and propose a procedure for generating correlated DG-mutations. We hypothesize that such mutations are suitable for integer spaces and can enhance nonseparable problem-solving. To begin, we use the 1/5th success-rule to test the DG mutation distribution in a minimal, elitist single-parent scenario. Then, we validate our hypotheses on an unconstrained quadratic integer test-suite across various dimensions. We show that replacing the conventional Truncated Normal distribution with the DG distribution usually achieves better outcomes in both separable and nonseparable scenarios.