Whitley, Darrell, authorOchoa, Gabriela, authorChicano, Francisco, authorACM, publisher2025-09-252025-09-252025-07-13Darrell Whitley, Gabriela Ochoa, and Francisco Chicano. 2025. How Partition Crossover Exposes Parallel Lattices and the Fractal Structure of k- Bounded Functions. In Genetic and Evolutionary Computation Conference (GECCO '25), July 14-18, 2025, Malaga, Spain. ACM, New York, NY, USA, 9 pages. https://doi.org/10.1145/3712256.3726340https://hdl.handle.net/10217/242032A combination of recombination and local search can expose the existence of an exponential number of parallel lattices that span the search space for all classes of k-bounded pseudo-Boolean functions, including MAX-kSAT problems. These "parallel" lattices sometimes have identical evaluations shifted by a constant. We use Partition Crossover to aid in the discovery of lattices, which are sets of 2q possible offspring from recombination events, organized into q-dimensional hypercubes, where q is the number of recombining components given two parents. Finally, we show that recursively embedded subspace lattices display a fractal structure, which can be captured using rewrite rules based on a Lindenmayer system that accurately model how local optima are distributed across different size lattices.born digitalarticleseng©Darrell Whitley, et al. ACM 2025. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in GECCO '25, https://dx.doi.org/10.1145/3712256.3726340.Partition Crossoverlatticesgenetic algorithmscombinatorial optimizationTexthttps://doi.org/10.1145/3712256.3726340