The Pitfalls and Potentials of Adding Gene-invariance to Optimal Mixing

Abstract: Optimal Mixing (OM) is a variation operator that integrates local search with genetic recombination. EAs with OM are capable of state-of-the-art optimization in discrete spaces, offering significant advantages over classic recombination-based EAs. This success is partly due to high selection pressure that drives rapid convergence. However, this can also negatively impact population diversity, complicating the solving of hierarchical problems, which feature multiple layers of complexity. While there have been attempts to address this issue, these solutions are often complicated and prone to bias. To overcome this, we propose a solution inspired by the Gene Invariant Genetic Algorithm (GIGA), which preserves gene frequencies in the population throughout the process. This technique is tailored to and integrated with the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), resulting in GI-GOMEA. The simple, yet elegant changes are found to have striking potential: GI-GOMEA outperforms GOMEA on a range of well-known problems, even when these problems are adjusted for pitfalls - biases in much-used benchmark problems that can be easily exploited by maintaining gene invariance. Perhaps even more notably, GI-GOMEA is also found to be effective at solving hierarchical problems, including newly introduced asymmetric hierarchical trap functions.