🤖 AI Summary
This work addresses the challenge of optimizing real-world problems involving heterogeneous parameters—such as integers, real numbers, booleans, categorical variables, complex-valued descriptors, and embedding vectors—which are poorly handled by standard evolutionary algorithms. To this end, we propose GSA, a type-decomposed coevolutionary framework that groups genes by data type, applies type-native genetic operators in parallel, and explicitly reassembles phenotypes for joint evaluation. GSA is the first method to directly support optimization over complex numbers and embedding vectors, overcoming the limitations of conventional flat encodings through elite credit assignment and an active assembly strategy. Evaluated on seven benchmarks including BBOB-MixInt, GSA uniquely handles complex and embedding types, matches or approaches state-of-the-art performance under high evaluation budgets, and demonstrates the necessity of its core components via ablation studies.
📝 Abstract
Many real-world optimization problems are not naturally homogeneous vectors but composite design objects with heterogeneous parameters: integers, real values, Booleans, categoricals, complex-valued descriptors, and embedding vectors. Standard evolutionary algorithms flatten these into a single chromosome and apply generic operators with rounding and repair, sacrificing representational fidelity. We introduce the Geno-Synthetic Algorithm (GSA), a type-factored coevolutionary framework in which gene families are partitioned by representational type, evolved in parallel with type-native operators, and assembled into executable phenotypes for joint fitness evaluation. GSA is formalized as a typed product-space search procedure with an explicit assembly operator. An open-source reference implementation (gsa-experiments, MIT-licensed) is released. A focused empirical study compares eight GSA variants against five baselines across seven benchmark problems (six synthetic plus the external COCO BBOB-MixInt suite) at budgets from 5,000 to 100,000 evaluations. The headline finding is architectural: GSA is the only method that operates when gene families include complex-valued descriptors or embedding vectors. On smooth synthetic multi-family problems, well-tuned flattened differential evolution remains the strongest baseline; on BBOB-MixInt at 100,000 evaluations, GSA_DIRECT becomes statistically indistinguishable from FLATTENED_DE while FLATTENED_EA drops from second to fifth rank, an asymptotic crossover. Ablations confirm that type-native operators are essential, elite credit dominates ensemble credit, and active assembly outperforms passive concatenation on gated benchmarks. The framework extends naturally to prompt and embedding optimization for large language model systems.