cgp recombination

Conventional wisdom holds that recombination operators offer little performance benefit in Cartesian Genetic Programming (CGP), leading to their long-standing neglect. This study systematically optimizes the hyperparameters of two recombination strategies—subgraph crossover and discrete phenotypic recombination—within the TinyverseGP framework on the SRBench benchmark platform. For the first time, it demonstrates that carefully tuned recombination significantly enhances CGP’s performance on symbolic regression tasks. Challenging the prevailing paradigm that CGP relies predominantly on mutation, this work establishes that recombination, when appropriately configured, possesses substantial potential. These findings open new avenues for the design of evolutionary algorithms by reintegrating recombination as a key operator in CGP.

Crossover operations in Cartesian Genetic Programming (CGP) commonly degrade performance, and existing remedies lack generality. Method: This paper introduces the Node Preservation Mechanism (NPM), which explicitly safeguards the structural integrity of functional modules during crossover and mutation. NPM is compatible with unary-point, uniform, and subgraph crossover, and synergizes with node-level mutation and standard point mutation. Contribution/Results: Systematic experiments across multiple symbolic regression benchmarks—first to rigorously evaluate NPM—demonstrate statistically significant improvements in convergence speed and solution quality, with consistent and reproducible outcomes. Beyond resolving the long-standing issue of crossover ineffectiveness in CGP, this work establishes a generalizable framework for enhancing evolutionary robustness in modular genetic representations, thereby opening a new research direction for structurally aware genetic programming.

This study investigates the runtime complexity of evolving Boolean functions using Cartesian Genetic Programming (CGP), with a focus on the stark efficiency differences between conjunction and XOR functions. Through theoretical analysis and empirical validation, the work establishes—using probabilistic methods, program graph representations, and both strict and non-strict selection mechanisms—the first asymptotic upper bound of $O(n D^4)$ on the expected number of fitness evaluations required to evolve conjunctions, demonstrating that accepting neutral moves significantly accelerates search. In contrast, it rigorously proves that evolving XOR functions necessitates exponential time. Experimental results corroborate these theoretical findings and further reveal that employing incomplete training sets can substantially reduce evaluation costs while maintaining strong generalization performance.

This work addresses the challenge of optimization stagnation in existing automated design methods for approximate arithmetic circuits, which often struggle to balance accuracy and hardware efficiency. To overcome this limitation, the study introduces a novel mutation operator that integrates the Transformer architecture into Cartesian Genetic Programming (CGP) for the first time. The proposed operator is trained on large-scale chromosome samples and embedded within a dynamic hybrid strategy that adaptively switches between standard and Transformer-based mutation during evolution. Evaluated on approximate multiplier synthesis, the method significantly enhances evolutionary efficiency and consistently yields designs that outperform the best entries in EvoApproxLib across multiple error constraints, achieving superior trade-offs among accuracy, area, and power consumption. These results demonstrate both notable innovation and strong practical potential.

In conventional genetic algorithms, two-parent recombination often introduces high-destructive variance, impairing convergence and stability. To address this, we propose a family of multi-parent recombination operators grounded in Pascal (binomial) coefficients: normalized binomial weights construct structured convex combinations, enabling centralized genetic search and substantially suppressing offspring variance fluctuations. This work introduces the binomial weighting mechanism to multi-parent recombination for the first time, enhancing schema preservation while natively supporting real-valued, binary, and permutation encodings—ensuring universality and plug-and-play compatibility. Theoretical analysis establishes its variance decay property and schema survival advantage. Empirical evaluation across four benchmark problem classes demonstrates 9–22% performance improvement over standard genetic algorithms, with markedly enhanced convergence stability and optimization efficiency.

This work addresses the inefficiency of traditional genetic algorithms in solving optimization problems due to their reliance on random mutation and recombination, which lack goal-directedness. The authors formulate the problem through the lens of query complexity and propose objective-guided mutation and recombination operators informed by the optimization target. Leveraging reinforcement learning and formal language theory, they analyze the theoretical properties of these operators. For the first time, the study mathematically characterizes the mechanism of goal-directed genetic operators and demonstrates the necessity of population diversity for certain classes of optimization problems. A general model of genetic algorithms is established, enabling the design of a tight algorithm for a specific problem class, and proving that the synergy among generation, mutation, and recombination is essential for efficient optimization.

This work addresses the well-known issue of code bloat in traditional genetic programming for symbolic regression, which often impedes stable recovery of the true underlying model. Inspired by the linguistic Minimalist Program, the authors reformulate program induction as a syntactic derivation task, abandoning the conventional evolutionary search paradigm. They propose a Markovian incremental construction mechanism based on a binary MERGE operator that systematically builds symbolic expressions from a lexicon of atomic syntactic objects. This approach reliably and accurately reconstructs ground-truth models on symbolic regression benchmarks where standard genetic programming fails, demonstrating significantly superior performance over traditional methods.

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.