Genetic Algorithms

Genetic Programming and its variants, such as grammatical evolution, are widely used in Symbolic Regression to derive mathematical expressions from multivariate data. In addition to predictive accuracy, models are appreciated for their potential to provide interpretability, offering explicit equations that relate input variables to outcomes. However, achieving interpretability and plausibility remains challenging, as evolved models may be complex or scientifically inconsistent. In this study, we explore whether Large Language Models, can assist in improving the explainability of Symbolic Regression models generated by evolutionary computation methods. Building upon our previous work on estimating body fat percentage using grammar-based Genetic Programming , we investigate the use of LLMs as post-processing tools to analyze and rank evolved expressions according to their interpretability and medical plausibility. Four symbolic expressions are analysed by three LLMs over three repeated runs, and the resulting interpretations and rankings are assessed by a panel of three clinicians. Across the three LLMs, comparative model-ranking outputs received more favorable clinician assessments than isolated term-level interpretations. However, the LLMs also produced physiologically and mathematically questionable explanations, indicating that they are better suited to comparative auditing under expert oversight than to autonomous validation.\blfootnote{The present work is an extended version of a paper submitted into a journal.

This paper introduces an evolutionary computation approach for consensus in structural Bayesian Network (BN) fusion under the constraint of limited treewidth. The consensus BN aims to reconcile multiple input BNs into a single one that retains key structural features present in the original networks. Treewidth, a graph-based parameter associated with computationally tractable inference, is utilized to restrict the complexity of the resulting network. A genetic algorithm is proposed to look for a BN that codifies as much information about the unrestricted fusion as possible while ensuring the treewidth restriction. Experimental evaluation demonstrates the genetic algorithm's ability to obtain consensus BNs with limited treewidth, providing a valuable tool for aggregating information from diverse sources while returning a computationally actionable model.

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

Constant optimization refines the numerical coefficients of candidate expressions in tree-based genetic programming for symbolic regression. But its per-generation cost has led modern GPU-accelerated frameworks to omit it or restrict it to lightweight forms. We present a GPU-resident, batched Levenberg--Marquardt solver that optimizes constants across a structurally heterogeneous population of expression trees using a fixed number of population-wide CUDA launches per iteration. Reverse-mode automatic differentiation assembles the per-tree Jacobian in one backward sweep, making the dominant per-iteration cost independent of the number of constants per tree, and a double-precision delivery guard guarantees that returned constants are never worse than their initial values. On early-generation populations, the solver sustains up to $5.1{\times}10^{5}$ trees per second on an NVIDIA A100; at a GPU-saturated benchmark configuration it delivers roughly $9.9{\times}$ the throughput of Operon running on a 64-core EPYC 7763, while matching fp64-reference quality. Integrated in-process into EvoGP, the solver enables end-to-end search to recover governing equations on $10$ of $18$ constructed problems versus 0 for stock EvoGP. Our code is at https://github.com/TensorConv/CuSR.

Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.

Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared on 15 instances using matched random seeds and fixed limits on distinct assignment evaluations. Because the evaluation budgets for test Instances 13-15 are smaller than the nominal population size, these experiments primarily assess the quality of learned initialization rather than multi-generation evolutionary search. A separate 400-evaluation experiment on exact test Instance 13 permits three complete offspring generations and a partial fourth pass, with GNN-GA outperforming GA in all 10 matched runs. Three independently generated exact-solvable instances provide a separate test of transfer. Ablation results show that learned initialization provides most of the improvement, while entropy-guided mutation has a smaller, instance-dependent effect. Per-instance solution times include GNN inference and search but exclude model training and one-time model setup.

Automated formulaic alpha discovery aims to generate predictive and interpretable trading signals from large symbolic factor spaces. Its effectiveness is constrained by noisy fitness estimates, market nonstationarity, costly backtesting, semantic redundancy, and conflicting practical objectives. Existing studies employ diverse techniques, including genetic programming (GP), evolutionary algorithms (EAs), reinforcement learning (RL), generative flow networks (GFlowNets), Monte Carlo tree search (MCTS), large language models (LLMs), and agentic workflows, but generally examine them as separate algorithmic families. This article introduces, for the first time, a unified evolutionary computation (EC) perspective on automated formulaic alpha discovery, formulating it as a noisy, dynamic, and multiobjective symbolic evolutionary optimization problem. A six-component analytical framework is developed to characterize existing methods through representation, variation, fitness evaluation, selection, memory, and adaptation. Furthermore, an eight-dimensional, autonomy-oriented evaluation framework is proposed, covering search efficiency, fitness reliability, residual alpha quality, economic diversity, tradability, evolutionary autonomy, robustness to nonstationarity, and reproducibility. Together, these frameworks provide a systematic foundation for unifying heterogeneous approaches, diagnosing component-level limitations, and guiding the development of reliable, adaptive, interpretable, and reproducible autonomous alpha discovery systems.

In dynamic multi-mode project scheduling, activities have alternative execution modes and uncertain durations, while precedence relations and limited resources constrain their execution. Heuristic priority rules support fast online decisions, but their design requires substantial domain expertise. Genetic programming (GP) hyper-heuristics can automatically evolve such rules. Large language models (LLMs), meanwhile, provide a flexible interface for interpreting scheduling information and explaining decisions. However, zero-shot LLM decisions may lack domain knowledge, consume many tokens, and vary across repeated queries. GP-evolved rules therefore provide a potential source of scheduling knowledge for guiding LLM decisions. Unlike existing LLM--GP hybrids that use LLMs to support heuristic evolution, we transfer knowledge in the reverse direction, using knowledge extracted from high-quality GP rules to guide an online LLM decision maker. We extract knowledge from high-quality GP rules and inject it through Feature Selection, Feature Hint, Rule Reference, and Rule Follow. These mechanisms are evaluated in terms of scheduling performance, token consumption, decision stability, and the feature focus expressed in generated rationales. GP-derived guidance generally improves the unguided LLM, but its representation matters. Simplifying the decision context or supplying explicit decision logic is more effective than highlighting important features. Feature Selection offers the best token efficiency, whereas Rule Follow achieves strong performance at greater token cost. Guidance also improves decision stability and changes the features expressed in generated rationales.

Parent selection significantly affects exploration, exploitation, and complexity control in genetic programming (GP) for symbolic regression. It is unclear whether large language models (LLMs) can synthesize effective operators in a zero-shot setting without iterative meta-evolution. Here, zero-shot means that the model receives only the task description, with no reference operators or iterative feedback. In this work, we benchmark zero-shot synthesis of parent-selection operators across eight LLMs within a standard GP framework for symbolic regression. Each model receives the same natural-language prompt to generate a parent-selection operator, which is then evaluated in a standard GP framework with only the parent-selection operator replaced, while all other components and the evolutionary-search budget are held constant. For each LLM, ten independent zero-shot operators are evaluated on twelve OpenML regression benchmarks and compared against automatic lexicase and tournament selection baselines. Claude Sonnet4.6 and Gemini3.1 Pro stand out for consistently strong performance on both training and held-out test $R^2$. The strongest operator in our benchmark---a Kimi~K2.5 zero-shot synthesis---surpasses the automatic lexicase and tournament baselines in search effectiveness. These results suggest that zero-shot LLM synthesis is a viable approach to generating competitive GP selection operators. Analysis shows that many generated operators use semantics to guide selection, suggesting that LLMs can produce non-trivial search heuristics from the task description alone. We also examine the relationship between public LLM leaderboard rankings and GP performance. Widely used benchmarks, such as Humanity's Last Exam and SWE-bench Verified, strongly correlate with training $R^2$, while their relationship to held-out test $R^2$ is weaker and less clear.

The optimal allocation of academic resources to individual students is essential for addressing learner diversity and fostering equitable educational outcomes. Within the framework of the Erasmus+ KA220-SCH project, this paper models the selection of educational materials for high school mathematics students as a 0--1 binary combinatorial optimization problem subject to strict study time constraints. Given the NP-hard complexity of the formulation, exact solution methods become computationally intractable as resource catalogs scale. To address this challenge, we propose a Genetic Algorithm integrated with a specialized constraint repair mechanism to effectively search the binary decision space. Experimental evaluation across 10 independent runs demonstrates fast convergence, high solution quality, and strong algorithmic stability across different base seeds. These results confirm the practical utility of metaheuristic approaches for real-time decision-support systems in secondary education.

The paper develops the approach to the runtime analysis of evolutionary algorithms on the basis of limit theorems from probability theory. We consider the family of Jump$_k$ benchmark functions, defined on the search space of binary strings of length $n$, parametrized by the integer $k$, which have a plateau of multiple local optima at the Hamming distance $k$ from a unique global optimum. In this work, we consider the genetic algorithm $(1+(λ,λ)) GA$ from (Doerr, Doerr and Ebel, 2015) with tunable parameters of the mutation rate $p$, crossover bias $c$, and two intermediate population sizes $λ_M$ and $λ_C$. We study the time it escapes from the plateau of local optima and reaches the global optimum in the case of Jump$_k$ fitness function and tighten the upper bounds on the expected escape time, known from the work of Antipov, Doerr and Karavaev (2022). The obtained bounds also apply to a wider range of algorithmic parameters. The main result of this work applies to the case when $k\to \infty$ as $n \to \infty.$ The case of finite $k$ is investigated quite simply and considered tangentially.

Many-objective optimization has been a field of interest over the past two decades and several evolutionary optimization algorithms have been introduced to tackle these problems; yet two fundamental questions remain underexplored: (i) What happens when the number of objectives grows beyond the typical many-objective regime of about fifteen and becomes massive? (ii) How do problem characteristics, such as the nature of interactions between objectives, influence algorithmic performance? To answer these questions we employ a diagnostic benchmark suite that allows control over problem characteristics and can be scaled to extremely high objective counts. Using this framework we evaluate several state-of-the-art evolutionary algorithms including NSGA-II, NSGA-III, MOEA/D and lexicase selection across a range of dimensionalities and diagnostic problem landscapes. Our experiments reveal that problem characteristics significantly affect algorithm performance. In particular, the nature of interactions between objectives appears important. These results highlight the importance of understanding these properties before selecting an algorithm for a specific problem. We also show that lexicase selection, an algorithm originally designed for genetic programming, compares favorably with state-of-the-art many-objective optimization algorithms while avoiding the dependence on predefined reference directions.

The Beagle framework is a GPU-based genetic programming framework that enables highly efficient genetic programming search using large population sizes by leveraging NVIDIA GPUs. This technical guide provides an introduction to the Beagle framework and provides detailed instructions for using the framework for symbolic regression problems.

Recent advancements in agentic AI have increasingly moved toward graph-based methods, driven by the demand for explainable, human-centered, and non-linear reasoning workflows. A prominent example is Genetic Network Programming (GNP), a self-evolving algorithm that utilizes directed graphs to evolve interpretable decision structures for agents. As in most evolutionary algorithms, effectively balancing exploration and exploitation is a key aspect of GNP. However, this trade-off has received limited attention in the GNP literature. To address this gap, we draw inspiration from human developmental patterns, where children prioritize broad experimentation and action over deliberation, with this tendency reversing with age. By mapping transitions between GNP's judgment nodes to deliberation and processing nodes to action, we propose Human-Inspired GNP (HGNP), a novel adaptive framework that dynamically regulates the exploration-exploitation balance throughout the evolutionary process. The method consists of novel adaptive crossover and mutation operators, and a cycle elimination mechanism. HGNP not only improves the evolutionary process but also provides a framework for adjusting the exploration-exploitation balance based on the characteristics of the target environment and its search space. This approach is more effective than tuning via crossover and mutation probabilities in standard GNP. The modifications are general and can be applied to almost all GNP variants. When integrated with standard GNP and two recently introduced GNP variants and evaluated on the Tileworld benchmark, HGNP demonstrated significant performance improvement in agents' strategy. The combination of HGNP with Situation-based GNP (HGNP-SBGNP) achieved the best overall results.

The one-dimensional bin packing problem (1D-BPP) is a canonical NP-hard combinatorial optimization problem with broad industrial applications. We propose RL-HGGA, a hybrid algorithm that integrates Falkenauer's Hybrid Grouping Genetic Algorithm (HGGA) with a tabular Q-learning controller. Rather than applying genetic operators at fixed probabilities, a Q-learning agent dynamically selects among eight macro-actions -- including BPCX crossover, light and heavy mutation, Martello-Toth local search, and population restart -- based on an eight-dimensional state representation encoding generation progress, stagnation level, optimality gap, average fitness, population variance, and average bin fill rate. The agent is trained with an epsilon-greedy policy over 400 episodes, with epsilon decaying to 0.05. Experiments on standard benchmark families (Falkenauer T/U, Scholl 1-3, Hard28) show that RL-HGGA achieves an average optimality gap of 0.95% -- competitive with HGGA (0.75%) and well below FFD (2.47%) -- while reducing mean computation time from 64.22 s to 1.29 s, a 50x speedup. These results demonstrate that learned adaptive operator selection can achieve near-HGGA solution quality at a fraction of the computational cost.

We analyze the effect of optimizing the initial population of genetic programming (GP) for symbolic regression (SR) on the accuracy and complexity of solutions. We compare three well-established random initialization methods as well as initialization with small optimized solutions from exhaustive symbolic regression (ESR) using a GP/SR implementation which is based on the multi-objective evolutionary algorithm NSGA-II. We compare the final Pareto fronts found with each initialization method on twelve synthetic problems of varying complexity and one real-world dataset. We find no significant differences in accuracy or model complexity among the initialization methods. The initial advantage of initialization with ESR disappears after only a few generations. Our results show that, given similar diversity in the initial population, the effect of the initialization method in GP-based symbolic regression on the final Pareto front is negligible.

We show that the effective dynamics of the elitist $(1+M)$ genetic algorithm is, in the limit of small mutations, clipped gradient descent on the loss in the presence of anisotropic Gaussian white noise. In expectation, therefore, a simple mutation-selection genetic algorithm follows the gradient of the loss, without explicit calculation of gradients and without averaging over loss evaluations. The genetic algorithm is slower than gradient descent because of the noise that acts in directions transverse to the gradient. However, this slowdown is controlled not by the number of parameters of the search space but by the effective rank of the Hessian of the loss function. For the concentrated Hessian spectra observed in neural-network loss functions the effective rank can be far smaller than the number of parameters, which may explain why genetic algorithms can scale to large search spaces.

Deep learning models have achieved impressive performance across various fields but remain vulnerable to adversarial inputs, particularly in NLP, where such attacks can have significant real-world consequences. Adversarial attacks often involve small, semantically similar token replacements to fool NLP models, and recent methods have become more precise by targeting specific vulnerable words, often by exploiting some level of access to the model's internal structure. This paper proposes GAversary, a hybrid Genetic Algorithm (GA) to generate adversarial attacks on natural language models. The GA is able to treat the target model as a black box, requiring only the logit value output by the model to guide the search. GAversary differs from GAs previously proposed for this problem by using GloVe embeddings to propose word replacements (the mutation operator) to improve the semantic similarity of the adversarial examples. GAversary is applied to several benchmark data sets and well-known target models. GAversary is able to substantially reduce the target model's accuracy on test data compared to the BAE and A2T attacks compared against (in the best case, reducing a 76.8% accuracy to 5.8%, compared to BAE's 27.6%). The trade-off is that GAversary perturbs just under twice as many words as the other two methods, with a slightly lower semantic similarity to the original text and around a 5% increase in run-time.

This paper describes an automatic method for adjusting or tuning models of multi-agent motion. Simulating the motion of bird flocks, human crowds, vehicle traffic, and other multi-agent systems is a widely used technique. These simulations model the behavior of a single group member (bird, human, or vehicle). The group behaviors (flock, crowd, traffic) emerge from interactions between group members. These models typically have many numerical control parameters. Even if each parameter is intuitive in isolation, their interaction can be complex and nonlinear. It is challenging to determine which parameters to adjust for the desired change in group behavior. Changing one aspect of group behavior often causes other aspects to change, leading to a tedious process of incremental changes. This work takes an inverse design approach. The desired group behavior is measured with a user-defined objective(/fitness/loss) function and optimized with a genetic algorithm. The objective function used here for basic flocking rewards proper spacing with neighbors, flying near a desired speed, and avoiding obstacles. Interestingly, the vivid alignment seen in bird flocks appears to emerge from maintaining proper spacing between flockmates.

Traditional evaluation of machine learning (ML) models typically focuses on achieving the maximum possible accuracy irrespective of the computational cost. In this article, we propose a paradigm shift towards evaluating performance based on computational effort-explicitly defined here as the total number of gradient descent steps required to reach an acceptable level of accuracy with high probability. Building upon the concept of computational effort originally introduced by Koza for Genetic Programming, we extend this metric to any ML model trained via gradient descent. Furthermore, we demonstrate that minimising this effort acts as a novel form of Automatic Machine Learning (AutoML). By evaluating it across 11 diverse ML models and five standard classification datasets, we uncover significant insights into the dynamics of gradient-based learning. Our findings reveal that optimal hyper-parameters consistently favour unusually large learning rates. Crucially, we demonstrate that the rapid, aggressive landscape traversal enabled by these large rates not only promotes generalisation-as seen in phenomena like superconvergence-but also statistically minimises the expected computational effort for training. Furthermore, we identify distinct phase transitions in the optimal search strategy: while a single training run suffices for lower accuracy targets, reaching a model's performance limit requires a dramatic shift towards conducting numerous independent, short restarts. Finally, we illustrate how this effort-based paradigm provides a robust framework for model selection, allowing practitioners to choose optimal algorithms based on the difficulty of a problem as perceived by different models for a given target accuracy, or to maximise the achievable accuracy for a fixed budget of gradient descent steps.

Symbolic regression via genetic programming routinely fails on small, wide datasets - a regime common in clinical-trial monitoring, biostatistics, and engineering pilot studies - by converging on bloated, overfit expressions that exploit correlation rather than prediction. We present Evolutional Math, an open-source genetic programming system that combines four design choices to yield compact, interpretable formulas in this regime. First, fitness is measured by R-squared on held-out cross-validation folds rather than Pearson correlation on the training set, eliminating single-variable shortcuts that correlate but mis-scale. Second, a multi-island architecture runs independent populations seeded with distinct operator subsets (algebraic, logarithmic, trigonometric, and full) with ring-topology migration every M generations, preventing the search from collapsing into one region of formula space. Third, a structural deduplication scheme treats formulas differing only in constants as equivalent, so the elite archive contains structurally distinct candidates rather than near-duplicate variants. Fourth, top-k individuals undergo numerical constant refinement via scipy L-BFGS-B after each migration phase, decoupling structure search from parameter fitting. We evaluate the system on synthetic benchmarks of the form log(x_i) * x_j / (x_k * c), trigonometric mixtures, and an anonymized clinical site-monitoring dataset with 24 rows and approximately 290 candidate numeric features. The system consistently recovers compact ground-truth structures with R-squared at or above 0.99 within tens of thousands of unique formula evaluations. A reference implementation is released under a noncommercial source-available license.

Developing robust intrusion detection systems (IDS) for IoT environments requires large, labeled datasets capturing realistic traffic distributions across both benign and malicious activity. Existing public datasets suffer from fixed activity distributions and extreme class imbalance, while deep generative models (GANs, VAEs) provide no mechanism to enforce that synthetic packets remain within physically valid feature ranges. This paper proposes and compares two constraint-enforcing approaches for synthetic IoT network packet generation: (i) a statistical learning method combining PCA-based latent space sampling with dual One-Class SVM (OCSVM) and Isolation Forest (IF) boundary enforcement, and (ii) a genetic algorithm (GA) method that treats packet generation as a multi-objective optimization problem with explicit fitness criteria for anomaly model acceptance and distributional fidelity. Both methods embed hard validity constraints -- dual anomaly-detection gating, feature-range clamping, and independent validation -- directly into the synthesis pipeline. Evaluation on the complete ACI IoT 2023 dataset (1,231,411 packets, 12 attack categories, class imbalance up to 175,805:1) demonstrates that both methods achieve PASS status across all categories under independently trained validators with a 30% anomaly rate threshold: the statistical method attains 1.20% average anomaly rate with ~1,091 packets/s throughput, while the GA attains 0.62% average anomaly rate with organic per-class variance (0.00%-2.50%) at ~5.7 packets/s. Both methods successfully amplify the 5-sample ARP Spoofing category by 200x to 1,000 validated packets. The ~190:1 throughput ratio between methods, combined with their complementary quality profiles, provides evidence-based selection criteria for deployment contexts ranging from rapid dataset augmentation to adversarial robustness testing.

This paper presents an experimental study of motion planning for resilient continuum robots. In this study we mainly focused on multi-criteria decision-making, its application for path-planning algorithms, impact on the generated path and execution time. To do this, we used two well-known algorithms for path planning, namely Genetic algorithm and A star algorithm, and modified them by adding the Analytical Hierarchy Process algorithm to evaluate the quality of the paths generated. In our experiment the Analytical Hierarchy Process considers four different criteria, i.e. distance, motors damage, mechanical damage of the robot's arm and accuracy, each considered to contribute to the resilience of a continuum robot. The use of different criteria is necessary to increase the time to maintenance operations of the continuum robot. We conducted the experiments using two different simulated environments of the robot. Although we significantly simplified the robot's model and its environment, we still implemented some of the features of the environment based on the real robot prototype. In particular, one of the environments has single- as well as multi-path points, and other consists of the multi-path points only. The results show that, in contrast to A star, the performance time of Genetic algorithm does not depend on the environment's cardinality. It generates more diverse paths, which increases the robot's resilience.

Cartesian Genetic Programming (CGP) is among the practical and popular forms of Genetic Programming as it uses a graph-based representation of programs. This paper presents a first runtime analysis of CGP in evolving Boolean functions using complete training sets. We prove an asymptotic bound $O(n D^5)$ for the expected number of fitness evaluations of CGP to construct a conjunction of $n$ inputs using at most $D \geq n-1$ binary gates, a minimal function set, and even with a strict survival selection. When the non-strict selection is used, the bound is improved to $O(n D^4)$. Our analysis reveals interesting characteristics of CGP induced search, which have been only observed empirically. In particular, enabling the acceptance of equally good solutions, including those with connected gates non-contributing to fitness, can lead to a speedup, and consequently a better asymptotic time bound. In contrast to conjunctions, we also prove a negative result which shows that CGP requires exponential time to evolve an exclusive disjunction. Experiments evolving conjunctions complement our theoretical findings. The use of incomplete training sets is found to further reduce the average number of fitness evaluations while maintaining a good level of generalisation.

Create an optimization framework that combines fuzzy logic and genetic algorithms for risk assessment and coordination of generation, grid connection, load, and energy storage facilities in active distribution networks. In order to capture the system uncertainties caused by weather factors and dynamic user demands, this project uses fuzzy set representation to model renewable energy generation, load curves, and market prices. In the evolutionary process, genetic algorithms introduce fuzzy elements into system management, adjusting thru penalty factors to improve stability and seeking better scheduling or power dispatch solutions. At the same time, by penalizing uncertainty and constraint violations, the fitness function of the hybrid model aims to optimize the expected operational costs; it can produce feasible and economical results under unknown parameter conditions. Under conditions with a large supply of renewable energy and installed energy storage systems, simulation results for the IEEE-69 power system indicate that the fuzzy genetic algorithm strategy effectively reduces technical constraints compared to deterministic optimization schemes. The total investment remains at a similar level. Other data indicate that thru fuzzy reasoning optimization, unreasonable choices or impossible situations are avoided during the network adaptation process. This framework-based technical approach helps to construct an effective computational scheme that is aware of uncertainty in its outputs. This will provide a scientific basis for the uncertainty assessment in distribution network planning.

Recent work in ML applies genetic algorithms at inference time to iteratively improve solutions to optimization problems. The basic mutation and recombination operators involved are qualitatively different from those studied classically. Mutations are no longer random; an ML algorithm mutates a solution with the goal of improving an objective. Similarly, recombination is not based on random collages of parent solutions. Instead, it is an ML optimization-based operator whose goal is to synthesize improved solutions from its inputs. Thus, these mutation and recombination operators are more likely to improve the objective, but their computational cost is much higher. We introduce a general model of genetic algorithms and formulating optimization in this model as a query-complexity problem, using the language of reinforcement learning. We then study specialized models. We show that some optimization problems require generation, mutation, and recombination to be solved. We then obtain qualitatively tight algorithms for a family of problems within this framework that captures the nontrivial role of diversity in the solution pool, a key feature of practical ML genetic algorithms.

Genetic programming (GP) is based on two important insights. First, that any learning task can fundamentally be posed as a program induction problem, where the goal is to construct a symbolic hierarchical model that is expressed as a syntax tree. Second, to pose this task as a search problem, and use evolution to locate the desired model. Since it was proposed, GP has produced notable results in a wide range of tasks and problem domains. This work presents an alternative view by modifying the second core insight of GP, posing the problem as a syntactic derivation task instead. In particular, this paper presents Minimalist Genetic Programming (MGP), an algorithm that like GP is biologically inspired, but instead of evolution it takes inspiration from the Minimalist Program to human language, in which syntax is understood as an optimal solution to the problem of linking two other mental systems. In minimalism, the core computational process is a binary set formation operator called $MERGE$, than can be used to incrementally construct complex syntactic structures using a simple Markovian process. MGP is able to discover the core building blocks of the symbolic expressions, and to incrementally combined them using $MERGE$. The proposed system is benchmarked on symbolic regression tasks that are known to be difficult to solve with standard GP systems because of the propensity for bloat. Results show that when a proper lexicon of atomic syntactic objects are chosen, MGP is able to consistently produce the exact ground truth model on a set of symbolic regression tasks where standard GP struggles to do the same. The insights provided by minimalism are shown to be relevant to the problem of program induction, and should be explored further based on the potential exhibited by MGP in this work.

While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+($λ$,$λ$))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.

Urban traffic simulation is a critical tool for infrastructure planning, including the placement of electric vehicle charging stations. However, realistic traffic simulation across many cities is hindered by two fundamental data limitations: detailed real-world traffic measurements are available for only a small fraction of road segments in most cities, and employment distribution data critical for modeling commuter traffic is rarely available at the resolution needed for simulation. This paper presents a genetic algorithm-based framework that directly addresses both limitations, calibrating urban traffic simulations from sparse road observations without requiring detailed job location data. Using the SUMO traffic simulation platform for Greensboro, North Carolina, our approach optimizes job distributions and gate-traffic parameters to align simulated traffic with a small sample of roads with known traffic-flow rates. We demonstrate that this approach produces simulated traffic that correlates well with real-world measurements, generalizes to road segments withheld from training, and produces job distributions that show promising qualitative agreement with census employment data despite never directly training on that employment data. This work demonstrates that realistic urban traffic simulation can be achieved from minimal real-world observations, offering a scalable and data-light approach to simulation calibration that reduces the barrier to deploying traffic models across diverse cities.

Genetic programming (GP) approaches are among the state-of-the-art for symbolic regression, the task of constructing symbolic expressions that fit well with data. To find highly accurate symbolic expressions, both the expression structure and any contained real-valued constants, are important. GP-GOMEA, a modern model-based evolutionary algorithm, is one of the leading algorithms for finding accurate, yet compact expressions. Yet, GP-GOMEA does not perform dedicated constant optimization, but rather uses ephemeral random constants. Hence, the accuracy of GP-GOMEA may well still be improved upon by the incorporation of a constant optimization mechanism. Existing research into mixed discrete-continuous optimization with EAs has shown that a simultaneous and well-integrated approach to optimizing both discrete and continuous parts, leads to the best results on a variety of problems, especially when there are interactions between these parts. In this paper, we therefore propose a novel approach where constants in expressions are optimized at the same time as the expression structure by merging the real-valued variant of GOMEA with GP-GOMEA. The proposed approach is compared to other forms of handling constants in GP-GOMEA, and in the context of other commonly used techniques such as linear scaling, restarts, and constant tuning after GP optimization. Our results indicate that our novel approach generally performs best and confirms the importance of simultaneous constant optimization during evolution.

GP-GOMEA is a state-of-the-art evolutionary algorithm for symbolic regression, known for discovering small and interpretable models. However, its computational cost remains substantial, limiting its applicability to larger datasets and more complex target expressions. In contrast, the rise of modern subsymbolic approaches, particularly deep learning, has been driven largely by the massive parallelism offered by GPUs. In this work, we take the first major step toward a fully GPU-accelerated GP-GOMEA by introducing a GPU-based fitness evaluation scheme. We design a GPU-friendly representation of GP-GOMEA's template-based individuals and a corresponding evaluation strategy that exploits the inherent parallelism of population-based search. This substantially increases evaluation throughput, enabling orders of magnitude more evaluations within the same time budget. Across four standard symbolic regression benchmarks, this increased evaluation capacity yields performance improvements, particularly for larger datasets and larger population sizes. Moreover, the ability to efficiently evaluate much larger datasets and more complex templates enables analyses that were previously infeasible, allowing us to systematically analyze what makes expressions increasingly difficult for GP-GOMEA, providing new insights into how expression structure affects search difficulty. Finally, for the first time, this expanded capability allows a problem-agnostic evolutionary algorithm to reliably regress one of the largest Feynman equations within four hours.

Recently, the runtime analysis of multi-valued estimation-of-distribution algorithms in the framework of Ben Jedidia et al. (TCS 2024) has made significant advancements. However, almost all existing analyses are limited to multi-valued objective functions that in each dimension only distinguish between two types, also called categories, of values and hence can be treated with similar methods as pseudo-Boolean problems. Only recently, Adak and Witt (GECCO 2025) have presented a first runtime analysis of a multi-valued compact genetic algorithm (cGA) on the multi-valued OneMax function G-OneMax$\colon \{0,\dots,r-1\}^n \to \mathbf{N}$ defined by G-OneMax$(x_1,\dots,x_n)=\sum_{i=1}^n {x}_i$ and truly depending on all $r$ categories. We improve their runtime result from $\textrm{O}\bigl(n r^3 \log^2( n)\log (r)\bigr)$ to $\textrm{O}\bigl(n r \log^3(n)\log^3(r)\bigr)$, both for an optimal choice of the update strength $K$. Our result matches, up to polylogarithmic factors, the existing bound for the simpler $r$-valued OneMax function depending essentially only on two values and analyzed in several previous works. To show the new bound, we use improved drift theorems for processes with high self-loop probabilities and specifically derived concentration inequalities to analyze how probability mass in the multi-valued cGA moves into successively smaller and smaller intervals of the $r$-valued frequency matrix.

Traditional cryptography, rooted in problems, e.g., integer factorisation or discrete log, is inevitably vulnerable to a fully operational quantum computer. Although it remains an engineering frontier, the looming threat extends to encrypted data stored today, which could be decrypted in the future with quantum capabilities. To safeguard against this eventuality, the backbone of the modern quantum-safe cryptography is the Shortest Vector Problem (SVP). We enhance Laarhoven's treatment of Ajtai et al.'s sieving as a genetic algorithm (GA) for the SVP by incorporating domain-informed SVP representation and crossover while naturally extending application to the module lattices.

Generating realistic graph-structured data is challenging due to discrete connectivity, varying graph sizes, and class-specific structural patterns. Recent Generative Adversarial Networks (GAN)-based graph generation methods improve edge modelling by learning connectivity and matching class-specific density distributions. However these models still exhibit noticeable deviations such as in degree and spectral distribution when compared to real graphs, indicating that important structural properties are not fully preserved. This work aims to reduce these deviations by refining the graphs produced by an existing GAN-based graph generator framework with a Genetic Algorithm (GA). In the GAN framework, the generator produces both node features and connectivity patterns, while a GNN-based critic evaluates graph realism and class consistency to ensure global structural and class alignment. Building on this foundation, we apply a GA to refine the edges of generated graphs. The refinement process guides synthetic graphs toward closer agreement with real data, while preserving diversity and novelty. Experimental results show that the GA refinement consistently lowers combined Maximum Mean Discrepancy (MMD) compared to the base model, leading to graphs that more closely match real structural patterns. This demonstrates that evolutionary refinement is an effective and flexible way to correct residual structural deviations in GAN-based graph generators, improving their suitability for realistic graph synthesis and data augmentation.

Cartesian Genetic Programming has traditionally been using mutation as its main and often sole genetic operator to drive evolutionary search. Despite advancements in recent years, recombinationbased approaches have long been avoided, due to apparent lack of performance gains. This study examines two recently suggested recombination-based operators, subgraph crossover and discrete phenotypic recombination on SRBench, a benchmarking platform for symbolic regression. Using the implementations provided in the TinyverseGP framework, we perform hyperparameter optimisation of the respective representations with these two operators. Our work demonstrates that hyperparameter optimisation can lead to improvements in performance for recombination-based Cartesian Genetic Programming.

Selecting the most suitable algorithm for a given problem instance remains a challenging task, particularly in online or dynamic environments where problem characteristics evolve over time. Relying solely on instantaneous performance metrics can result in a reactive and unstable behaviour, often leading to suboptimal algorithm switching. This paper introduces a computationally efficient approach for aggregating an algorithm's performance across multiple problem instances that is fairly immune to erratic variations in instance features. Inspired by features inherent to Reinforcement Learning (RL), this technique encapsulates rewards and penalties into a latent yield that, in turn, triggers exploitation and exploration, consequently resulting in adaptive algorithm switching. The proposed technique employs island models, inspired by Genetic Algorithms, to facilitate parallel exploration and performance exchanges among algorithm populations inhabiting local repertoires. Experimental evaluations on sorting algorithms and robotic obstacle avoidance tasks demonstrate the feasibility and effectiveness of the approach, highlighting its potential in domains where adaptive algorithm selection is critical.

Negative Selection Algorithms (NSAs), inspired by the self/non-self discrimination mechanism of the human immune system, have been widely employed in anomaly detection. However, their effectiveness is often constrained by the efficiency of detector generation. This paper presents the Quantum Genetic Negative Selection Algorithm (QGNSA), a novel approach that integrates a Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA algorithm, replacing its classical evolutionary optimization process. The proposed method exploits quantum superposition and probabilistic amplitude adjustment to enhance search space exploration and convergence efficiency in the detector generation process. Empirical evaluations using the Metaverse Financial Transactions Dataset demonstrate that QGNSA achieves superior anomaly detection accuracy compared to its classical counterpart while maintaining robustness under varying hyperparameter configurations. The experimental results highlight the potential advantages of quantum computing in artificial immune systems, particularly in high-dimensional anomaly detection tasks. Future research will focus on further optimizing quantum circuit design, deploying the algorithm on real quantum hardware, and exploring hybrid quantum-classical approaches for improved computational efficiency.

Symbolic regression with genetic programming (GPSR) may suffer from overfitting and structural bloat, especially when noise is present. In this paper we evaluate description length (DL) and fractional Bayes factor (FBF) criteria as principled, data-efficient alternatives to heuristics for selecting compact expressions that generalise well. We implement DL using a Fisher-information-based parameter encoding and compare it to AIC and BIC across multiple datasets, including noisy synthetic benchmarks and real-world regression problems. We study three search/selection strategies: (i) multi-objective search for accuracy and program length followed by DL/FBF selection; (ii) multi-objective search using DL directly as an objective; and (iii) single-objective optimisation with DL/FBF as the fitness. Across datasets we find that DL/FBF post-selection improves test performance compared to AIC/BIC baseline and that BIC in combination with the same function complexity penalty from DL/FBF produces similar results. In contrast, using DL/FBF directly as a fitness function in single-objective GPSR frequently induces premature convergence to overly simple models. We conclude with practical guidance for using DL/FBF as robust model-selection tools in genetic programming workflows.

A recent trend is to leverage machine learning models to improve the evolutionary design and optimization process. We propose a novel transformer-based mutation operator for Cartesian genetic programming (CGP) for the automated design of approximate arithmetic circuits. We introduce a hybrid scheme for CGP in which the proposed mutation operator is switched with the standard mutation operator to prevent stagnation of the circuit approximation process. We also develop a new training scheme for the underlying transformer that utilizes training vectors composed of thousands of CGP chromosomes representing various approximate multipliers. For several target error constraints, the approximate multipliers evolved with CGP utilizing the transformer-based mutation achieve better trade-offs than the highly optimized designs available in the state-of-the-art EvoApproxLib library of approximate circuits. Although both training and evolutionary processes are computationally demanding, they appear to be necessary steps for improving existing approximate circuits and producing new, potentially patentable circuit designs.

Network Intrusion Detection System is a critical means of ensuring cybersecurity. However, existing Genetic Algorithm-based feature selection methods face several limitations when dealing with high-dimensional redundant traffic features. For example, population diversity is difficult to maintain, and evolutionary operators lack guidance. To solve these problems, this study proposes the Multi-Population Diversity-Guided Genetic Algorithm (MPDGGA). First, we build a chained multi-population evolutionary structure. Second, we introduce a diversity-guided operator based on information gain ratio. Experiments on NSL-KDD, UNSW-NB15, and 9 UCI datasets show that the proposed model significantly outperforms four other advanced multi-population feature selection models. Across the 11 datasets, it attains the highest accuracy on 10 datasets and at least 2.26% of the features were selected.

Vision Transformers (ViTs) achieve state-of-the-art performance on challenging vision tasks, but their deployment on edge devices is severely hindered by the computational complexity and global reduction bottleneck imposed by layer normalization. Recent methods attempt to bypass this by replacing normalization layers with hardware-friendly scalar approximations. However, these homogeneous replacements do not optimally fit to all layers' behaviour and rely on expensive model retraining. In this work, we propose a highly efficient, hardware-aware framework that utilizes genetic programming (GP) to evolve heterogeneous, layer-specific scalar functions directly from pre-trained weights. Coupled with a novel post-training re-alignment strategy, our approach eliminates the need to retrain models from scratch entirely. Our evolved expressions accurately approximate the target normalization behaviours, capturing $91.6\%$ of the variance ($R^2$) compared to only $70.2\%$ for homogeneous baselines, allowing our modified architecture to recover $84.25\%$ Top-1 ImageNet-1K accuracy in only 20 epochs. By preserving this performance while eliminating the global reduction bottleneck, our approach establishes a highly favourable trade-off between arithmetic complexity and off-chip memory traffic, removing a primary barrier to the efficient deployment of ViTs on edge accelerators.

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.

Aim/Introduction: Distance-encoding biomorphic-informational neural network (DEBI-NN) is a recently proposed architecture in which connection weights are defined by the distances between neurons positioned in a Euclidian space. This approach drastically reduces the number of trainable parameters compared to classical neural networks in which weights are directly trained. The training process for DEBI-NN is based on a genetic algorithm (GA), rather than gradient descent (GD) which remains the prevailing optimization algorithm in deep learning. We aim to design and implement a GD learner for DEBI-NN and assess its performance compared to GA. Materials and Methods: We designed a spatial backpropagation scheme tailored to DEBI-NN and carried out a comparison between GD and GA for classification tasks, using a synthetic non-linear "two-moons" dataset, two clinical medical imaging radiomic datasets and a fetal cardiotocography dataset with a sample sizes ranging from n=85 to n=2126. Each optimizer was tuned through targeted hyperparameter searches adapted to each dataset. Results: Across all experiments, GA consistently produced superior decision boundaries and classification performance (Synthetic: 100% vs 83%; DLBCL: 83% vs 78%; HECKTOR: 80% vs 67%; Fetal: 81% vs 66%), whereas GD exhibited instability and failed to fully capture the non-linear patterns inherent to DEBI-NN's spatial encoding. The entangled gradients resulting from neuron interdependencies limit the effectiveness of classical backpropagation. Conclusion: These findings highlight fundamental limitations of gradient-based methods in architectures with highly interdependent spatial parameters and confirm the suitability of evolutionary strategies for training DEBI-NN.

Effective model selection is critical in symbolic regression (SR) to identify mathematical expressions that balance accuracy and complexity, and have low expected error on unseen data. Many modern implementations of genetic programming (GP) for SR generate a set of Pareto optimal candidate solutions, but reliable automatic selection of solutions that generalize well remains an open issue. Current literature offers various information-theoretic and Bayesian approaches, yet comprehensive comparisons of their performance across different data regimes are limited. This study presents a systematic empirical comparison of widely used selection criteria: the Akaike information criterion (AIC), the corrected AIC (AICc), the Bayesian information criterion (BIC), minimum description length (MDL), as well as Efron's bootstrap estimate for the in-sample prediction error on seven synthetic datasets with Gaussian noise. We rank candidate expressions generated by perturbing ground-truth functions to assess generalization error and selection probability of the ground-truth expression. Our findings reveal that MDL consistently identifies models with the lowest test error and the shortest length across most datasets. While no single criterion dominates all results, MDL and BIC produced the highest probability of selecting the ground-truth expressions.

Mathematical formulas serve as a language through which humans communicate with nature. Discovering mathematical laws from scientific data to describe natural phenomena has been a long-standing pursuit of humanity for centuries. In the field of artificial intelligence, this challenge is known as the symbolic regression problem. Among existing symbolic regression approaches, Genetic Programming (GP) based on evolutionary algorithms remains one of the most classical and widely adopted methods. GP simulates the evolutionary process across generations through genetic mutation and crossover. However, mutations and crossovers in GP are entirely random. While this randomness effectively mimics natural evolution, it inevitably produces both beneficial and detrimental variations. If there existed a metaphorical God capable of foreseeing which genetic mutations or crossovers would yield superior outcomes and performing targeted gene editing accordingly, the efficiency of evolution could be substantially improved. Motivated by this idea, we propose in this paper a symbolic regression approach based on gene editing, termed GESR. In GESR, we trained two "hands of God" (two BERT models). Among them, the first leverages the BERT's masked language modeling capability to guide the mutation of genes (expression symbols). The other BERT model guides the crossover of individual genes by predicting the crossover point. Experimental results demonstrate that GESR significantly improves computational efficiency compared with traditional GP algorithms and achieves strong overall performance across multiple symbolic regression tasks.

The popular 2009 voxel based videogame, Minecraft, contains several distinct disciplines. One of which is "parkour," gameplay that focuses on traversing a world's environment with maximum efficiency. The Minecraft online community has turned the game's physics engine into dynamic puzzles, requiring players to masterfully manipulate motion mechanics through frame precise timing of keystrokes. Actions such as sprinting, sneaking, and mouse direction are all combined to clear specific difficult jumps. Through this project, we design a genetic algorithm to generate weights for a neural network to autonomously evaluate inputs for block distances, terrain, and obstacles to determine the most optimal pathing.

Time series classification is an important analytical task across diverse domains. However, its practical application is often hindered by the scarcity of labeled data and the requirement for substantial computational resources. To address these challenges, this paper proposes EvoTSC, a novel genetic programming approach designed to automatically evolve lightweight feature learning models for time series classification. The core of EvoTSC is a carefully designed multi-layer program structure that strategically embeds diverse forms of prior expert knowledge into the evolutionary process, effectively guiding the search toward operations known to be highly effective for time series analysis. To mitigate the common overfitting problem in time series classification, a tailored Pareto tournament selection strategy is proposed to favor models that perform consistently well across varying training data subsets, promoting the discovery of highly generalizable models. Extensive experiments conducted on univariate time series classification datasets demonstrate that EvoTSC significantly outperforms eleven benchmark methods in most comparisons. Further analyses verify the contribution of each component and the resource efficiency of the evolved models.

Over the past few decades, machine learning has been widely used to learn complex tasks. Reinforcement Learning (RL), inspired by human behavior, is a great example, as it involves developing specific behaviours for specific tasks. To further challenge algorithms, Multi-Task RL (MTRL) environments have been introduced, requiring a single model to learn multiple behaviors. The Tangled Program Graph (TPG) algorithm is a Genetic Programming (GP) algorithm designed for discrete MTRL environments. Recently, the MAPLE algorithm has been proposed, as another GP algorithm that achieves high results in single task continuous RL environments. A variation of the TPG is proposed alongside MAPLE, named Multi-Action TPG (MATPG) that aggregates MAPLE agents, and creates a control flow to activate them. Initially tested on single task RL environments only, MATPG achieved similar results to MAPLE. In this work, we present a new benchmark based on the MuJoCo Half Cheetah from Gymnasium. This benchmark features five distinct obstacles that are randomly positioned in front of the agent, each of which demands a unique behavior. This benchmark serves as a use case for MATPG, to prove its ability as a GP solution for continuous MTRL environments. Our experiments demonstrate its superiority in this multi-task use case when combined with lexicase selection. Furthermore, we examine the interpretability of the evolved graph, revealing that the decision flow of the model is fully interpretable.

The Beagle framework, through GPU-based Genetic Programming, enables population dynamics previously unattainable (within practical time frames) by CPU-constrained Genetic Programming systems. This work explores how GPU-enabled population sizes impact the success of training for symbolic regression problems. Specifically, when using constant population sizes, we see benefits of using very narrow and deep searches (as narrow as 1000 individuals) for some problems, while other problems benefit from very broad and shallow searches (as broad as 10 million individuals). We also explore stepped population sizes that start with large populations and drop to small populations to balance the breadth and depth of search.

An artificial world of barriers and plains scattered with food is used to test the feasibility of using genetic algorithms to optimize hebbian neural networks to perform on problems without apriori knowledge of the problem domain. A formal L-System based genetic alphabet for neural networks, titled Lsys, and a neural network genetic modeling tool titled Wp1hgn are introduced. Lsys and Matrix neural network topology genetic encoding methods are compared across 24 experimental runs. Lsys encoding achieved a mean maximum food count of 3802 +- 197 at generation 1000 across 8 runs with varied parameters, compared to 1388 +- 610 for Matrix encoding, a 2.74x performance advantage with an 8.5-fold improvement in consistency as measured by coefficient of variation (5.2% vs 44.0%). All 8 Lsys populations successfully learned to navigate the environment, while 4 of 8 Matrix populations failed to achieve competitive performance at any point during 1000 generations. When transferred to a novel maze environment, Lsys populations demonstrated immediate robust generalization, achieving a mean maximum food count of 2455 +- 176 compared to 422 +- 212 for Matrix populations, a 5.82x advantage that exceeded the training world performance gap. A MatrixLSG control condition, in which initial populations were generated using Lsys genotypes and then evolved using Matrix operators, demonstrated that the performance advantage of Lsys encoding derives primarily from the genetic algorithm operating on the compressed symbolic Lsys alphabet throughout evolution rather than from initial population structure. Lsys encoding is shown to provide faster convergence, higher peak performance, dramatically greater reliability, and superior generalization to novel environments compared to Matrix encoding across all experimental conditions tested.

Satellite constellation design requires optimizing orbital parameters across multiple satellites to maximize mission specific metrics. For many types of mission, it is desirable to maximize coverage and minimize revisit gaps over ground targets. Existing approaches to constellation design either restrict the design space to symmetric parametric families such as Walker constellations, or rely on metaheuristic methods that require significant compute and many iterations. Gradient-based optimization has been considered intractable due to the non-differentiability of coverage and revisit metrics, which involve binary visibility indicators and discrete max operations. We introduce four continuous relaxations: soft sigmoid visibility, noisy-OR multi-satellite aggregation, leaky integrator revisit gap tracking, and LogSumExp soft-maximum, which when composed with the $\partial$SGP4 differentiable orbit propagator, yield a fully differentiable pipeline from orbital elements to mission-level objectives. We show that this scheme can recover Walker-Delta geometry from irregular initializations, and discovers elliptical Molniya-like orbits with apogee dwell over extreme latitudes from only gradients. Compared to simulated annealing (SA), genetic algorithm (GA), and differential evolution (DE) baselines, our gradient-based method recovers Walker-equivalent geometry within ${\sim}750$ evaluations, whereas the three black-box baselines plateau at with significantly worse revisit even with roughly four times the evaluation budget.

Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data. Despite its strong empirical success, the theoretical understanding of why GP-based SR generalizes beyond the training data remains limited. In this work, we provide a learning-theoretic analysis of SR models represented as expression trees. We derive a generalization bound for GP-style SR under constraints on tree size, depth, and learnable constants. Our result decomposes the generalization gap into two interpretable components: a structure-selection term, reflecting the combinatorial complexity of choosing an expression-tree structure, and a constant-fitting term, capturing the complexity of optimizing numerical constants within a fixed structure. This decomposition provides a theoretical perspective on several widely used practices in GP, including parsimony pressure, depth limits, numerically stable operators, and interval arithmetic. In particular, our analysis shows how structural restrictions reduce hypothesis-class growth while stability mechanisms control the sensitivity of predictions to parameter perturbations. By linking these practical design choices to explicit complexity terms in the generalization bound, our work offers a principled explanation for commonly observed empirical behaviors in GP-based SR and contributes towards a more rigorous understanding of its generalization properties.

Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve monotone Boolean functions with high nonlinearity, both in the balanced and imbalanced settings. We consider three solution encodings: the standard truth table representation, a balanced truth table encoding that preserves Hamming weight, and a symbolic tree-based genetic programming representation. To guide the search toward monotone increasing functions, we introduce a non-monotonicity penalty and combine it with fitness functions targeting balancedness and nonlinearity. Experimental results are reported for dimensions from $n=5$ to $n=14$. The results show that evolutionary search can discover monotone Boolean functions with nonlinearities clearly exceeding those of majority functions, and in several cases approaching the best currently known values for monotone functions. At the same time, the experiments reveal substantial differences between encodings: the balanced truth table encoding performs poorly for larger dimensions, while the standard truth table and genetic programming encodings remain competitive, with genetic programming becoming especially relevant in the largest tested dimensions.

Landauer's principle bounds the heat generated by logical operations, but in practice the thermodynamic cost of computation is dominated by the control systems that implement logic. CMOS gates dissipate energy far above the Landauer bound, while laboratory demonstrations of near-Landauer erasure rely on external measurement or feedback systems whose energy costs exceed that of the logic operation by many orders of magnitude. Here we use simulations to show that a genetic algorithm can program a thermodynamic computer to implement logic operations in which the total heat emitted by the control system is of a similar order of magnitude to that of the information-bearing degrees of freedom. Moreover, the computer can be programmed so that heat is drawn away from the information-bearing degrees of freedom and dissipated within the control unit, suggesting the possibility of computing architectures in which heat management is an integral part of the program design.

According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining different variables and calculating entropy differently. In this paper we discuss how this concept may be applied in information entropy; how Shannon's definition of entropy can fit in Jayne's and Wigner's statement. This is achieved by generalizing Shannon's notion of information entropy and this is the main contribution of the paper. Then we discuss how entropy under these considerations may be used for the comparison of password complexity and as a measure of diversity useful in the analysis of the behavior of genetic algorithms.

In general, we can not use algebraic or enumerative methods to optimize a quality control (QC) procedure so as to detect the critical random and systematic analytical errors with stated probabilities, while the probability for false rejection is minimum. Genetic algorithms (GAs) offer an alternative, as they do not require knowledge of the objective function to be optimized and search through large parameter spaces quickly. To explore the application of GAs in statistical QC, we have developed an interactive GAs based computer program that designs a novel near optimal QC procedure, given an analytical process. The program uses the deterministic crowding algorithm. An illustrative application of the program suggests that it has the potential to design QC procedures that are significantly better than 45 alternative ones that are used in the clinical laboratories.