Genetic Algorithms

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.

We study day-ahead transmission topology control for high-voltage grid operation under $N-1$ security constraints. The operational task is to select, over a 24-hour horizon, a sequence of substation topologies obtained via busbar-coupler switching to relieve line overloads while limiting switching effort and topological complexity. We formulate this task as a sequential multi-objective optimization problem with four objectives used in TSO decision making: worst-case $N-1$ line loading, maximum topological depth, number of topology changes, and time spent outside the reference topology. We propose an exact block algorithm that exploits the temporal structure of topology plans: consecutive hours with the same topology are represented as blocks, enabling enumeration of the complete Pareto front over the admissible set of topologies under fixed operational bounds on depth and switching. We also develop a tailored NSGA-III-based evolutionary heuristic and evaluate it against the exact front. Using real operational data from the Dutch high-voltage transmission grid operated by TenneT, the block algorithm computes the exact front for a highly congested day in under three minutes after topology-level load-flow preprocessing. The exact front reveals low-switching plans with no DC $N-1$ thermal overloads that the tested evolutionary search fails to find. The proposed method, therefore, provides both a practical day-ahead decision-support tool for transmission operators and a benchmark for heuristic and learning-based topology-control methods.

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.

Expensive optimization problems (EOPs) are black-box tasks with costly objective evaluations and no gradient access, making the evaluation budget the key bottleneck. Surrogate-assisted evolutionary algorithms (SAEAs) reduce evaluations via surrogate predictions, but conventional surrogates often require frequent retraining as populations evolve, incurring overhead. This paper proposes R2SAEA, a reinforcement-trained relation-based large language model (LLM) surrogate assisted evolutionary algorithm. We cast relation-based surrogate modeling as an in-context pairwise reasoning task. To enable efficient inference in evolutionary loops, we develop an anchor-based iterative context construction strategy that reduces prompt complexity from quadratic to linear in population size, and a voting-based aggregation scheme that converts predicted relations into scores for offspring selection. We further build an RL pipeline from evolutionary trajectories and fine-tune Qwen2.5 with GRPO. Experiments on single- and multi-objective benchmarks show improved relation prediction and state-of-the-art optimization performance over strong SAEA baselines and general LLMs. Quantization also enables efficient edge deployment, supporting a zero-shot surrogate paradigm without per-generation retraining. Code and models are available at https://github.com/Septend9/R2SAEA.

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.

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.

Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-objective evolutionary algorithms (MOEAs) has predominantly focussed on continuous problems. However, multi-objective combinatorial optimisation problems (MOCOPs) differ from continuous ones. Their discrete and rigid structure often brings rugged landscape, numerous local optimal solutions and disjoint global optimal regions. This leads to different behaviour of MOEAs. For example, SEMO, a simple MOEA without mating selection and diversity maintenance mechanisms, has been shown to be highly competitive, and in many cases to outperform more sophisticated MOEAs on MOCOPs. Yet, it remains unclear whether such findings hold for large-scale cases. In this paper, we conduct an empirical investigation into the scalability of MOEAs on combinatorial problems, with problem size from 50 to 5,000. Our results show that SEMO experiences a decline in convergence speed as dimensionality increases, compared to other MOEAs such as NSGA-II, SMS-EMOA and MOEA/D. We further demonstrate that the absence of crossover is a major contributor to SEMO's underperformance in large-scale problems, and that incorporating crossover into SEMO can substantially accelerate convergence in general, despite being detrimental in spreading solutions over the Pareto front.

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.