Biological evolution is realised through the same mechanisms of birth and death that underlie change in population density. The deep interdependence between ecology and evolution is well-established, and recent models focus on integrating eco-evolutionary dynamics to demonstrate how ecological and evolutionary processes interact and feed back upon each other. Nevertheless, a gap remains between the logical foundations of ecology and evolution. Population ecology and evolution have fundamental equations that define how the size of a population (ecology) and the average characteristic within a population (evolution) change over time. These fundamental equations are a complete and exact description of change for any closed population, but how they are formally linked remains unclear. We link the fundamental equations of population ecology and evolution with an equation that sums how individual characteristics interact with individual fitness in a population. From this equation, we derive the fundamental equations of population ecology and evolutionary biology (the Price equation). We thereby identify an overlooked bridge between ecology and biological evolution. Our unification formal
As Evolutionary Dynamics moves from the realm of theory into application, algorithms are needed to move beyond simple models. Yet few such methods exist in the literature. Ecological and physiological factors are known to be central to evolution in realistic contexts, but accounting for them generally renders problems intractable to existing methods. We introduce a formulation of evolutionary games which accounts for ecology and physiology by modeling both as computations and use this to analyze the problem of directed evolution via methods from Reinforcement Learning. This combination enables us to develop first-of-their-kind results on the algorithmic problem of learning to control an evolving population of cells. We prove a complexity bound on eco-evolutionary control in situations with limited prior knowledge of cellular physiology or ecology, give the first results on the most general version of the mathematical problem of directed evolution, and establish a new link between AI and biology.
Computer vision (CV) is a big and important field in artificial intelligence covering a wide range of applications. Image analysis is a major task in CV aiming to extract, analyse and understand the visual content of images. However, image-related tasks are very challenging due to many factors, e.g., high variations across images, high dimensionality, domain expertise requirement, and image distortions. Evolutionary computation (EC) approaches have been widely used for image analysis with significant achievement. However, there is no comprehensive survey of existing EC approaches to image analysis. To fill this gap, this paper provides a comprehensive survey covering all essential EC approaches to important image analysis tasks including edge detection, image segmentation, image feature analysis, image classification, object detection, and others. This survey aims to provide a better understanding of evolutionary computer vision (ECV) by discussing the contributions of different approaches and exploring how and why EC is used for CV and image analysis. The applications, challenges, issues, and trends associated to this research field are also discussed and summarised to provide fur
The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In practice, these optimization problems often involve stochastic and dynamic components. Evolutionary algorithms provide a flexible framework for addressing such problems under uncertainty and dynamic changes. In this paper, we investigate a stochastic and dynamic variant of MKP with chance constraints, where the item weights are modeled as independent normally distributed random variables and knapsack capacities change during the optimization process. We formulate the problem as a bi-objective optimization formulation that balances profit maximization and probabilistic capacity satisfaction at a given confidence level. We conduct an empirical comparison of four widely used multi-objective evolutionary algorithms (MOEAs), representing both decomposition- and dominance-based search paradigms. The algorithms are evaluated under varying uncertainty levels, confidence thresholds, and dynamic change settings. The results provide comparative insights into t
Traditionally, studies in experimental physiology have been conducted in small groups of human participants, animal models or cell lines. Identifying optimal study designs that achieve sufficient power for drawing proper statistical inferences to detect group level effects with small sample sizes has been challenging. Moreover, average effects derived from traditional group-level inference do not necessarily apply to individual participants. Here, we introduce N-of-1 trials as an innovative study design that can be used to draw valid statistical inference about the effects of interventions on individual participants and can be aggregated across multiple study participants to provide population-level inferences more efficiently than standard group randomized trials. N-of-1 trials have been used in healthcare settings since the late 1980s, but without large-scale adoption and with few applications in experimental physiology research settings. In this manuscript, we introduce the key components and design features of N-of-1 trials, describe statistical analysis and interpretations of the results, and describe some available digital tools to facilitate their use using examples from exp
We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline mutation operator can lead to interesting image transition processes in terms of visual effects and artistic features. Using feature-based analysis we investigate the evolutionary image transition behaviour with respect to different features and evaluate the images constructed during the image transition process. Afterwards, we investigate how modifications of our biased random walk approaches can be used for evolutionary image painting. We introduce an evolutionary image painting approach whose underlying biased random walk can be controlled by a parameter influencing the bias of the random walk and thereby creating different artistic painting effects.
Evolutionary Computation (EC) has emerged as a powerful field of Artificial Intelligence, inspired by nature's mechanisms of gradual development. However, EC approaches often face challenges such as stagnation, diversity loss, computational complexity, population initialization, and premature convergence. To overcome these limitations, researchers have integrated learning algorithms with evolutionary techniques. This integration harnesses the valuable data generated by EC algorithms during iterative searches, providing insights into the search space and population dynamics. Similarly, the relationship between evolutionary algorithms and Machine Learning (ML) is reciprocal, as EC methods offer exceptional opportunities for optimizing complex ML tasks characterized by noisy, inaccurate, and dynamic objective functions. These hybrid techniques, known as Evolutionary Machine Learning (EML), have been applied at various stages of the ML process. EC techniques play a vital role in tasks such as data balancing, feature selection, and model training optimization. Moreover, ML tasks often require dynamic optimization, for which Evolutionary Dynamic Optimization (EDO) is valuable. This paper
We explore how physical scale and population size shape the emergence of complex behaviors in open-ended ecological environments. In our setting, agents are unsupervised and have no explicit rewards or learning objectives but instead evolve over time according to reproduction, mutation, and selection. As they act, agents also shape their environment and the population around them in an ongoing dynamic ecology. Our goal is not to optimize a single high-performance policy, but instead to examine how behaviors emerge and evolve across large populations due to natural competition and environmental pressures. We use modern hardware along with a new multi-agent simulator to scale the environment and population to sizes much larger than previously attempted, reaching populations of over 60,000 agents, each with their own evolved neural network policy. We identify various emergent behaviors such as long-range resource extraction, vision-based foraging, and predation that arise under competitive and survival pressures. We examine how sensing modalities and environmental scale affect the emergence of these behaviors and find that some of them appear only in sufficiently large environments an
There are many areas of scientific endeavour where large, complex datasets are needed for benchmarking. Evolutionary computing provides a means towards creating such sets. As a case study, we consider Conway's Surreal numbers. They have largely been treated as a theoretical construct, with little effort towards empirical study, at least in part because of the difficulty of working with all but the smallest numbers. To advance this status, we need efficient algorithms, and in order to develop such we need benchmark data sets of surreal numbers. In this paper, we present a method for generating ensembles of random surreal numbers to benchmark algorithms. The approach uses an evolutionary algorithm to create the benchmark datasets where we can analyse and control features of the resulting test sets. Ultimately, the process is designed to generate networks with defined properties, and we expect this to be useful for other types of network data.
Exposing an Evolutionary Algorithm that is used to evolve robot controllers to variable conditions is necessary to obtain solutions which are robust and can cross the reality gap. However, we do not yet have methods for analyzing and understanding the impact of the varying morphological conditions which impact the evolutionary process, and therefore for choosing suitable variation ranges. By morphological conditions, we refer to the starting state of the robot, and to variations in its sensor readings during operation due to noise. In this article, we introduce a method that permits us to measure the impact of these morphological variations and we analyze the relation between the amplitude of variations, the modality with which they are introduced, and the performance and robustness of evolving agents. Our results demonstrate that (i) the evolutionary algorithm can tolerate morphological variations which have a very high impact, (ii) variations affecting the actions of the agent are tolerated much better than variations affecting the initial state of the agent or of the environment, and (iii) improving the accuracy of the fitness measure through multiple evaluations is not always u
We present a comprehensive global sensitivity analysis of two single-objective and two multi-objective state-of-the-art global optimization evolutionary algorithms as an algorithm configuration problem. That is, we investigate the quality of influence hyperparameters have on the performance of algorithms in terms of their direct effect and interaction effect with other hyperparameters. Using three sensitivity analysis methods, Morris LHS, Morris, and Sobol, to systematically analyze tunable hyperparameters of covariance matrix adaptation evolutionary strategy, differential evolution, non-dominated sorting genetic algorithm III, and multi-objective evolutionary algorithm based on decomposition, the framework reveals the behaviors of hyperparameters to sampling methods and performance metrics. That is, it answers questions like what hyperparameters influence patterns, how they interact, how much they interact, and how much their direct influence is. Consequently, the ranking of hyperparameters suggests their order of tuning, and the pattern of influence reveals the stability of the algorithms.
Image classification currently faces significant security challenges due to adversarial attacks, which consist of intentional alterations designed to deceive classification models based on artificial intelligence. This article explores an approach to generate adversarial attacks against image classifiers using a combination of evolutionary algorithms and generative adversarial networks. The proposed approach explores the latent space of a generative adversarial network with an evolutionary algorithm to find vectors representing adversarial attacks. The approach was evaluated in two case studies corresponding to the classification of handwritten digits and object images. The results showed success rates of up to 35% for handwritten digits, and up to 75% for object images, improving over other search methods and reported results in related works. The applied method proved to be effective in handling data diversity on the target datasets, even in problem instances that presented additional challenges due to the complexity and richness of information.
This study explores a novel approach to neural network pruning using evolutionary computation, focusing on simultaneously pruning the encoder and decoder of an autoencoder. We introduce two new mutation operators that use layer activations to guide weight pruning. Our findings reveal that one of these activation-informed operators outperforms random pruning, resulting in more efficient autoencoders with comparable performance to canonically trained models. Prior work has established that autoencoder training is effective and scalable with a spatial coevolutionary algorithm that cooperatively coevolves a population of encoders with a population of decoders, rather than one autoencoder. We evaluate how the same activity-guided mutation operators transfer to this context. We find that random pruning is better than guided pruning, in the coevolutionary setting. This suggests activation-based guidance proves more effective in low-dimensional pruning environments, where constrained sample spaces can lead to deviations from true uniformity in randomization. Conversely, population-driven strategies enhance robustness by expanding the total pruning dimensionality, achieving statistically un
The relationships among ecological variables are usually obtained by fitting statistical models that go through the conditional means of the dependent variables. For example, the nonparametric loess and the parametric piecewise linear regression models, which pass through the conditional mean of the response variable given the predictor, are used to analyze simple to complex relationships among variables. We used loess and bootstrapped confidence interval to subjectively identify the number and positions of potential ecological breakpoints in a bivariate relationship, and a piecewise linear regression model (PLRM) to quantitatively estimate the location of breakpoints and the associated precision. We also estimated breakpoint location and precision using a piecewise linear quantile regression model (PQRM), which is fitted to the quantiles of the conditional distribution of the response variable given the predictor and provides much richer information in terms of estimating relationships and breakpoints. We compared the precision of breakpoints estimated by PQRM relative to PLRM. We compared the precision of the methods using two examples from the ecological literature suspected to
Separate artificial neural network (ANN) models were developed from data in two geographical regions and years apart for a marsh-nesting bird, the red-winged blackbird Agelaius phoeniceus. Each model was independently tested on the spatially and temporally distinct data from the other region to determine how generalizable it was. The first model was developed to predict occurrence of nests in two wetlands on Lake Erie, Ohio in 1995 and 1996. The second model was developed to predict breeding success in two marshes in Connecticut, USA in 1969 and 1970. Independent variables were vegetation durability, stem density, stem/nest height, distance to open water, distance to edge, and water depth. With input variable relevances, sensitivity analyses and neural interpretation diagrams we were able to understand how the different models predicted nest occurrence and breeding success and compare their differences and similarities. Both models also predicted increasing nest occurrence/breeding success with increasing water depth under the nest and increasing distance to edge. However, relationships for prediction differed in the models. Generalizability of the models was poor except when the m
Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/a
Some quality indicators have been proposed for benchmarking preference-based evolutionary multi-objective optimization algorithms using a reference point. Although a systematic review and analysis of the quality indicators are helpful for both benchmarking and practical decision-making, neither has been conducted. In this context, first, this paper reviews existing regions of interest and quality indicators for preference-based evolutionary multi-objective optimization using the reference point. We point out that each quality indicator was designed for a different region of interest. Then, this paper investigates the properties of the quality indicators. We demonstrate that an achievement scalarizing function value is not always consistent with the distance from a solution to the reference point in the objective space. We observe that the regions of interest can be significantly different depending on the position of the reference point and the shape of the Pareto front. We identify undesirable properties of some quality indicators. We also show that the ranking of preference-based evolutionary multi-objective optimization algorithms depends on the choice of quality indicators.
We present an empirical study of a range of evolutionary algorithms applied to various noisy combinatorial optimisation problems. There are three sets of experiments. The first looks at several toy problems, such as OneMax and other linear problems. We find that UMDA and the Paired-Crossover Evolutionary Algorithm (PCEA) are the only ones able to cope robustly with noise, within a reasonable fixed time budget. In the second stage, UMDA and PCEA are then tested on more complex noisy problems: SubsetSum, Knapsack and SetCover. Both perform well under increasing levels of noise, with UMDA being the better of the two. In the third stage, we consider two noisy multi-objective problems (CountingOnesCountingZeros and a multi-objective formulation of SetCover). We compare several adaptations of UMDA for multi-objective problems with the Simple Evolutionary Multi-objective Optimiser (SEMO) and NSGA-II. We conclude that UMDA, and its variants, can be highly effective on a variety of noisy combinatorial optimisation, outperforming many other evolutionary algorithms.
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and configuration. However, constructing graphs that preserve high-level properties across a broad range of graph classes remains a challenging problem. We present a novel evolutionary approach to evolve graphs based on the Laplacian graph spectra descriptor. This descriptor can be used as part of a fitness function to evaluate graphs according to their desired high-level properties. Our evolutionary algorithm evolves graphs towards this descriptor in order to obtain graphs having properties that are consistent with it but are different from each other in terms of non-spectral graph metrics, such as path length, clustering coefficient and betweenness centrality. Our experimental results show that our approach is successful for different classes of graphs and a wide range of Laplacian graph spectra.
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to achieve high quality results. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for chance constrained optimization. We study the scenario of stochastic components that are independent and normally distributed. Considering the simple single-objective (1+1) EA, we show that imposing an additional uniform constraint already leads to local optima for very restricted scenarios and an exponential optimization time. We therefore introduce a multi-objective formulation of the problem which trades off the expected cost and its variance. We show that multi-objective evolutionary algorithms are highly effective when using this formulation and obtain a set of solutions that contains an optimal solution for any possible confidence level imposed on the constraint. Furthermore, we prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem. In ord