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Artificial Intelligence (AI) has driven innovations and created new opportunities across various sectors. However, leveraging domain-specific knowledge often requires automated tools to design and configure models effectively. In the case of Deep Neural Networks (DNNs), researchers and practitioners usually resort to Neural Architecture Search (NAS) approaches, which are resource- and time-intensive, requiring the training and evaluation of numerous candidate architectures. This raises sustainability concerns, particularly due to the high energy demands involved, creating a paradox: the pursuit of the most effective model can undermine sustainability goals. To mitigate this issue, zero-cost proxies have emerged as a promising alternative. These proxies estimate a model's performance without the need for full training, offering a more efficient approach. This paper addresses the challenges of model evaluation by automatically designing zero-cost proxies to assess DNNs efficiently. Our method begins with a randomly generated set of zero-cost proxies, which are evolved and tested using the NATS-Bench benchmark. We assess the proxies' effectiveness using both randomly sampled and stratified subsets of the search space, ensuring they can differentiate between low- and high-performing networks and enhance generalizability. Results show our method outperforms existing approaches on the stratified sampling strategy, achieving strong correlations with ground truth performance, including a Kendall correlation of 0.89 on CIFAR-10 and 0.77 on CIFAR-100 with NATS-Bench-SSS and a Kendall correlation of 0.78 on CIFAR-10 and 0.71 on CIFAR-100 with NATS-Bench-TSS., Comment: Submitted to CVPR 2025

Adversarial examples, designed to trick Artificial Neural Networks (ANNs) into producing wrong outputs, highlight vulnerabilities in these models. Exploring these weaknesses is crucial for developing defenses, and so, we propose a method to assess the adversarial robustness of image-classifying ANNs. The t-distributed Stochastic Neighbor Embedding (t-SNE) technique is used for visual inspection, and a metric, which compares the clean and perturbed embeddings, helps pinpoint weak spots in the layers. Analyzing two ANNs on CIFAR-10, one designed by humans and another via NeuroEvolution, we found that differences between clean and perturbed representations emerge early on, in the feature extraction layers, affecting subsequent classification. The findings with our metric are supported by the visual analysis of the t-SNE maps.

The increasing usage of Artificial Intelligence (AI) models, especially Deep Neural Networks (DNNs), is increasing the power consumption during training and inference, posing environmental concerns and driving the need for more energy-efficient algorithms and hardware solutions. This work addresses the growing energy consumption problem in Machine Learning (ML), particularly during the inference phase. Even a slight reduction in power usage can lead to significant energy savings, benefiting users, companies, and the environment. Our approach focuses on maximizing the accuracy of Artificial Neural Network (ANN) models using a neuroevolutionary framework whilst minimizing their power consumption. To do so, power consumption is considered in the fitness function. We introduce a new mutation strategy that stochastically reintroduces modules of layers, with power-efficient modules having a higher chance of being chosen. We introduce a novel technique that allows training two separate models in a single training step whilst promoting one of them to be more power efficient than the other while maintaining similar accuracy. The results demonstrate a reduction in power consumption of ANN models by up to 29.2% without a significant decrease in predictive performance.

Spiking Neural Networks (SNNs) have attracted recent interest due to their energy efficiency and biological plausibility. However, the performance of SNNs still lags behind traditional Artificial Neural Networks (ANNs), as there is no consensus on the best learning algorithm for SNNs. Best-performing SNNs are based on ANN to SNN conversion or learning with spike-based backpropagation through surrogate gradients. The focus of recent research has been on developing and testing different learning strategies, with hand-tailored architectures and parameter tuning. Neuroevolution (NE), has proven successful as a way to automatically design ANNs and tune parameters, but its applications to SNNs are still at an early stage. DENSER is a NE framework for the automatic design and parametrization of ANNs, based on the principles of Genetic Algorithms (GA) and Structured Grammatical Evolution (SGE). In this paper, we propose SPENSER, a NE framework for SNN generation based on DENSER, for image classification on the MNIST and Fashion-MNIST datasets. SPENSER generates competitive performing networks with a test accuracy of 99.42% and 91.65% respectively.

The design of cable-stayed bridges requires the determination of several design variables' values. Civil engineers usually perform this task by hand as an iteration of steps that stops when the engineer is happy with both the cost and maintaining the structural constraints of the solution. The problem's difficulty arises from the fact that changing a variable may affect other variables, meaning that they are not independent, suggesting that we are facing a deceptive landscape. In this work, we compare two approaches to a baseline solution: a Genetic Algorithm and a CMA-ES algorithm. There are two objectives when designing the bridges: minimizing the cost and maintaining the structural constraints in acceptable values to be considered safe. These are conflicting objectives, meaning that decreasing the cost often results in a bridge that is not structurally safe. The results suggest that CMA-ES is a better option for finding good solutions in the search space, beating the baseline with the same amount of evaluations, while the Genetic Algorithm could not. In concrete, the CMA-ES approach is able to design bridges that are cheaper and structurally safe., Comment: Accepted in EvoApps at Evostar2023

With the increasing demand for high-quality internet services, deploying GPON/Fiber-to-the-Home networks is one of the biggest challenges that internet providers have to deal with due to the significant investments involved. Automated network design usage becomes more critical to aid with planning the network by minimising the costs of planning and deployment. The main objective is to tackle this problem of optimisation of networks that requires taking into account multiple factors such as the equipment placement and their configuration, the optimisation of the cable routes, the optimisation of the clients' allocation and other constraints involved in the minimisation problem. An AI-based solution is proposed to automate network design, which is a task typically done manually by teams of engineers. It is a difficult task requiring significant time to complete manually. To alleviate this tiresome task, we proposed a Genetic Algorithm using a two-level representation to design the networks automatically. To validate the approach, we compare the quality of the generated solutions with the handmade design ones that are deployed in the real world. The results show that our method can save costs and time in finding suitable and better solutions than existing ones, indicating its potential as a support design tool of solutions for GPON/Fiber-to-the-Home networks. In concrete, in the two scenarios where we validate our proposal, our approach can cut costs by 31% and by 52.2%, respectively, when compared with existing handmade ones, showcasing and validating the potential of the proposed approach., Comment: Accepted in EvoApps at EvoStar 2023

Maintaining genetic diversity as a means to avoid premature convergence is critical in Genetic Programming. Several approaches have been proposed to achieve this, with some focusing on the mating phase from coupling dissimilar solutions to some form of self-adaptive selection mechanism. In nature, genetic diversity can be the consequence of many different factors, but when considering reproduction Sexual Selection can have an impact on promoting variety within a species. Specifically, Mate Choice often results in different selective pressures between sexes, which in turn may trigger evolutionary differences among them. Although some mechanisms of Sexual Selection have been applied to Genetic Programming in the past, the literature is scarce when it comes to mate choice. Recently, a way of modelling mating preferences by ideal mate representations was proposed, achieving good results when compared to a standard approach. These mating preferences evolve freely in a self-adaptive fashion, creating an evolutionary driving force of its own alongside fitness pressure. The inner mechanisms of this approach operate from personal choice, as each individual has its own representation of a perfect mate which affects the mate to be selected. In this paper, we compare this method against a random mate choice to assess whether there are advantages in evolving personal preferences. We conducted experiments using three symbolic regression problems and different mutation rates. The results show that self-adaptive mating preferences are able to create a more diverse set of solutions when compared to the traditional approach and a random mate approach (with statistically significant differences) and have a higher success rate in three of the six instances tested.

This work proposes Adaptive Facilitated Mutation, a self-adaptive mutation method for Structured Grammatical Evolution (SGE), biologically inspired by the theory of facilitated variation. In SGE, the genotype of individuals contains a list for each non-terminal of the grammar that defines the search space. In our proposed mutation, each individual contains an array with a different, self-adaptive mutation rate for each non-terminal. We also propose Function Grouped Grammars, a grammar design procedure, to enhance the benefits of the proposed mutation. Experiments were conducted on three symbolic regression benchmarks using Probabilistic Structured Grammatical Evolution (PSGE), a variant of SGE. Results show our approach is similar or better when compared with the standard grammar and mutation., Comment: 16 pages, 6 figures, 5 tables

Grammar-Guided Genetic Programming (GGGP) employs a variety of insights from evolutionary theory to autonomously design solutions for a given task. Recent insights from evolutionary biology can lead to further improvements in GGGP algorithms. In this paper, we apply principles from the theory of Facilitated Variation and knowledge about heterogeneous mutation rates and mutation effects to improve the variation operators. We term this new method of variation Facilitated Mutation (FM). We test FM performance on the evolution of neural network optimizers for image classification, a relevant task in evolutionary computation, with important implications for the field of machine learning. We compare FM and FM combined with crossover (FMX) against a typical mutation regime to assess the benefits of the approach. We find that FMX in particular provides statistical improvements in key metrics, creating a superior optimizer overall (+0.48\% average test accuracy), improving the average quality of solutions (+50\% average population fitness), and discovering more diverse high-quality behaviors (+400 high-quality solutions discovered per run on average). Additionally, FM and FMX can reduce the number of fitness evaluations in an evolutionary run, reducing computational costs in some scenarios.

NeuroEvolution automates the generation of Artificial Neural Networks through the application of techniques from Evolutionary Computation. The main goal of these approaches is to build models that maximize predictive performance, sometimes with an additional objective of minimizing computational complexity. Although the evolved models achieve competitive results performance-wise, their robustness to adversarial examples, which becomes a concern in security-critical scenarios, has received limited attention. In this paper, we evaluate the adversarial robustness of models found by two prominent NeuroEvolution approaches on the CIFAR-10 image classification task: DENSER and NSGA-Net. Since the models are publicly available, we consider white-box untargeted attacks, where the perturbations are bounded by either the L2 or the Linfinity-norm. Similarly to manually-designed networks, our results show that when the evolved models are attacked with iterative methods, their accuracy usually drops to, or close to, zero under both distance metrics. The DENSER model is an exception to this trend, showing some resistance under the L2 threat model, where its accuracy only drops from 93.70% to 18.10% even with iterative attacks. Additionally, we analyzed the impact of pre-processing applied to the data before the first layer of the network. Our observations suggest that some of these techniques can exacerbate the perturbations added to the original inputs, potentially harming robustness. Thus, this choice should not be neglected when automatically designing networks for applications where adversarial attacks are prone to occur.

In the context of generative models, text-to-image generation achieved impressive results in recent years. Models using different approaches were proposed and trained in huge datasets of pairs of texts and images. However, some methods rely on pre-trained models such as Generative Adversarial Networks, searching through the latent space of the generative model by using a gradient-based approach to update the latent vector, relying on loss functions such as the cosine similarity. In this work, we follow a different direction by proposing the use of Covariance Matrix Adaptation Evolution Strategy to explore the latent space of Generative Adversarial Networks. We compare this approach to the one using Adam and a hybrid strategy. We design an experimental study to compare the three approaches using different text inputs for image generation by adapting an evaluation method based on the projection of the resulting samples into a two-dimensional grid to inspect the diversity of the distributions. The results evidence that the evolutionary method achieves more diversity in the generation of samples, exploring different regions of the resulting grids. Besides, we show that the hybrid method combines the explored areas of the gradient-based and evolutionary approaches, leveraging the quality of the results.

The grammars used in grammar-based Genetic Programming (GP) methods have a significant impact on the quality of the solutions generated since they define the search space by restricting the solutions to its syntax. In this work, we propose Probabilistic Structured Grammatical Evolution (PSGE), a new approach that combines the Structured Grammatical Evolution (SGE) and Probabilistic Grammatical Evolution (PGE) representation variants and mapping mechanisms. The genotype is a set of dynamic lists, one for each non-terminal in the grammar, with each element of the list representing a probability used to select the next Probabilistic Context-Free Grammar (PCFG) derivation rule. PSGE statistically outperformed Grammatical Evolution (GE) on all six benchmark problems studied. In comparison to PGE, PSGE outperformed 4 of the 6 problems analyzed., Comment: arXiv admin note: text overlap with arXiv:2204.08985

This work proposes an extension to Structured Grammatical Evolution (SGE) called Co-evolutionary Probabilistic Structured Grammatical Evolution (Co-PSGE). In Co-PSGE each individual in the population is composed by a grammar and a genotype, which is a list of dynamic lists, each corresponding to a non-terminal of the grammar containing real numbers that correspond to the probability of choosing a derivation rule. Each individual uses its own grammar to map the genotype into a program. During the evolutionary process, both the grammar and the genotype are subject to variation operators. The performance of the proposed approach is compared to 3 different methods, namely, Grammatical Evolution (GE), Probabilistic Grammatical Evolution (PGE), and SGE on four different benchmark problems. The results show the effectiveness of the approach since Co-PSGE is able to outperform all the methods with statistically significant differences in the majority of the problems., Comment: 9 pages, 10 figures, The Genetic and Evolutionary Computation Conference

Neuroevolutionary algorithms, automatic searches of neural network structures by means of evolutionary techniques, are computationally costly procedures. In spite of this, due to the great performance provided by the architectures which are found, these methods are widely applied. The final outcome of neuroevolutionary processes is the best structure found during the search, and the rest of the procedure is commonly omitted in the literature. However, a good amount of residual information consisting of valuable knowledge that can be extracted is also produced during these searches. In this paper, we propose an approach that extracts this information from neuroevolutionary runs, and use it to build a metamodel that could positively impact future neural architecture searches. More specifically, by inspecting the best structures found during neuroevolutionary searches of generative adversarial networks with varying characteristics (e.g., based on dense or convolutional layers), we propose a Bayesian network-based model which can be used to either find strong neural structures right away, conveniently initialize different structural searches for different problems, or help future optimization of structures of any type to keep finding increasingly better structures where uninformed methods get stuck into local optima.

Artificial Neural Networks (ANNs) became popular due to their successful application difficult problems such image and speech recognition. However, when practitioners want to design an ANN they need to undergo laborious process of selecting a set of parameters and topology. Currently, there are several state-of-the art methods that allow for the automatic selection of some of these aspects. Learning Rate optimizers are a set of such techniques that search for good values of learning rates. Whilst these techniques are effective and have yielded good results over the years, they are general solution i.e. they do not consider the characteristics of a specific network. We propose a framework called AutoLR to automatically design Learning Rate Optimizers. Two versions of the system are detailed. The first one, Dynamic AutoLR, evolves static and dynamic learning rate optimizers based on the current epoch and the previous learning rate. The second version, Adaptive AutoLR, evolves adaptive optimizers that can fine tune the learning rate for each network eeight which makes them generally more effective. The results are competitive with the best state of the art methods, even outperforming them in some scenarios. Furthermore, the system evolved a classifier, ADES, that appears to be novel and innovative since, to the best of our knowledge, it has a structure that differs from state of the art methods., Comment: 10 pages, 5 figures

Grammatical Evolution (GE) is one of the most popular Genetic Programming (GP) variants, and it has been used with success in several problem domains. Since the original proposal, many enhancements have been proposed to GE in order to address some of its main issues and improve its performance. In this paper we propose Probabilistic Grammatical Evolution (PGE), which introduces a new genotypic representation and new mapping mechanism for GE. Specifically, we resort to a Probabilistic Context-Free Grammar (PCFG) where its probabilities are adapted during the evolutionary process, taking into account the productions chosen to construct the fittest individual. The genotype is a list of real values, where each value represents the likelihood of selecting a derivation rule. We evaluate the performance of PGE in two regression problems and compare it with GE and Structured Grammatical Evolution (SGE). The results show that PGE has a a better performance than GE, with statistically significant differences, and achieved similar performance when comparing with SGE.

Generative Adversarial Networks (GANs) are powerful generative models that achieved strong results, mainly in the image domain. However, the training of GANs is not trivial, presenting some challenges tackled by different strategies. Evolutionary algorithms, such as COEGAN, were recently proposed as a solution to improve the GAN training, overcoming common problems that affect the model, such as vanishing gradient and mode collapse. In this work, we propose an evaluation method based on t-distributed Stochastic Neighbour Embedding (t-SNE) to assess the progress of GANs and visualize the distribution learned by generators in training. We propose the use of the feature space extracted from trained discriminators to evaluate samples produced by generators and from the input dataset. A metric based on the resulting t-SNE maps and the Jaccard index is proposed to represent the model quality. Experiments were conducted to assess the progress of GANs when trained using COEGAN. The results show both by visual inspection and metrics that the Evolutionary Algorithm gradually improves discriminators and generators through generations, avoiding problems such as mode collapse., Comment: To be published in EvoApplications 2021

Generative adversarial networks (GANs) achieved relevant advances in the field of generative algorithms, presenting high-quality results mainly in the context of images. However, GANs are hard to train, and several aspects of the model should be previously designed by hand to ensure training success. In this context, evolutionary algorithms such as COEGAN were proposed to solve the challenges in GAN training. Nevertheless, the lack of diversity and premature optimization can be found in some of these solutions. We propose in this paper the application of a quality-diversity algorithm in the evolution of GANs. The solution is based on the Novelty Search with Local Competition (NSLC) algorithm, adapting the concepts used in COEGAN to this new proposal. We compare our proposal with the original COEGAN model and with an alternative version using a global competition approach. The experimental results evidenced that our proposal increases the diversity of the discovered solutions and leverage the performance of the models found by the algorithm. Furthermore, the global competition approach was able to consistently find better models for GANs., Comment: Published in GECCO 2020

The choice of a proper learning rate is paramount for good Artificial Neural Network training and performance. In the past, one had to rely on experience and trial-and-error to find an adequate learning rate. Presently, a plethora of state of the art automatic methods exist that make the search for a good learning rate easier. While these techniques are effective and have yielded good results over the years, they are general solutions. This means the optimization of learning rate for specific network topologies remains largely unexplored. This work presents AutoLR, a framework that evolves Learning Rate Schedulers for a specific Neural Network Architecture using Structured Grammatical Evolution. The system was used to evolve learning rate policies that were compared with a commonly used baseline value for learning rate. Results show that training performed using certain evolved policies is more efficient than the established baseline and suggest that this approach is a viable means of improving a neural network's performance.

Generative Adversarial Networks (GANs) are an adversarial model that achieved impressive results on generative tasks. In spite of the relevant results, GANs present some challenges regarding stability, making the training usually a hit-and-miss process. To overcome these challenges, several improvements were proposed to better handle the internal characteristics of the model, such as alternative loss functions or architectural changes on the neural networks used by the generator and the discriminator. Recent works proposed the use of evolutionary algorithms on GAN training, aiming to solve these challenges and to provide an automatic way to find good models. In this context, COEGAN proposes the use of coevolution and neuroevolution to orchestrate the training of GANs. However, previous experiments detected that some of the fitness functions used to guide the evolution are not ideal. In this work we propose the evaluation of a game-based fitness function to be used within the COEGAN method. Skill rating is a metric to quantify the skill of players in a game and has already been used to evaluate GANs. We extend this idea using the skill rating in an evolutionary algorithm to train GANs. The results show that skill rating can be used as fitness to guide the evolution in COEGAN without the dependence of an external evaluator., Comment: Published in EvoApplications 2020

The deployment of Machine Learning (ML) models is a difficult and time-consuming job that comprises a series of sequential and correlated tasks that go from the data pre-processing, and the design and extraction of features, to the choice of the ML algorithm and its parameterisation. The task is even more challenging considering that the design of features is in many cases problem specific, and thus requires domain-expertise. To overcome these limitations Automated Machine Learning (AutoML) methods seek to automate, with few or no human-intervention, the design of pipelines, i.e., automate the selection of the sequence of methods that have to be applied to the raw data. These methods have the potential to enable non-expert users to use ML, and provide expert users with solutions that they would unlikely consider. In particular, this paper describes AutoML-DSGE - a novel grammar-based framework that adapts Dynamic Structured Grammatical Evolution (DSGE) to the evolution of Scikit-Learn classification pipelines. The experimental results include comparing AutoML-DSGE to another grammar-based AutoML framework, Resilient ClassificationPipeline Evolution (RECIPE), and show that the average performance of the classification pipelines generated by AutoML-DSGE is always superior to the average performance of RECIPE; the differences are statistically significant in 3 out of the 10 used datasets., Comment: EvoApps 2020

NeuroEvolution (NE) methods are known for applying Evolutionary Computation to the optimisation of Artificial Neural Networks(ANNs). Despite aiding non-expert users to design and train ANNs, the vast majority of NE approaches disregard the knowledge that is gathered when solving other tasks, i.e., evolution starts from scratch for each problem, ultimately delaying the evolutionary process. To overcome this drawback, we extend Fast Deep Evolutionary Network Structured Representation (Fast-DENSER) to incremental development. We hypothesise that by transferring the knowledge gained from previous tasks we can attain superior results and speedup evolution. The results show that the average performance of the models generated by incremental development is statistically superior to the non-incremental average performance. In case the number of evaluations performed by incremental development is smaller than the performed by non-incremental development the attained results are similar in performance, which indicates that incremental development speeds up evolution. Lastly, the models generated using incremental development generalise better, and thus, without further evolution, report a superior performance on unseen problems., Comment: European Conference on Genetic Programming (EuroGP) 2020

Generative adversarial networks (GAN) present state-of-the-art results in the generation of samples following the distribution of the input dataset. However, GANs are difficult to train, and several aspects of the model should be previously designed by hand. Neuroevolution is a well-known technique used to provide the automatic design of network architectures which was recently expanded to deep neural networks. COEGAN is a model that uses neuroevolution and coevolution in the GAN training algorithm to provide a more stable training method and the automatic design of neural network architectures. COEGAN makes use of the adversarial aspect of the GAN components to implement coevolutionary strategies in the training algorithm. Our proposal was evaluated in the Fashion-MNIST and MNIST dataset. We compare our results with a baseline based on DCGAN and also with results from a random search algorithm. We show that our method is able to discover efficient architectures in the Fashion-MNIST and MNIST datasets. The results also suggest that COEGAN can be used as a training algorithm for GANs to avoid common issues, such as the mode collapse problem., Comment: Published in GECCO 2019. arXiv admin note: text overlap with arXiv:1912.06172

Generative adversarial networks (GAN) became a hot topic, presenting impressive results in the field of computer vision. However, there are still open problems with the GAN model, such as the training stability and the hand-design of architectures. Neuroevolution is a technique that can be used to provide the automatic design of network architectures even in large search spaces as in deep neural networks. Therefore, this project proposes COEGAN, a model that combines neuroevolution and coevolution in the coordination of the GAN training algorithm. The proposal uses the adversarial characteristic between the generator and discriminator components to design an algorithm using coevolution techniques. Our proposal was evaluated in the MNIST dataset. The results suggest the improvement of the training stability and the automatic discovery of efficient network architectures for GANs. Our model also partially solves the mode collapse problem., Comment: Published in EvoApplications 2019

Machine learning models are widely adopted in scenarios that directly affect people. The development of software systems based on these models raises societal and legal concerns, as their decisions may lead to the unfair treatment of individuals based on attributes like race or gender. Data preparation is key in any machine learning pipeline, but its effect on fairness is yet to be studied in detail. In this paper, we evaluate how the fairness and effectiveness of the learned models are affected by the removal of the sensitive attribute, the encoding of the categorical attributes, and instance selection methods (including cross-validators and random undersampling). We used the Adult Income and the German Credit Data datasets, which are widely studied and known to have fairness concerns. We applied each data preparation technique individually to analyse the difference in predictive performance and fairness, using statistical parity difference, disparate impact, and the normalised prejudice index. The results show that fairness is affected by transformations made to the training data, particularly in imbalanced datasets. Removing the sensitive attribute is insufficient to eliminate all the unfairness in the predictions, as expected, but it is key to achieve fairer models. Additionally, the standard random undersampling with respect to the true labels is sometimes more prejudicial than performing no random undersampling.

The goal of this work is to investigate the possibility of improving current gamma/hadron discrimination based on their shower patterns recorded on the ground. To this end we propose the use of Convolutional Neural Networks (CNNs) for their ability to distinguish patterns based on automatically designed features. In order to promote the creation of CNNs that properly uncover the hidden patterns in the data, and at same time avoid the burden of hand-crafting the topology and learning hyper-parameters we resort to NeuroEvolution; in particular we use Fast-DENSER++, a variant of Deep Evolutionary Network Structured Representation. The results show that the best CNN generated by Fast-DENSER++ improves by a factor of 2 when compared with the results reported by classic statistical approaches. Additionally, we experiment ensembling the 10 best generated CNNs, one from each of the evolutionary runs; the ensemble leads to an improvement by a factor of 2.3. These results show that it is possible to improve the gamma/hadron discrimination based on CNNs that are automatically generated and are trained with instances of the ground impact patterns.

This paper proposes a new extension to Deep Evolutionary Network Structured Evolution (DENSER), called Fast-DENSER++ (F-DENSER++). The vast majority of NeuroEvolution methods that optimise Deep Artificial Neural Networks (DANNs) only evaluate the candidate solutions for a fixed amount of epochs; this makes it difficult to effectively assess the learning strategy, and requires the best generated network to be further trained after evolution. F-DENSER++ enables the training time of the candidate solutions to grow continuously as necessary, i.e., in the initial generations the candidate solutions are trained for shorter times, and as generations proceed it is expected that longer training cycles enable better performances. Consequently, the models discovered by F-DENSER++ are fully-trained DANNs, and are ready for deployment after evolution, without the need for further training. The results demonstrate the ability of F-DENSER++ to effectively generate fully-trained DANNs; by the end of evolution, whilst the average performance of the models generated by F-DENSER++ is of 88.73%, the performance of the models generated by the previous version of DENSER (Fast-DENSER) is 86.91% (statistically significant), which increases to 87.76% when allowed to train for longer.