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A first and second order progress rate analysis was conducted for the intermediate multi-recombinative Evolution Strategy ( μ / μ I , λ)-ES with isotropic scale-invariant mutations on the highly multimodal Rastrigin test function. Closed-form analytic solutions for the progress rates are obtained in the limit of large dimensionality and large populations. The first order results are able to model the one-generation progress including local attraction phenomena. Furthermore, a second order progress rate is derived yielding additional correction terms and further improving the progress model. The obtained results are compared to simulations and show good agreement, even for moderately large populations and dimensionality. The progress rates are applied within a dynamical systems approach, which models the evolution using difference equations. The obtained dynamics are compared to real averaged optimization runs and yield good agreement. The results improve further when dimensionality and population size are increased. Local and global convergence is investigated within given model showing that large mutations are needed to maximize the probability of global convergence, which comes at the expense of efficiency. An outlook regarding future research goals is provided., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The highly multimodal Rastrigin test function is analyzed by deriving a new aggregated progress rate measure. It is derived as a function of the residual distance to the optimizer by assuming normally distributed positional coordinates around the global optimizer. This assumption is justified for successful ES-runs operating with sufficiently slow step-size adaptation. The measure enables the investigation of further convergence properties. For moderately large mutation strengths a characteristic distance-dependent Rastrigin noise floor is derived. For small mutation strengths local attraction is analyzed and an escape condition is established. Both mutation strength regimes combined pose a major challenge optimizing the Rastrigin function, which can be counteracted by increasing the population size. Hence, a population scaling relation to achieve high global convergence rates is derived which shows good agreement with experimental data.

Background: When designing a treatment in orthodontics, especially for children and teenagers, it is crucial to be aware of the changes that occur throughout facial growth because the rate and direction of growth can greatly affect the necessity of using different treatment mechanics. This paper presents a Bayesian network approach for facial biotype classification to classify patients' biotypes into Dolichofacial (long and narrow face), Brachyfacial (short and wide face), and an intermediate kind called Mesofacial, we develop a novel learning technique for tree augmented Naive Bayes (TAN) for this purpose., Results: The proposed method, on average, outperformed all the other models based on accuracy, precision, recall, [Formula: see text], and kappa, for the particular dataset analyzed. Moreover, the proposed method presented the lowest dispersion, making this model more stable and robust against different runs., Conclusions: The proposed method obtained high accuracy values compared to other competitive classifiers. When analyzing a resulting Bayesian network, many of the interactions shown in the network had an orthodontic interpretation. For orthodontists, the Bayesian network classifier can be a helpful decision-making tool., (© 2022. The Author(s).)

This paper validates a sinusoidal approach for the proton-exchange membrane fuel cell (PEMFC) model as a supplement to experimental studies. An FC simulation or hardware emulation is necessary for prototype design, testing, and fault diagnosis to reduce the overall cost. For this objective, a sinusoidal model that is capable of accurately estimating the voltage behavior from the operating current value of the DC was developed. The model was tested using experimental data from the Ballard Nexa 1.2 kW fuel cell (FC). This methodology offers a promising approach for static and current-voltage, characteristic of the three regions of operation. A study was carried out to evaluate the effectiveness and superiority of the proposed FC Sinusoidal model compared with the Diffusive Global model and the Evolution Strategy.

An accurate model of a proton-exchange membrane fuel cell (PEMFC) is important for understanding this fuel cell's dynamic process and behavior. Among different large-scale energy storage systems, fuel cell technology does not have geographical requirements. To provide an effective operation estimation of PEMFC, this paper proposes a support vector machine (SVM) based model. The advantages of the SVM, such as the ability to model nonlinear systems and provide accurate estimations when nonlinearities and noise appear in the system, are the main motivations to use the SVM method. This model can capture the static and dynamic voltage-current characteristics of the PEMFC system in the three operating regions. The validity of the proposed SVM model has been verified by comparing the estimated voltage with the real measurements from the Ballard Nexa® 1.2 kW fuel cell (FC) power module. The obtained results have shown high accuracy between the proposed model and the experimental operation of the PEMFC. A statistical study is developed to evaluate the effectiveness and superiority of the proposed SVM model compared with the diffusive global (DG) model and the evolution strategy (ES)-based model.

The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically efficient, as attested by respectable performance on the BBOB testbed, even on rather irregular functions. In this article, we formally prove two strong guarantees for the (1 + 4)-HE-ES, a minimal elitist member of the family: stability of the covariance matrix update, and as a consequence, linear convergence on all convex quadratic problems at a rate that is independent of the problem instance., (© 2021 Massachusetts Institute of Technology.)

This paper proposes a Gaussian approach for the proton-exchange membrane fuel cell (PEMFC) model that estimates its voltage behavior from the operating current value. A multi-parametric Gaussian model and an unconstrained optimization formulation based on a conventional non-linear least squares optimizer is mainly considered. The model is tested using experimental data from the Ballard Nexa 1.2 kW fuel cell (FC). This methodology offers a promising approach for static and current-voltage, characteristic of the three regions of operation. A statistical study is developed to evaluate the effectiveness and superiority of the proposed FC Gaussian model compared with the Diffusive Global model and the Evolution Strategy. In addition, an approximation to the exponential function for a Gaussian model simplification can be used in systems that require real-time emulators or complex long-time simulations.

Among underwater vehicles, fish-inspired designs are often selected for their efficient gaits; these designs, however, remain limited in their maneuverability, especially in confined spaces. This paper presents a new design for a fish-inspired robot with two degree-of-freedom pectoral fins and a single degree-of-freedom caudal fin. This robot has been designed to operate in open-channel canals in the presence of external disturbances. With the complex interactions of water in mind, the composition of goal-specific swimming gaits is trained via a machine learning workflow in which automated trials in the lab are used to select a subset of potential gaits for outdoor trials. The goal of this process is to minimize the time cost of outdoor experimentation through the identification and transfer of high-performing gaits with the understanding that, in the absence of complete replication of the intended target environment, some or many of these gaits must be eliminated in the real world. This process is motivated by the challenge of balancing the optimization of complex, high degree-of-freedom robots for disturbance-heavy, random, niche environments against the limitations of current machine learning techniques in real-world experiments, and has been used in the design process as well as across a number of locomotion goals. The key contribution of this paper involves finding strategies that leverage online learning methods to train a bio-inspired fish robot by identifying high-performing gaits that have a consistent performance both in the laboratory experiments and the intended operating environment. Using the workflow described herein, the resulting robot can reach a forward swimming speed of 0.385 m s -1 (0.71 body lengths per second) and can achieve a near-zero turning radius., (© 2021 IOP Publishing Ltd.)

Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Nonlinear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs.

This paper investigates how to efficiently charge sensor nodes in a wireless rechargeable sensor network (WRSN) with radio frequency (RF) chargers to make the network sustainable. An RF charger is assumed to be equipped with a uniform circular array (UCA) of 12 antennas with the radius λ , where λ is the RF wavelength. The UCA can steer most RF energy in a target direction to charge a specific WRSN node by the beamforming technology. Two evolutionary algorithms (EAs) using the evolution strategy (ES), namely the Evolutionary Beamforming Optimization (EBO) algorithm and the Evolutionary Beamforming Optimization Reseeding (EBO-R) algorithm, are proposed to nearly optimize the power ratio of the UCA beamforming peak side lobe (PSL) and the main lobe (ML) aimed at the given target direction. The proposed algorithms are simulated for performance evaluation and are compared with a related algorithm, called Particle Swarm Optimization Gravitational Search Algorithm-Explore (PSOGSA-Explore), to show their superiority., Competing Interests: The authors declare no conflict of interest.

This paper presents a method to design Spiking Central Pattern Generators (SCPGs) to achieve locomotion at different frequencies on legged robots. It is validated through embedding its designs into a Field-Programmable Gate Array (FPGA) and implemented on a real hexapod robot. The SCPGs are automatically designed by means of a Christiansen Grammar Evolution (CGE)-based methodology. The CGE performs a solution for the configuration (synaptic weights and connections) for each neuron in the SCPG. This is carried out through the indirect representation of candidate solutions that evolve to replicate a specific spike train according to a locomotion pattern (gait) by measuring the similarity between the spike trains and the SPIKE distance to lead the search to a correct configuration. By using this evolutionary approach, several SCPG design specifications can be explicitly added into the SPIKE distance-based fitness function, such as looking for Spiking Neural Networks (SNNs) with minimal connectivity or a Central Pattern Generator (CPG) able to generate different locomotion gaits only by changing the initial input stimuli. The SCPG designs have been successfully implemented on a Spartan 6 FPGA board and a real time validation on a 12 Degrees Of Freedom (DOFs) hexapod robot is presented.

Adaptive population sizing aims at improving the overall progress of an evolution strategy. At each generation, it determines the parental population size that promises the largest fitness gain, based on the information collected during the evolutionary process. In this paper, we develop an adaptive variant of a (μ/μ, λ) evolution strategy. Based on considerations on the sphere, we derive two approaches for adaptive population sizing. We then test these approaches empirically on the sphere model using a normalized mutation strength and cumulative mutation strength adaption. Finally, we compare the methodology on more general functions with a fixed population, covariance matrix adaption evolution strategy (CMA-ES). The results confirm that our adaptive population sizing methods yield better results than even the best fixed population size.

Computational modelling of biochemical systems based on top-down and bottom-up approaches has been well studied over the last decade. In this research, after illustrating how to generate atomic components by a set of given reactants and two user pre-defined component patterns, we propose an integrative top-down and bottom-up modelling approach for stepwise qualitative exploration of interactions among reactants in biochemical systems. Evolution strategy is applied to the top-down modelling approach to compose models, and simulated annealing is employed in the bottom-up modelling approach to explore potential interactions based on models constructed from the top-down modelling process. Both the top-down and bottom-up approaches support stepwise modular addition or subtraction for the model evolution. Experimental results indicate that our modelling approach is feasible to learn the relationships among biochemical reactants qualitatively. In addition, hidden reactants of the target biochemical system can be obtained by generating complex reactants in corresponding composed models. Moreover, qualitatively learned models with inferred reactants and alternative topologies can be used for further web-lab experimental investigations by biologists of interest, which may result in a better understanding of the system.