Covariance Matrix Adaptation Research Articles

Automatic Calibration of Bed Friction Coefficients to Reduce the Influence of Seasonal Variation: Case of the Gironde Estuary

An automatic procedure to identify the bed friction coefficient is tested on a 2D hydrodynamic model of the Gironde estuary (France). The proposed procedure involves an optimization algorithm based on evolution strategy, namely Covariance Matrix Adaptation Evolution Strategy. Without optimization, application of the same friction distribution to different hydrological conditions leads to significant relative error in water level prediction up to 20%–30%. For the tested configuration, 300 runs seemed to be sufficient to reach an optimal value whereas an additional 200 runs would help to gain an accuracy of a few millimeters (or 0.3%). In order to reach the same level of accuracy for the different hydrological configurations, it is necessary to adapt for each configuration of the bed friction coefficient. Such behavior tends to confirm a seasonal variation of the friction coefficient and this is particularly the case in the central part of the estuary. Different relationships of the friction coefficient according to the flowrate have been incorporated inside the 2D hydrodynamic model. These relationships effectively maintain an accurate prediction of the water levels close to 10% for a wide range of hydrological configurations.

Variational Bayesian adaptation of process noise covariance matrix in Kalman filtering

Adaptive Kalman filtering with unknown constant or varying process noise covariance matrix is studied. A resolution is proposed to directly estimate or tune the process noise covariance matrix in Kalman filtering using variational Bayesian technique. By state augmentation, conjugacy of the process noise covariance matrix's inverse-Wishart distribution is realized in the estimation at each time instant. The methodological development is given. Illustration examples are presented to demonstrate the improved state filtering performance and the process noise covariance tracking performance of the new method.

An Optimized Method for 3D Magnetic Navigation of Nanoparticles inside Human Arteries

A computational method for optimum magnetic navigation of nanoparticles that are coated with anticancer drug inside the human vascular system is presented in this study. For this reason a 3D carotid model is employed. The present model use Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) techniques along with Covariance Matrix Adaptation (CMA) evolution strategy for the evaluation of the optimal values of the gradient magnetic field. Under the influence of the blood flow the model evaluates the effect of different values of the gradient magnetic field in order to minimize the distance of particles from a pre-described desired trajectory. Results indicate that the diameter of particles is a crucial parameter for an effective magnetic navigation. The present numerical model can navigate nanoparticles with diameter above 500 nm with an efficiency of approximately 99%. It is found that the velocity of the blood seems to play insignificant role in the navigation process. A reduction of 25% in the inlet velocity leads the particles only 3% closer to the desired trajectory. Finally, the computational method is more efficient as the diameter of the vascular system is minimized because of the weak convective flow. Under a reduction of 50% in the diameter of the carotid artery the computational method navigate the particles approximately 75% closer to the desired trajectory. The present numerical model can be used as a tool for the determination of the parameters that mostly affect the magnetic navigation method.

Multi-Stage Dynamic Transmission Network Expansion Planning Using LSHADE-SPACMA

This paper introduces a multi-stage dynamic transmission network expansion planning (MSDTNEP) model considering the N-1 reliability constraint. The integrated planning problem of N-1 security and transmission expansion planning is essential because a single line outage could be a triggering event to rolling blackouts. Two suggested scenarios were developed to obtain the optimal configuration of the Egyptian West Delta Network’s realistic transmission (WDN) to meet the demand of the potential load growth and ensure the system reliability up to the year 2040. The size of a blackout, based on the amount of expected energy not supplied, was calculated to evaluate both scenarios. The load forecasting (up to 2040) was obtained based on an adaptive neuro-fuzzy inference system because it gives excellent results compared to conventional methods. The linear population size reduction—Success-History-based Differential Evolution with semi-parameter adaptation (LSHADE-SPA) hybrid—covariance matrix adaptation evolution strategy (CMA-ES) algorithm (LSHADE-SPACMA)—is applied to solve the problem. The semi-adaptive nature of LSHADE-SPACMA and the hybridization between LSHADE and CMA-ES are able to solve complex optimization problems. The performance of LSHADE-SPACMA in solving the problem is compared to other well-established methods using three testing systems to validate its superiority. Then, the MSDTNEP of the Egyptian West Delta Network is presented, and the numerical results of the two scenarios are compared to obtain an economic plan and avoid a partial or total blackout.

Dynamic optimal power flow with cross entropy covariance matrix adaption evolutionary strategy for systems with electric vehicles and renewable generators

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

Combining Optimization Objectives: New Modeling Attacks on Strong PUFs

Strong Physical Unclonable Functions (PUFs), as a promising security primitive, are supposed to be a lightweight alternative to classical cryptography for purposes such as device authentication. Most of the proposed candidates, however, have been plagued by modeling attacks breaking their security claims. The Interpose PUF (iPUF), which has been introduced at CHES 2019, was explicitly designed with state-of-the-art modeling attacks in mind and is supposed to be impossible to break by classical and reliability attacks. In this paper, we analyze its vulnerability to reliability attacks. Despite the increased difficulty, these attacks are still feasible, against the original authors’ claim. We explain how adding constraints to the modeling objective streamlines reliability attacks and allows us to model all individual components of an iPUF successfully. In order to build a practical attack, we give several novel contributions. First, we demonstrate that reliability attacks can be performed not only with covariance matrix adaptation evolution strategy (CMA-ES) but also with gradient-based optimization. Second, we show that the switch to gradient-based reliability attacks makes it possible to combine reliability attacks, weight constraints, and Logistic Regression (LR) into a single optimization objective. This framework makes modeling attacks more efficient, as it exploits knowledge of responses and reliability information at the same time. Third, we show that a differentiable model of the iPUF exists and how it can be utilized in a combined reliability attack. We confirm that iPUFs are harder to break than regular XOR Arbiter PUFs. However, we are still able to break (1,10)-iPUF instances, which were originally assumed to be secure, with less than 107 PUF response queries.

Large-Scale Evolution Strategy Based on Search Direction Adaptation.

The covariance matrix adaptation evolution strategy (CMA-ES) is a powerful evolutionary algorithm for single-objective real-valued optimization. However, the time and space complexity may preclude its use in high-dimensional decision space. Recent studies suggest that putting sparse or low-rank constraints on the structure of the covariance matrix can improve the efficiency of CMA-ES in handling large-scale problems. Following this idea, this paper proposes a search direction adaptation evolution strategy (SDA-ES) which achieves linear time and space complexity. SDA-ES models the covariance matrix with an identity matrix and multiple search directions, and uses a heuristic to update the search directions in a way similar to the principal component analysis. We also generalize the traditional 1/5th success rule to adapt the mutation strength which exhibits the derandomization property. Numerical comparisons with nine state-of-the-art algorithms are carried out on 31 test problems. The experimental results have shown that SDA-ES is invariant under search-space rotational transformations, and is scalable with respect to the number of variables. It also achieves competitive performance on generic black-box problems, demonstrating its effectiveness in keeping a good tradeoff between solution quality and computational efficiency.

Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems

The Slime Mould Algorithm (SMA) is a recent metaheuristic inspired by the oscillation of slime mould. Similar to other original metaheuristic algorithms (MAs), SMA may suffer from drawbacks, such as being trapped in minimum local regions and improper balance between exploitation and exploration phases. To overcome these weaknesses, this paper proposes a hybrid algorithm: SMA combined to Adaptive Guided Differential Evolution Algorithm (AGDE) (SMA-AGDE). The AGDE mutation method is employed to enhance the swarm agents’ local search, increase the population’s diversity, and help avoid premature convergence. The SMA-AGDE’s performance is evaluated on the CEC’17 test suite, three engineering design problems – tension/compression spring, pressure vessel, and rolling element bearing – and two combinatorial optimization problems – bin packing and quadratic assignment. The SMA-AGDE is compared with three categories of optimization methods: (1) The well-studied MAs, i.e., Biogeography-Based Optimizer (BBO), Gravitational Search Algorithm (GSA), and Teaching Learning-Based Optimization (TLBO), (2) Recently developed MAs, i.e., Harris Hawks Optimization (HHO), Manta Ray Foraging optimization (MRFO), and the original SMA, and (3) High-performance MAs, i.e., Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), and AGDE. The overall simulation results reveal that the SMA-AGDE ranked first among the compared algorithms, and so, over different function landscapes. Thus, the proposed SMA-AGDE is a promising optimization tool for global and combinatorial optimization problems and engineering design problems.

Optimal design of wave barriers in dry and saturated poroelastic grounds using Covariance Matrix Adaptation Evolution Strategy

In this paper, Covariance Matrix Adaption Evolution Strategy (CMA-ES) is used to optimally design soft and hard wave barriers in half-space soil medium subjected to moving train loadings. Special focus is given to two-phase saturated porous medium of soil and the differences between the barrier characteristics in saturated and dry media are highlighted. Wave propagation caused by moving trains in saturated ground is modeled using Biot’s poroelastodynamic theory and time-domain finite element (FE) numerical simulations. The poroelastodynamic solution is then coupled to CMA-ES as the fitness function of the optimal design procedure. The obtained results show that the optimal barrier characteristics and amplitude reduction spectra (ARS) depend on the ground saturation as well as on the lading frequency and barrier material. It is observed that open trenches, as air-filled barriers, have a very good screening effect in both dry and saturated grounds and their optimal shape has a vertical rectangular configuration. On the other hand, hard barriers such as concrete, have less screening effects and their optimal shape takes slab-like pattern. The effectiveness of double trenches is also explored and it is found that optimal double barriers have better screening effect as compared to that of single barriers.

A hybrid approach based on IGDT‐MOCMA‐ES method for optimal operation of smart distribution network under severe uncertainties

Uncertainties involved in renewable generation and electrical demand pose significant technical challenges with the concomitant financial consequences in smart distribution networks (SDNs), particularly in the current electricity market, which is restructured and features smart grids. The present paper introduces a decision-making tool based on a risk-averse strategy to help with the smart distribution network operator (SDNO) in day-ahead operational practices, including optimal unit commitment (UC) and optimal distribution feeder reconfiguration (DFR). The tool is meant to reduce electricity prices presented to the electrical consumers and to optimize financial transactions with the energy market, distributed generation (DG) reliability, electricity storage system (ESS) dispatch, and planning interruptible electrical demands to secure specified revenue targets for SDNO with the risk-averse strategy. A bi-level stochastic optimization problem based on Information gap decision theory (IGDT) is considered to keep the SDNO from risks inherent in the information gap present between the predicted and actual uncertainty variables. The bi-level stochastic optimization problem is reorganized into a single-level problem obtained by Karush-Kuhn-Tucker method. As uncertainty variables compete to expand their enveloped-bounds, multi-objective covariance matrix adaptation-evolution strategy (MOCMA-ES) is employed to address the multifaceted IGDT-based stochastic optimization problem proposed in the study. Finally, the efficiency and efficacy of the suggested model are appraised on an IEEE 33-bus SDN. Simulation results show that optimal UC with both DFR and demand response program increases the total revenue by 8.1% compared to optimal operation without them.

Artificial bee colony algorithm with adaptive covariance matrix for hearing loss detection

Artificial bee colony algorithm (ABC) is an efficient and popular evolutionary algorithm (EAs), which has been attracted wide attention by researchers, and improved ABC with various characteristics (ABCs) have been proposed. It is widely acknowledged that the search operator is the core element in the performance of ABC. However, the generally designed search operators of ABCs are rotation-variable processes and are dependent mainly on the natural coordinates and, as a result, the performance of those ABC is limited. In this paper, the mathematical characteristic of the search operator is deeply analyzed, and on this basis, ABC with adaptive covariance matrix (ACoM-ABC) is proposed, the adaptive covariance matrix (ACoM) is used to establish a proper coordinates by making use of the population distribution information, which can relieve the dependence of ABC on the coordinates to a certain extent and improve the exploitation capability. To balance the exploitation and exploration abilities of ABC, the search operators of ABC are implemented on eigen coordinates and natural coordinates Then, to estimate the performance of ACoM-ABC, which compares with six ABCs and other six EAs, and tests on CEC2014. The excellent experimental result shows that ACoM-ABC is an efficient and outstanding algorithm. Moreover, the proposed algorithm is applied to hearing loss detection, and the experiment result shows that the overall accuracy is 96.67%, which higher than the other five state-of-the-art approaches about 1%. Therefore, the ACoM-ABC has the practicability for realistic problems.

Optimization of rotation patterns of a mangle-type magnetic field source using covariance matrix adaptation evolution strategy

A mangle-type magnetic field source with four permanent magnets is capable of generating a magnetic field with an arbitrary magnitude and direction. In this study, the rotation pattern of magnets was optimized to maximize the field uniformity by using a covariance matrix adaptation evolution strategy. Starting with random angles of magnets, angles generating the highest magnitude of the magnetic field were calculated with values similar to those of a Halbach cylinder. Although reproducible results were not obtained for a zero magnetic field, a symmetric pattern about the origin after multiple trials of optimization is likely. As the rotation pattern for continuously varying magnitude and direction of the magnetic field could not be found using the covariance matrix adaptation evolution strategy alone, artificial initial guesses were introduced, and the optimization was successful. It was demonstrated that the application of an optimized pattern requires caution with regard to the degradation of the maximum magnetic field and linearity of change in the magnitude and direction of the magnetic field.

Estimating a Stoichiometric Solid’s Gibbs Free Energy Model by Means of a Constrained Evolutionary Strategy

Modeling of thermodynamic properties, like heat capacities for stoichiometric solids, includes the treatment of different sources of data which may be inconsistent and diverse. In this work, an approach based on the covariance matrix adaptation evolution strategy (CMA-ES) is proposed and described as an alternative method for data treatment and fitting with the support of data source dependent weight factors and physical constraints. This is applied to a Gibb’s Free Energy stoichiometric model for different magnesium sulfate hydrates by means of the NASA9 polynomial. Its behavior is proved by: (i) The comparison of the model to other standard methods for different heat capacity data, yielding a more plausible curve at high temperature ranges; (ii) the comparison of the fitted heat capacity values of MgSO4·7H2O against DSC measurements, resulting in a mean relative error of a 0.7% and a normalized root mean square deviation of 1.1%; and (iii) comparing the Van’t Hoff and proposed Stoichiometric model vapor-solid equilibrium curves to different literature data for MgSO4·7H2O, MgSO4·6H2O, and MgSO4·1H2O, resulting in similar equilibrium values, especially for MgSO4·7H2O and MgSO4·6H2O. The results show good agreement with the employed data and confirm this method as a viable alternative for fitting complex physically constrained data sets, while being a potential approach for automatic data fitting of substance data.

Reliability assessment of train control and management system based on evidential reasoning rule and covariance matrix adaptation evolution strategy algorithm

The reliability assessment of train control and management system (TCMS) is essential for the condition monitoring of high-speed train. Different from other general complex systems, the TCMS has the characteristics of multi-system unit, strong coupling and multiple factors. Considering the special system operating environment and high safety requirements of high-speed train. In this paper, for the reliability assessment of TCMS, we propose a new quantitative model based on the evidential reasoning rule and covariance matrix adaptation evolution strategy algorithm, the proposed model offers the following advantages: it has a strong modeling capability for the TCMS reliability, it has an interpretable model assessment process, it can describe the assessment result under probabilistic uncertainty and ignorance uncertainty, and it possesses considerable robustness. To make the model interpretable, an assessment hierarchy is established for the TCMS; to improve model robustness, weights interval is applied to replace the trained weights as the model weights. Several traditional methods are compared with the proposed model to demonstrate its performance, the results show that the proposed model has a better training accuracy. Moreover, a case study is conducted to verify the model’s functional feasibility.

Enhancing the competitive swarm optimizer with covariance matrix adaptation for large scale optimization

Competitive swarm optimizer (CSO) has been shown to be an effective optimization algorithm for large scale optimization. However, the learning strategy of a loser particle used in CSO is axis-parallel. Then, it may not be able to solve the high ill-conditioned test functions due to the lack of considering the correlation of different component. This paper presents an enhanced competitive swarm optimizer with covariance matrix adaptation to alleviate this problem. Since covariance matrix is independent of the coordinate system, covariance matrix adaptation evolution strategy (CMA-ES) is embedded into CSO. On the one hand, better particles generated by CMA-ES can provide an effective way to capture the efficient search direction. On the other hand, some high-quality particles are employed to estimate the covariance matrix of Gaussian model. Then, the evolution direction information is integrated into the learned Gaussian model to improve search efficiency of the proposed algorithm. Experimental and statistical analyses are performed on CEC2014 benchmark functions, engineering design problems and time series prediction problems. Results show that the proposed algorithm has a superior performance in comparison with other state-of-the-art optimization algorithms and some variants of CSO.

A Dynamically Configurable PUF and Dynamic Matching Authentication Protocol

A physical unclonable function (PUF) is a hardware security primitive, which can be used secure various hardware-based applications. As a type of PUFs, strong PUFs have a large number of challenge-response pairs (CRPs), which can be used for authentication. At present, most strong PUF structures follow a one-to-one input/output relationship, i.e. linear function. As such, strong PUF designs are vulnerable to machine learning (ML) based modeling attacks. To address the issue, a dynamically configurable PUF structure is proposed in this paper. A mathematical model of the proposed dynamic PUF is presented and the design is proposed against the effective ML based attacks, such as deep neural network (DNN), logistic regression (LR) and reliability-based covariance matrix adaptation evolution strategies (CMA-ES). Experimental results on field programmable gate arrays (FPGAs) show that the proposed dynamic structure has achived good uniqueness and reliability. It is also shown that the dynamic PUF has a strong resistance to the CMA-ES attack. Due to the dynamic nature of the proposed PUF structure, an authentication protocol is also designed to generate recognizable authentication bits string. The protocol shows strong resistance to classical machine learning attacks including the new variant of CMA-ES.

Topology optimization for controlling thermal wave in macroscale

In this paper, we develop topology optimization for controlling thermal wave, which is a temperature wave in macro scale. Assuming a porous system in macro scale, the thermal wave is analyzed by the finite element method. The level set function that expresses the structure is optimized by the optimal solution search based on the covariance matrix adaptation evolution strategy (CMA-ES), and the temperature distribution of the thermal wave disturbed by the obstacle is cloaked by the topology optimization using the level set method.

Enhanced Computational Intelligence Algorithm for Coverage Optimization of 6G Non-Terrestrial Networks in 3D Space

The next generation 6G communication network is typically characterized by the full connectivity and coverage of Users Equipment (UEs). This leads to the need for moving beyond the traditional two-dimensional (2D) coverage service to the three-dimensional (3D) full-service one. The 6G 3D architecture leverages different types of non-terrestrial or aerial nodes that can act as mobile Base Stations (BSs) such as Unmanned Aerial Vehicles (UAVs), Low Altitude Platforms (LAPs), High-Altitude Platform Stations (HAPSs), or even Low Earth Orbit (LEO) satellites. Moreover, aided technologies have been added to the 6G architecture to dynamically increase its coverage efficiency such as the Reconfigurable Intelligent Surfaces (RIS). In this paper, an enhanced Computational Intelligence (CI) algorithm is introduced for optimizing the coverage of UAV-BSs with respect to their location from RIS in the 3D space of 6G architecture. The regarded problem is formulated as a constrained 3D coverage optimization problem. In order to increase the convergence of the proposed algorithm, it is hybridized with a crossover operator. For the validation of the proposed method, it is tested on different scenarios with large-scale coordinates and compared with many recent and hybrid CI algorithms, as Slime Mould Algorithm (SMA), Levy Flight Distribution (LFD), hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA), the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and hybrid Grey Wolf Optimizer and Cuckoo Search (GWOCS). The experiment and the statistical analysis show the significant efficiency of the proposed algorithm in achieving complete coverage with a lower number of UAV-BSs and without constraints violation.

Estimation of natural streams longitudinal dispersion coefficient using hybrid evolutionary machine learning model

Among several indicators for river engineering sustainability, the longitudinal dispersion coefficient () is the main parameter that defines the transport of pollutants in natural streams. Accurate estimation of has been challenging for hydrologists due to the high stochasticity and non-linearity of this hydraulic-environmental parameter. This study presents a new hybrid machine learning (ML) model integrating a Gaussian Process Regression (GPR) and an evolutionary feature selection (FS) approach (i.e. Covariance Matrix Adaptation Evolution Strategy (CMAES)) to estimate in natural streams. The dataset consists of geometric and hydraulic river system parameters from 29 streams in the United States. The modeling results showed that the proposed model outperformed other models in the literature, producing more stable and accurate estimations. The FS approach evidenced the significance of the cross-sectional average flow velocity (U), channel width (B), and channel sinuosity σ to estimate the dispersion coefficient. In quantitative terms, the integrated GPR model with feature selection approach attained the minimum root mean square error () and maximum coefficient of determination (). The proposed hybrid evolutionary ML model arises as robust, flexible and reliable alternative computer aid technology for predicting the longitudinal dispersion coefficient in natural streams.

Generalized ground motion prediction model using hybrid recurrent neural network

AbstractModern seismic hazard analysis utilizes various ground motion prediction equations (GMPEs) to estimate intensity measures (IMs) such as spectral acceleration (Sa), Arias intensity (Ia), significant duration (D5‐95), and cumulative absolute velocity (CAV) as scalar parameters. The use of these GMPEs leads to independent estimations of IMs for the same earthquake scenario. Since the IMs belonging to the same earthquake scenario are naturally correlated, the GMPEs used for characterization of seismic hazard are expected to incorporate such correlation structure. Particularly, Sa corresponding to different periods of a single‐degree‐of‐freedom oscillator is estimated by GMPEs that do not explicitly account for internal correlations between the Sa at various periods for the same ground motion. The current approach to incorporate such a correlation for Sa spectrum is through a post‐processing technique developed by Baker and Jayaram; their method relates the spectral accelerations of different periods using functional forms describing linear correlations. However, the proposed correlation functions can be further improved and extended to more accurately estimate the spectrum of near‐fault high‐magnitude ground motions using high order dependencies among the spectral accelerations. This study proposes a generalized ground motion prediction model (GGMPM) using a hybrid recurrent neural network (RNN) framework that can be used to estimate a 29 × 1 correlated vector (denoted as IM) of RotD50 Sa at 26 periods and geometric means of Ia, D5‐95, and CAV using a set of seismic source and site parameters as inputs. This is an improvement to the current body of knowledge because the high order dependencies between the individual components of IM are incorporated. A RNN framework is developed that estimates the median vector of IM. The discrepancy between the IM estimated using the RNN framework and the IM computed from recorded motions is further minimized using the covariance matrix adaptation evolution strategy (CMA‐ES), which is a non‐convex optimization method. The residuals of the RNN framework are used to construct the inter‐event and the intra‐event covariance matrices to account for the inter‐event and intra‐event variabilities of the ground motions. Hence, given the source and site parameters, the RNN‐framework returns a median prediction of the IM, which is then combined with estimated inter‐event and intra‐event covariance matrices to obtain the probabilistic estimation of IM. Furthermore, this GGMPM framework is compared against various currently used GMPEs, and the results of these comparisons demonstrate that the proposed GGMPM leads to improved predictions while maintaining the internal dependencies of the IM components.