Covariance Matrix Adaptation Research Articles

Efficient Optimization: Unveiling the Application of Ensemble Learning Combined with the CMA-ES Algorithm in Hydraulic Fracturing Design

Optimizing fracturing parameters is crucial for enhancing production and reducing costs in oil and gas exploration and development. Effectively integrating geological and engineering parameters for the automated optimization of fracturing design continues to pose challenges. This study utilizes the cluster-based local outlier factor method for anomaly detection and removal from the dataset, significantly enhancing data quality. By integrating diverse models, including tree-based models and neural networks, an ensemble model for production prediction was developed. This approach successfully addresses the limitations of relying on a single model and achieves high-precision production forecasting. Furthermore, a Covariance Matrix Adaptation Evolution Strategy (CMA-ES)-based framework was established to comprehensively optimize the design parameters of fracturing projects. Optimization practices for two selected wells resulted in a 168.54% increase in production and identified the optimal design parameter configuration for all cases studied. The results of this study demonstrate the feasibility and effectiveness of the proposed ensemble prediction model and optimization framework in practical applications. Data-driven optimization strategies are expected to play a larger role in future oil and gas development, driving technological innovation and advancement in the field.

An adaptive helper and equivalent objective evolution strategy for constrained optimization

The matrix adaptation evolution strategy is a simplified covariance matrix adaptation evolution strategy with reduced computational cost. Using it as a search engine, several algorithms have been recently proposed for constrained optimization and have shown excellent performance. However, these algorithms require the simultaneous application of multiple techniques to handle constraints, and also require gradient information. This makes them inappropriate for handling non-differentiable functions. This paper proposes a new matrix adaption evolutionary strategy for constrained optimization using helper and equivalent objectives. The method optimizes two objectives but with no need for special handling of infeasible solutions and without gradient information. A new mechanism is designed to adaptively adjust the weights of the two objectives according to the convergence rate. The efficacy of the proposed algorithm is evaluated using computational experiments on the IEEE CEC 2017 Constrained Optimization Competition benchmarks. Experimental results demonstrate that it outperforms current state-of-the-art evolutionary algorithms. Furthermore, this paper provides sufficient conditions for the convergence of helper and equivalent objective evolutionary algorithms and proves that using helper objectives can reduce the likelihood of premature convergence.

Knowledge-Based Perturbation LaF-CMA-ES for Multimodal Optimization

Multimodal optimization presents a significant challenge in optimization problems due to the existence of multiple attraction basins. Balancing exploration and exploitation is essential for the efficiency of algorithms designed to solve these problems. In this paper, we propose the KbP-LaF-CMAES algorithm to address multimodal optimization problems based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) framework. The Leaders and Followers (LaF) and Knowledge-based Perturbation (KbP) strategies are the primary components of the KbP-LaF-CMAES algorithm. The LaF strategy is utilized to extensively explore the potential local spaces, where two cooperative populations evolve in synergy. The KbP strategy is employed to enhance exploration capabilities. Improved variants of CMA-ES are used to exploit specific domains containing local optima, thereby potentially identifying the global optimum. Simulation results on the test suite demonstrate that KbP-LaF-CMAES significantly outperforms other meta-heuristic algorithms.

An efficient weighted slime mould algorithm for engineering optimization

In engineering applications, optimal parameter design is crucial. While Slime Mould Algorithm (SMA) excels in parameter discovery under constrained conditions, it faces challenges in achieving global convergence and avoiding local opsecttimal traps in complex tasks. This paper introduces an enhanced variant of SMA, termed CCHSMA, which integrates a Chaotic Local Search (CLS) mechanism to improve initial population diversity and combines Covariance Matrix Adaptation (CMA) and Harris Hawks Optimization (HHO) strategies to enhance global search efficiency. CCHSMA aims to improve search quality and reduce the likelihood of getting trapped in local optima. We evaluated CCHSMA's effectiveness by benchmarking it against the standard SMA and its variants using 30 CEC2017 test functions, and compared its performance with seven notable meta-heuristic algorithms and ten advanced swarm intelligence variants. The experimental results demonstrate that CCHSMA outperforms the other algorithms tested on the benchmark functions. To further validate its practical utility, CCHSMA's performance was also benchmarked against leading algorithms in real-world engineering applications. This paper uses detailed statistical methods, including the Wilcoxon signed-rank test and the Friedman test, to validate the comparative results. Our findings show that CCHSMA outperforms other algorithms in solving complex engineering optimization problems such as tension/compression spring design, pressure vessel design, and three-bar truss design, proving to be a robust tool for complex engineering optimization. Its enhanced initial population diversity and improved global search efficiency are essential for effectively addressing diverse engineering challenges.

Adapting the population size in CMA-ES using nearest-better clustering method for multimodal optimization

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the advanced algorithms for solving continuous single-objective optimization. In this algorithm, the population size is an important parameter which represents the number of candidate points generated in each iteration. A larger population size allows for better exploration of the search space and is typically required for handling multimodal functions, while a smaller population size facilitates quicker convergence. Adapting the population size in this algorithm raises a question about how to increase/decrease/keep it in an efficient way to solve specific problems. In this paper, we propose a novel approach for this purpose based on the information of niches observed during the evolution process. Firstly, the nearest-better clustering (NBC) technique is employed to detect the number of niches in each iteration, then the information will be used to adapt the population size accordingly. Additionally, a quasi-Newton method, which serves as a local search, can be incorporated into the algorithm in order to speed it up. We evaluate the effectiveness of our method through numerical simulations on multimodal test functions, the black-box optimization benchmarking (BBOB) noiseless testbed, and the CEC 2014 and CEC 2017 benchmark testing suites.

Far field reconstruction of antennas via single‐surface phaseless spherical near‐field scans: A novel approach based on dipole equivalence

AbstractA novel approach is proposed in this paper to reconstruct the far‐field radiation pattern from the phaseless electric field of an antenna scanned on a single near‐field sphere. It adopts the dipole equivalence approach to project the near‐field electric field into a spherically distributed array of electric dipoles. A term representing the error from the linearly correlated portion in the least‐square problem associated with the dipole equivalence, namely the linear correlation error, is introduced. It is demonstrated that by iterative search to minimize the linear correlation error using the covariance matrix adaptation evolution strategy, near‐field phase distributions can be found efficiently from the magnitude‐only near‐field, and the far‐field radiation pattern can be computed. Two representative case studies are given here to validate the proposed method. Results demonstrate good agreements between computations and simulations.

CMA-ES with Learning Rate Adaptation

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving continuous black-box optimization problems. A practically useful aspect of CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact on performance, especially for difficult tasks, such as solving multimodal or noisy problems. This study comprehensively explores the impact of learning rate on CMA-ES performance and demonstrates the necessity of a small learning rate by considering ordinary differential equations. Thereafter, it discusses the setting of an ideal learning rate. Based on these discussions, we develop a novel learning rate adaptation mechanism for CMA-ES that maintains a constant signal-to-noise ratio. Additionally, we investigate the behavior of CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments and compare the results with those obtained for CMA-ES with a fixed learning rate and with population size adaptation. The results show that CMA-ES with the proposed learning rate adaptation works well for multimodal and/or noisy problems without extremely expensive learning rate tuning.

Computationally optimized multi‐port antenna systems for WLAN/Wi‐Fi (IEEE 802.11a/h/j/n/ac/ax), 5G (mid‐band), and UWB applications

SummaryThis paper presents computationally optimized 2‐element and 4‐element Multiple‐Input, Multiple‐Output (MIMO) antennas for WLAN/Wi‐Fi, 5G, and UWB applications. The antenna configuration is constructed with the orthogonal placement of sawtooth‐shaped circular monopole radiating elements. The Particle Swarm Optimization (PSO) and Covariance Matrix Adaptation Evolution Strategy (CMA‐ES) optimization techniques are employed to achieve the best performance and size of the proposed antenna. Among these optimization techniques, CMA‐ES is identified as the better approach. The final optimized geometry of the 2‐element and 4‐element MIMO antennas is 49.40 mm × 24.22 mm and 49.44 mm × 45 mm, respectively. Both optimized antennas are fabricated and experimentally verified. The fractional bandwidth of the antenna is more than 110.3%, and more than −20 dB isolation is attained without employing any decoupling method. The Envelop Correlation Coefficient (ECC), Directivity Gain (DG), Total Active Reflection Coefficient (TARC), and Channel Capacity Limit (CCL) are 0.0001, 9.99, < −15 dB, and 0.1 bits/s/Hz, respectively. The proposed antenna is a good candidate for numerous current wireless applications due to its size and performance.

CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

Machine-learning approach for operating electron beam at KEK electron/positron injector linac

In current accelerators, numerous parameters and monitored values are to be adjusted and evaluated, respectively. In addition, fine adjustments are required to achieve the target performance. Therefore, the conventional accelerator-operation method, in which experts manually adjust the parameters, is reaching its limits. We are currently investigating the use of machine learning for accelerator tuning as an alternative to expert-based tuning. In recent years, machine-learning algorithms have progressed significantly in terms of speed, sensitivity, and application range. In addition, various libraries are available from different vendors and are relatively easy to use. Herein, we report the results of electron-beam tuning experiments using Bayesian optimization, a tree-structured Parzen estimator, and a covariance matrix-adaptation evolution strategy. Beam-tuning experiments are performed at the KEK e−/e+ injector Linac to maximize the electron-beam charge and reduce the energy-dispersion function. In each case, the performance achieved is comparable to that of a skilled expert. Published by the American Physical Society 2024

Proximal evolutionary strategy: improving deep reinforcement learning through evolutionary policy optimization

Evolutionary Algorithms (EAs), including Evolutionary Strategies (ES) and Genetic Algorithms (GAs), have been widely accepted as competitive alternatives to Policy Gradient techniques for Deep Reinforcement Learning (DRL). However, they remain eclipsed by cutting-edge DRL algorithms in terms of time efficiency, sample complexity, and learning effectiveness. In this paper, aiming at advancing evolutionary DRL research, we develop an evolutionary policy optimization algorithm with three key technical improvements. First, we design an efficient layer-wise strategy for training DNNs through Covariance Matrix Adaptation Evolutionary Strategies (CMA-ES) in a highly scalable manner. Second, we establish a surrogate model based on proximal performance lower bound for fitness evaluations with low sample complexity. Third, we embed a gradient-based local search technique within the evolutionary policy optimization process to further improve the learning effectiveness. The three technical innovations jointly forge a new EA for DRL method named Proximal Evolutionary Strategies (PES). Our experiments on ten continuous control problems show that PES with layer-wise training can be more computationally efficient than CMA-ES; our surrogate model can remarkably reduce the sample complexity of PES in comparison to latest EAs for DRL including CMA-ES, OpenAI-ES, and Uber-GA; PES with gradient-based local search can significantly outperform several promising DRL algorithms including TRPO, AKCTR, PPO, OpenAI-ES, and Uber-GA.

Meta-model structural monitoring with cutting-edge AAE-VMD fusion alongside optimized machine learning methods

Transfer learning significantly enhances machine learning by leveraging knowledge from one dataset to boost performance on another, which is particularly beneficial when labelled data ares limited or costly. Sensor fusion, an essential technique in structural health monitoring, improves the effectiveness of transfer learning by combining data from multiple sensors to extract more informative features. This article proposes a novel meta-model structural monitoring using a new data fusion method named the adversarial autoencoder (AAE)–variational mode decomposition (VMD) algorithm, which integrates optimization algorithms, transfer learning, and machine learning techniques for damage detection tasks. The proposed meta-model combines transfer learning with an optimized machine learning framework for training and employs pretrained models for testing across diverse datasets. First, the tensors are fused using the AAE approach into 300 data points, reducing noise and outliers, performing dimensionality reduction, and enriching the training and test datasets. Then, a preprocessing step involves decomposing and denoising tensors using the VMD algorithm, followed by selecting the most informative intrinsic mode functions (IMFs) based on their variance. These selected IMFs are concatenated, and 13 statistical features are extracted from them and used as inputs for machine learning models. Various optimization algorithms are employed to fine-tune the hyperparameters of the machine learning models for optimal classification results. Validation of this meta-model utilizes the dataset collected from a steel grandstand structure, available in benchmark dataset format. For decomposed fused tensors, both particle swarm optimization and covariance matrix adaptation evolution strategy emerge as equally effective optimization techniques for K-nearest neighbours (KNN), consistently achieving the highest mean test accuracy and F1 score of 99.5%. Conversely, KNN stands out as a robust and reliable classification algorithm for denoised fused tensors in transfer learning classification problems, consistently demonstrating perfect accuracy and an F1 score of 1.0 ± 0.0 across all optimization techniques.

Landscape Analysis for Surrogate Models in the Evolutionary Black-Box Context.

Surrogate modeling has become a valuable technique for black-box optimization tasks with expensive evaluation of the objective function. In this paper, we investigate the relationships between the predictive accuracy of surrogate models, their settings, and features of the black-box function landscape during evolutionary optimization by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) state-of-the-art optimizer for expensive continuous black-box tasks. This study aims to establish the foundation for specific rules and automated methods for selecting and tuning surrogate models by exploring relationships between landscape features and model errors, focusing on the behavior of a specific model within each generation in contrast to selecting a specific algorithm at the outset. We perform a feature analysis process, identifying a significant number of non-robust features and clustering similar landscape features, resulting in the selection of 14 features out of 384, varying with input data selection methods. Our analysis explores the error dependencies of four models across 39 settings, utilizing three methods for input data selection, drawn from surrogate-assisted CMA-ES runs on noiseless benchmarks within the Comparing Continuous Optimizers framework.

A New Student Performance Prediction Method Based on Belief Rule Base with Automated Construction

Student performance prediction (SPP) is a pivotal task in educational analytics, enabling proactive interventions and optimized resource allocation by educators. Traditional SPP models are often hindered by their complexity and lack of interpretability. This study introduces a novel SPP framework, the Belief Rule Base with automated construction (Auto–BRB), designed to address these issues. Firstly, reference values are derived through data mining techniques. The model employs an IF–THEN rule-based system integrated with evidential reasoning to ensure both transparency and interpretability. Secondly, parameter optimization is achieved using the Projected Covariance Matrix Adaptive Evolution Strategy (P–CMA–ES), significantly enhancing model accuracy. Moreover, the Akaike Information Criterion (AIC) is then applied to fine-tune the balance between model accuracy and complexity. Finally, case studies on SPP have shown that the Auto–BRB model has an advantage over traditional models in terms of accuracy, while maintaining good interpretability. Therefore, Auto–BRB has excellent application effects in educational data analysis.

Using Machine Learning Methods to Assess Module Performance Contribution in Modular Optimization Frameworks.

Modular algorithm frameworks not only allow for combinations never tested in manually selected algorithm portfolios, but they also provide a structured approach to assess which algorithmic ideas are crucial for the observed performance of algorithms. In this study, we propose a methodology for analyzing the impact of the different modules on the overall performance. We consider modular frameworks for two widely used families of derivative-free black-box optimization algorithms, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and differential evolution (DE). More specifically, we use performance data of 324 modCMA-ES and 576 modDE algorithm variants (with each variant corresponding to a specific configuration of modules) obtained on the 24 BBOB problems for 6 different runtime budgets in 2 dimensions. Our analysis of these data reveals that the impact of individual modules on overall algorithm performance varies significantly. Notably, among the examined modules, the elitism module in CMA-ES and the linear population size reduction module in DE exhibit the most significant impact on performance. Furthermore, our exploratory data analysis of problem landscape data suggests that the most relevant landscape features remain consistent regardless of the configuration of individual modules, but the influence that these features have on regression accuracy varies. In addition, we apply classifiers that exploit feature importance with respect to the trained models for performance prediction and performance data, to predict the modular configurations of CMA-ES and DE algorithm variants. The results show that the predicted configurations do not exhibit a statistically significant difference in performance compared to the true configurations, with the percentage varying depending on the setup (from 49.1% to 95.5% for mod-CMA and 21.7% to 77.1% for DE).

Deep Learning-Based Multifidelity Surrogate Modeling for High-Dimensional Reliability Prediction

Abstract Multifidelity surrogate modeling offers a cost-effective approach to reducing extensive evaluations of expensive physics-based simulations for reliability prediction. However, considering spatial uncertainties in multifidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multifidelity surrogate modeling approach that fuses multifidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network (ConvDR) is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low-dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy (CMA-ES) to encourage an unbiased linear pattern in the latent space for reliability prediction. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process (GP) regression. Finally, Monte Carlo simulation (MCS) is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.

Ship Autonomous Berthing Strategy Based on Improved Linear-Quadratic Regulator

There has been significant interest in the research field of ship automatic navigation, particularly in the area of autonomous berthing. To address the key challenges of path planning and control during ship berthing, we propose an enhanced Linear−Quadratic Regulator (LQR) control approach, reinforced by the Covariance Matrix Adaptation Evolution Strategy (CMA−ES), along with an adaptive berthing strategy decision model. This integrated framework encompasses ship motion control, path planning, and berthing strategy selection to facilitate adaptive and autonomous ship berthing. Initially, a dynamic mathematical model of ship motion is established, taking into account wind and current interference effects. Subsequently, an adaptive environment−aware berthing strategy model is introduced to enable automatic selection of berthing strategies based on spatial relationships between environmental factors and the berth. By utilizing the refined LQR method, autonomous motion control for ship berthing is achieved. To validate the effectiveness of our controller, comprehensive simulation analyses are conducted under varying operating conditions to encompass crucial factors such as large drift angle characteristics of ships, shallow water effects, and bank effects across seven diverse working conditions. The simulation results underscore the robustness of our proposed method in responding to environmental interference while demonstrating its capability to select appropriate berthing strategies based on varying operational scenarios.

Solving dynamic multimodal optimization problems via a niching-based brain storm optimization with two archives algorithm

Dynamic and multimodal properties are simultaneously possessed in the dynamic multimodal optimization problems (DMMOPs), which aim to find multiple optimal solutions in a dynamic environment. However, more work still needs to be devoted to solving DMMOPs, which still require significant attention. A niching-based brain storm optimization with two archives (NBSO2A) algorithm is proposed to solve DMMOPs. The two niching methods, i.e., neighborhood-based speciation (NS), and nearest-better clustering (NBC), are incorporated into a BSO algorithm to generate new solutions. The two archives preserve the optimal solutions that meet the requirements and practical, inferior solutions discarded during the generation. Improved taboo area (ITA) removes highly similar individuals from the population. An evolution strategy with covariance matrix adaptation (CMA-ES) is adopted to enhance the local search ability and improve the quality of the solutions. The NBSO2A algorithm and four other algorithms were tested on 12 benchmark problems to validate the performance of the NBSO2A algorithm on DMMOPs. The experimental results show that the NBSO2A algorithm outperforms the other compared algorithms on most tested benchmark problems.

Combinatorial study of coherent multi-channel phase-locking based on covariance matrix adaptation evolution strategy

Combinatorial study of coherent multi-channel phase-locking based on covariance matrix adaptation evolution strategy

An optimal operation strategy of wind farm for frequency regulation reserve considering wake effects

When wind farms (WFs) participate in power system frequency regulation, deloaded control can increase the stored rotational kinetic energy in the wind turbines (WTs), thereby enhancing their frequency support capability. However, due to the wake effects and deloaded control of turbines, this method can also lead to increased power losses. An optimal operation strategy has been proposed to balance power generation and frequency regulation reserve in WFs, taking wake effects into account. Initially, a WF deloaded control model that considers wake effects, and an adaptive combined frequency control model based on kinetic energy reserve, are established for participation in power system frequency regulation. Subsequently, the Covariance Matrix Adaptation Evolution Strategy (CMAES) is utilized to determine the optimal operation allocation of maximum WF output power within the FLORIS wake model, meeting frequency regulation reserve requirements. A comparative analysis of the optimal allocation results under various wind conditions is conducted to test the frequency support capabilities. The results indicate that the proposed strategy can achieve varying levels of frequency regulation reserve, reduce wake losses to maximize output power under deloaded control, and improve frequency support capability.