Using Evolution Strategy with Meta-models for Well Placement Optimization

Variable metric evolution strategies by mutation matrix adaptation

Randomized direct search algorithms for continuous domains, such as evolution strategies, are basic tools in machine learning. They are especially needed when the gradient of an objective function (e.g., loss, energy, or reward function) cannot be computed or estimated efficiently. Application areas include supervised and reinforcement learning as well as model selection. These randomized search strategies often rely on normally distributed additive variations of candidate solutions. In order to efficiently search in non-separable and ill-conditioned landscapes the covariance matrix of the normal distribution must be adapted, amounting to a variable metric method. Consequently, covariance matrix adaptation (CMA) is considered state-of-the-art in evolution strategies. In order to sample the normal distribution, the adapted covariance matrix needs to be decomposed, requiring in general Θ(n 3) operations, where n is the search space dimension. We propose a new update mechanism which can replace a rank-one covariance matrix update and the computationally expensive decomposition of the covariance matrix. The newly developed update rule reduces the computational complexity of the rank-one covariance matrix adaptation to Θ(n 2) without resorting to outdated distributions. We derive new versions of the elitist covariance matrix adaptation evolution strategy (CMA-ES) and the multi-objective CMA-ES. These algorithms are equivalent to the original procedures except that the update step for the variable metric distribution scales better in the problem dimension. We also introduce a simplified variant of the non-elitist CMA-ES with the incremental covariance matrix update and investigate its performance. Apart from the reduced time-complexity of the distribution update, the algebraic computations involved in all new algorithms are simpler compared to the original versions. The new update rule improves the performance of the CMA-ES for large scale machine learning problems in which the objective function can be evaluated fast.

Comparing the performance of a nested to a continuous evolution strategy with covariance matrix adaption for optimization of drilling EDM

Application of evolutionary algorithms to optimise one- and two-dimensional gradient chromatographic separations.

Many high-performance ultra-wideband array topologies have recently arisen that utilize mathematical constructs such as fractals or simple mathematical expressions to determine element locations [1] – [2]. The main motivation of these methods is to reduce the scale of the optimization problem such that it is feasible for the evolutionary strategy. In this manner, large arrays can be successfully optimized with a reasonably small set of controlling parameters. However, for an array with a small number of elements, these methods can be constraining and lead to less than acceptable peak sidelobe level performances and poor bandwidths. For these small arrays, the element locations can be directly specified with the optimization tool if it is capable of handling the large parameter set. Previous attempts using the genetic algorithm (GA) [3] with array sizes of eight to 24 elements and large scan angles (analogous to a small bandwidth) were preformed in [4]. With a more powerful evolutionary strategy, problems with large parameter sets become much more practical and yield better results. The covariance matrix adaptation evolutionary strategy (CMA-ES) is a recently developed and extremely powerful optimization tool that has shown itself to be a leader in speed and possesses an excellent capacity for handling problems of large dimensions [5]. It is applied here to the direct optimization of element spacings for relatively small to moderate size ultrawideband antenna arrays in order to extract the best performance possible from a limited number of antenna elements.

First, the covariance matrix adaptation (CMA) with rank-one update is introduced into the (1+1)-evolution strategy. An improved implementation of the 1/5-th success rule is proposed for step size adaptation, which replaces cumulative path length control. Second, an incremental Cholesky update for the covariance matrix is developed replacing the computational demanding and numerically involved decomposition of the covariance matrix. The Cholesky update can replace the decomposition only for the update without evolution path and reduces the computational effort from O(n3) to O(n2). The resulting (1+1)-Cholesky-CMA-ES is an elegant algorithm and the perhaps simplest evolution strategy with covariance matrix and step size adaptation. Simulations compare the introduced algorithms to previously published CMA versions.

Covariance Matrix Adaptation - Evolutionary Strategy (CMA-ES) is a black-box optimization method useful for applications where no direct inversion is possible. We present the development of a parallel CMA-ES algorithm that reduces the runtime for a specific geophysical data analysis, dipole localization. We compare our parallel algorithm against several other parallel CMA-ES variants on a sample dataset for dipole localization. We improve the performance of CMA-ES for the problem of finding dipoles in a subsurface environment as part of a closed-loop near-real-time wireless bioremediation system, REACTS (near-REal-time Autonomous bioremediation of ConTamination in the Subsurface). The goal of the performance improvement is to enable near-real-time analysis of geophysical data. For this application, our algorithm shows significant performance improvement over the other variants.

A robust atlas-to-subject registration using a statistical deformation model (SDM) is presented. The SDM uses statistics of voxel-wise displacement learned from pre-computed deformation vectors of a training dataset. This allows an atlas instance to be directly translated into an intensity volume and compared with a patient’s intensity volume. Rigid and nonrigid transformation parameters were simultaneously optimized via the Covariance Matrix Adaptation – Evolutionary Strategy (CMA-ES), with image similarity used as the objective function. The algorithm was tested on CT volumes of the pelvis from 55 female subjects. A performance comparison of the CMA-ES and Nelder-Mead downhill simplex optimization algorithms with the mutual information and normalized cross correlation similarity metrics was conducted. Simulation studies using synthetic subjects were performed, as well as leave-one-out cross validation studies. Both studies suggested that mutual information and CMA-ES achieved the best performance. The leave-one-out test demonstrated 4.13 mm error with respect to the true displacement field, and 26,102 function evaluations in 180 seconds, on average.

The covariance matrix adaptation evolutionary strategy (CMA-ES) is explored here as an improved alternative to well-established algorithms used in electromagnetic (EM) optimization. In the past, methods such as the genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE) have commonly been used for EM design. In this article, we examine and compare the performance of CMA-ES, PSO, and DE when applied to test functions and several challenging EM design problems. Of particular interest is demonstrating the ability of the relatively new CMA-ES to more quickly and more reliably find acceptable solutions compared with those of the more classical optimization strategies. In addition, it will be shown that due to its self-adaptive scheme, CMA-ES is a more user-friendly algorithm that requires less knowledge of the problem for preoptimization configuration.

ReaxFF is a computationally efficient force field to simulate complex reactive dynamics in extended molecular models with diverse chemistries, if reliable force-field parameters are available for the chemistry of interest. If not, they must be optimized by minimizing the error ReaxFF makes on a relevant training set. Because this optimization is far from trivial, many methods, in particular genetic algorithms (GAs), have been developed to search for the global optimum in parameter space. Recently, two alternative parameter calibration techniques were proposed, i.e. Monte-Carlo Force Field optimizer (MCFF) and Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). In this work, CMA-ES, MCFF and a GA method (OGOLEM) are systematically compared using three training sets from the literature. GA shows the smallest risk of getting trapped into a local minimum, whereas CMA-ES is capable of reaching the lowest errors for two third of the cases. For each method, we provide reasonable default settings and our analysis offers useful guidelines for their usage in future work. An important side effect impairing the parameter optimization is numerical noise. A detailed analysis reveals that it can be reduced, e.g. by using exclusively unambiguous geometry optimizations in the training set. Even without this noise, many distinct near-optimal parameter vectors can be found, which opens new avenues for improving the training set and detecting overfitting artifacts.

Car classification, using different machine learning models with optimization frameworks, is done for evaluation in this work. We used different models, namely, Extra Trees, XGBoost, Gaussian Naive Bayes, K-Nearest Neighbors, Histogram-based Gradient Boosting (Hist Gradient Boosting), and Linear Discriminant Analysis, for classification. The car samples are classified as “very good,” “good,” “acceptable,” and “unacceptable.” Among these, Hist Gradient Boosting has the highest value for precision, accuracy, recall, and F1 score. We further tuned this model using Evolutionary Strategies, Evolutionary Programming, Covariance Matrix Adaptation Evolution Strategy, and the Flower Pollination Algorithm. Our outcomes indicate that the Covariance Matrix Adaptation Evolution Strategy and Flower Pollination Algorithm significantly enhanced the performance of the model and outperformed Evolutionary Programming. This work investigates the potential of integrating advanced machine learning models with sophisticated optimization strategies to deliver an effective car evaluation classification process that will be useful in this industry and, perhaps, in many other classification tasks.

An ultrafast pulse shaper for coherent control applications is described, complete with a simple, reliable calibration technique and an advanced learning control algorithm. The calibration technique makes use of a common-path interferometer, producing less noisy measurements than a conventional Mach-Zehnder interferometer. A covariance matrix adaptation evolutionary strategy (ES) is demonstrated to perform better than a traditional ES for high-dimensional search landscapes.

Monte Carlo Tree Search (MCTS) is a novel machine learning paradigm that is used to find good solutions for complex optimization problems with very large search spaces (like playing GO). We combine MCTS with Covariance Matrix Adaptation Evolution Strategies (CMA-ES) to efficiently optimize real-parameter single objective problems by balancing the exploitation of promising areas with the exploration of new regions of the search space. The novel algorithm is called hierarchical CMA-ES and it is influenced by both machine learning and evolutionary computation research areas. Like in evolutionary computation, we use a population of individuals to explore the commonalities of CMA-ES solvers. These CMA-ES solvers are structured using a MCTS tree like structure. Our experiments compare the performance of hierarchical CMA-ES solvers with two other algorithms: the standard CMA-ES optimizer, and an adaptation of MCTS to solve real-parameter problems. The hierarchical CMA-ES optimizer has the best empirical performance on several benchmark problems.

This paper presents an extended variant of the distance-weighted exponential natural evolution strategy (DXNES) that works well in uncertain environments. Since we often face objective functions with uncertain parameters in real-world problems, function optimization in uncertain environments is an important problem. The covariance matrix adaptation evolution strategy (CMA-ES) and DX-NES have been proposed as promising methods for function optimization in deterministic environments. The performance of these methods, however, deteriorates in uncertain environments. The uncertain handling CMA-ES (TIH-CMA-ES) has been proposed as an extended variant of CMA-ES for uncertain environments and has shown relatively good performance on problems with uncertain parameters. In this paper, we propose an extended variant of DX-NES named DX-NES for uncertain environments (DX-NES-TIE). DX-NES-TIE approximates the objective function by a quadratic function. DXNES-TIE uses approximation function values for updating the mutation distribution if the noise is strong; otherwise it uses observed objective function values. The strength of the noise is quantified by using the approximation function and the evolution path. Through numerical experiments on 20-dimensional uncertain benchmark problems, we demonstrate that DX-NES-TIE can find ten to 2,000 times as accurate solutions as TIH-CMA-ES can. We also apply DX-NES-TIE to 80-dimensional problems and confirm that DX-NES-TIE is scalable with respect to problem dimensionality.

Multi types DG expansion dynamic planning in distribution system under stochastic conditions using Covariance Matrix Adaptation Evolutionary Strategy and Monte-Carlo simulation