Derivative-free Optimization Methods Research Articles

Anomaly detection for data accountability of Mars telemetry data

The Mars Curiosity rover is frequently sending engineering and science data that goes through a pipeline of systems before reaching its final destination at the mission operations center making it prone to volume loss and data corruption. A ground data system analysis (GDSA) team is charged with the monitoring of this flow of information and the detection of anomalies in that data to request a re-transmission when necessary. So far, this task relied primarily on the expertise of GDSA analysts who, especially with new missions launching, require the assistance of an autonomous and effective detection tool. Variational autoencoders are powerful deep neural networks that can learn to isolate such anomalies yet, as any deep network, they require an architectural search and fine-tuning to yield exploitable performance. Furthermore, this process needs to be repeated periodically to adjust to the changing flow of transmissions. This work presents Δ-MADS, a hybrid derivative-free optimization method designed to quickly produce efficient variational autoencoders in order to assist the GDSA team in their mission.

Distributed quasi-Newton derivative-free optimization method for optimization problems with multiple local optima

Distributed quasi-Newton derivative-free optimization method for optimization problems with multiple local optima

Derivative-free optimization adversarial attacks for graph convolutional networks.

In recent years, graph convolutional networks (GCNs) have emerged rapidly due to their excellent performance in graph data processing. However, recent researches show that GCNs are vulnerable to adversarial attacks. An attacker can maliciously modify edges or nodes of the graph to mislead the model’s classification of the target nodes, or even cause a degradation of the model’s overall classification performance. In this paper, we first propose a black-box adversarial attack framework based on derivative-free optimization (DFO) to generate graph adversarial examples without using gradient and apply advanced DFO algorithms conveniently. Second, we implement a direct attack algorithm (DFDA) using the Nevergrad library based on the framework. Additionally, we overcome the problem of large search space by redesigning the perturbation vector using constraint size. Finally, we conducted a series of experiments on different datasets and parameters. The results show that DFDA outperforms Nettack in most cases, and it can achieve an average attack success rate of more than 95% on the Cora dataset when perturbing at most eight edges. This demonstrates that our framework can fully exploit the potential of DFO methods in node classification adversarial attacks.

Investigating the Generalization Ability of Parameterized Quantum Circuits with Hierarchical Structures

Quantum computing provides prospects for improving machine learning, which are mainly achieved through two aspects, one is to accelerate the calculation, and the other is to improve the performance of the model. As an important feature of machine learning models, generalization ability characterizes models' ability to predict unknown data. Aiming at the question of whether the quantum machine learning model provides reliable generalization ability, quantum circuits with hierarchical structures are explored to classify classical data as well as quantum state data. We also compare three different derivative-free optimization methods, i.e., Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Constrained Optimization by Linear Approximation (COBYLA) and Powell. Numerical results show that these quantum circuits have good performance in terms of trainability and generalization ability.

Black box operation optimization of basic oxygen furnace steelmaking process with derivative free optimization algorithm

Mastering the smelting status and making the material adding strategy are important and challenging issue in the basic oxygen furnace (BOF) steelmaking process. Unfortunately, complex physicochemical reaction with multi-input and multi-output makes the first-principles models unusable. To this end, a black box operation optimization (BBOO) problem integrated black box data analytics modeling and optimization is abstracted from the BOF steelmaking process. Moreover, a derivative free optimization (DFO) method based on the trust region framework is developed to solve the operation optimization problem. In the proposed algorithm, we integrate quadratic interpolation and sparse modeling to construct the surrogate model. Wherein, l0-norm optimization, which is solved through converting it into a convex optimization problem with introducing the slack variables, is used to determine the sparse surrogate model. Finally, we apply the proposed DFO algorithm and other DFO algorithms to solve the BBOO problem in BOF steelmaking process. The results demonstrate that the proposed method can be an alternative for providing solutions and insights of material addition in BOF process and the proposed algorithm is comparable.

Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

A novel derivative-free algorithm, called optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to accelerate convergence of model-based optimization strategies. The dimension-reducing subspace is updated as the trust region moves through the function domain, allowing OMoRF to be applied to functions with no known global low-dimensional structure. Furthermore, its low computational requirement allows it to make rapid progress when optimizing high-dimensional functions. Its performance is examined on a set of test problems of moderate to high dimension and a high-dimensional design optimization problem. The results show that OMoRF compares favourably with other common derivative-free optimization methods, even for functions in which no underlying global low-dimensional structure is known.

Population-Based Parameter Identification for Dynamical Models of Biological Networks with an Application to Saccharomyces cerevisiae

One of the central elements in systems biology is the interaction between mathematical modeling and measured quantities. Typically, biological phenomena are represented as dynamical systems, and they are further analyzed and comprehended by identifying model parameters using experimental data. However, all model parameters cannot be found by gradient-based optimization methods by fitting the model to the experimental data due to the non-differentiable character of the problem. Here, we present POPI4SB, a Python-based framework for population-based parameter identification of dynamic models in systems biology. The code is built on top of PySCeS that provides an engine to run dynamic simulations. The idea behind the methodology is to provide a set of derivative-free optimization methods that utilize a population of candidate solutions to find a better solution iteratively. Additionally, we propose two surrogate-assisted population-based methods, namely, a combination of a k-nearest-neighbor regressor with the Reversible Differential Evolution and the Evolution of Distribution Algorithm, that speeds up convergence. We present the optimization framework on the example of the well-studied glycolytic pathway in Saccharomyces cerevisiae.

An inverse bilevel equilibrium problem for public transport demand estimation

We consider the problem of demand estimation for public transport networks. Given an origin-destination matrix representing the public transport demand, the distribution of flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by an optimization problem. The knowledge of the origin-destination matrix is expensive and sometimes unaffordable in practice. Traditionally, it is estimated using statistical or econometrical considerations. In this work, we explore the estimation through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions, therefore we proposed a derivative-free method for the resolution of the optimization problem. The method is firstly tested on small networks using a derivative-free optimization method and then, using an approach based on simulation. This simulation-optimization methodology showed as good results as analytical modeling, opening the door to handle bigger networks where analytical computation is hard to accomplish.

Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

Global Bayesian optimization (GBO) is a derivative-free optimization method that is used widely in the tech-industry to optimize objective functions that are expensive to evaluate, numerically or otherwise. We discuss the use of GBO in ensemble data assimilation (DA), where the goal is to update the state of a numerical model in view of noisy observations. Specifically, we consider three tasks: (i) the estimation of model parameters; (ii) the tuning of localization and inflation in ensemble DA; (iii) doing both, i.e. estimating model parameters while simultaneously tuning the localization and inflation of the ensemble DA. For all three tasks, the GBO works ‘offline’, i.e. a set of ‘training’ observations are used within GBO to determine appropriate model or localization/inflation parameters, which are subsequently deployed within an ensemble DA system. Because of the offline nature of the technique, GBO can easily be combined with existing DA systems and it can effectively decouple (nearly) linear/Gaussian aspects of a problem from highly nonlinear/non-Gaussian ones. We illustrate the use of GBO in simple numerical experiments with the classical Lorenz problems. Our main goals are to introduce GBO in the context of ensemble DA and to spark an interest in GBO and its uses for streamlining important tasks in ensemble DA.

$l_p$ Regularization for Ensemble Kalman Inversion

Ensemble Kalman inversion (EKI) is a derivative-free optimization method that lies between the deterministic and probabilistic approaches for inverse problems. EKI iterates the Kalman update of ens...

Wavelength Tunable Matched-Pair Vernier Multi-Ring Filters Using Derivative-Free Optimization Algorithms

We demonstrate matched pairs of multi-ring Vernier filters that mutually suppress the out-of-band resonances resulting from the Vernier effect to increase the free-spectral range (FSR) while achieving high out-of-band extinction ratio. These filters can be aligned to any center wavelength within the Vernier FSR. Both the design methodology and alignment procedure rely on derivative-free optimization methods. We report on an O-band silicon microring optical filter achieving out-of-band extinction of -52 dB over an FSR >100 nm.

A Derivative-Free Optimization Method With Application to Functions With Exploding and Vanishing Gradients

In this letter, we propose a bio-inspired derivative-free optimization algorithm capable of minimizing objective functions with vanishing or exploding gradients. The proposed method searches for improvements by leveraging a PCA-based strategy similar to fish foraging. The strategy does not require explicit gradient computation or estimation and is shown in simulation to require few function evaluations. Additionally, our analysis proves that the proposed algorithm’s search direction converges to the gradient direction everywhere outside of small neighborhoods around local minima. Applications to a data-driven LQR problem and noisy Rosenbrock optimization problem are demonstrated. Empirical results show the proposed method exhibits fast convergence and is able to find the LQR gains for any controllable system, including unstable systems, and is robust to noisy function evaluations.

A novel three-dimensional surface reconstruction method for the complex fabrics based on the MVS

To solve the existing problems occurring in the field of digital fabric appearance analysis, such as information loss, visual expression difficulty and low accuracy, a novel three-dimensional (3-D) surface reconstruction method based on the multi-view stereo (MVS) technology was proposed for the appearance evaluation of complex fabrics in this paper. Initially, the fabric images were captured by the self-developed multiple image acquisition system. Subsequently, the dense point cloud of fabric surface could be obtained by the operations of feature point detection and matching, camera intrinsic and extrinsic parameter calculation, image pre-processing, sparse point cloud generation, patch expansion and patch filtering. For the sake of acquiring the high accuracy and great completeness of dense point cloud, planar patches with different scales were used to fit the fabric surface, the normalized cross correlation (NCC) algorithm was adopted to improve the accuracy of photo-consistency measurement, and besides, a derivative-free particle swarm optimization (PSO) method was applied to obtain the optimal patches. Our experimental results show that the fabric surface model could be reconstructed by this method accurately, which can be used to characterize the surface texture and 3D weaving profile of woven fabrics. The reconstructed 3D fabric surface model with high precision can be used not only for three-dimensional illustration or rendering but also for structural analysis, quality evaluation of fabric appearance and etc., it provides a useful solution for artificial intelligence production in the textile industry.

ОПТИМАЛЬНОЕ ПРОЕКТИРОВАНИЕ БЕЗРЕДУКТОРНОЙ МАШИНЫ С ПЕРЕКЛЮЧЕНИЕМ ПОТОКА ДЛЯ ВЕТРОГЕНЕРАТОРА

Актуальность исследования обусловлена возрастающей потребностью применения автономных гибридных электростанций, использующих возобновляемые источники с целью уменьшения потребления органического топлива. Улучшение рабочих свойств и уменьшение стоимости безредукторных ветрогенераторов, применяемых в составе таких электростанций, способствует улучшению их технико-экономических характеристик. Цель: поиск эффективного подхода для оптимизации генератора с переключением потока для безредуктороной ветроустановки, позволяющего сократить применение вычислительных ресурсов, в сравнение с существующими подходами; выработка рекомендаций к проектированию ветрогенератора с переключением потока с постоянными магнитами на статоре; улучшение характеристик конструкции генератора, спроектированной ранее. Объекты: математическая модель и конструкция генератора с переключением потока с магнитами на статоре, математическая модель безредуктороной ветротурбины. Методы: безградиентный метод оптимизации, математическое моделирование, двухмерный метод конечных элементов, оценка и анализ скорости ветра в различных мировых регионах, статистические методы. Результаты. Произведена многокритериальная оптимизация конструкции безредуктороного ветрогенератора с переключением потока. В результате были улучшены энергетические характеристики генератора, снижены пульсации момента, а также снижена номинальная мощность электронного преобразователя ветроустановки. Получены общие рекомендации, относительно геометрии конструкции, которые могут быть использованы при проектировании таких генераторов. Предложен метод расчета замещающих профилей для характеристики цикла работы ветротурбины, которой может быть использован для снижения вычислительных затрат в процессе оптимизации ветрогенераторов. Показано сокращение вычислительных затрат с помощью полученного метода на примере замены исходной девятиточечной характеристики цикла работы ветротурбины на замещающий двухточечный профиль.

Derivative-free parameter tuning for a well multiphase flow simulator

The analysis of multiphase flow from wells is periodically performed in test separators, producing data on fluid and reservoir properties such as the gas–oil ratio, water cut, pressure, and temperature measurements from sensors. Such data enables the tuning of multiphase flow simulators to reflect the prevailing conditions of reservoir and production processes. Besides meeting demands from the regulatory agency, a well-adjusted model empowers engineers to plan production and derive representative models for production optimization. This work proposes the use of derivative-free optimization methods for tuning an in-house multiphase flow simulator widely used by Petrobras. The tuning algorithm was coupled to the simulation software to free engineers from lengthy analyses, allowing the timely update of processes that are key in decision making and production optimization.

A Stochastic Derivative-Free Optimization Method with Importance Sampling: Theory and Learning to Control

We consider the problem of unconstrained minimization of a smooth objective function in ℝn in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine learning practitioners to accelerate the convergence of their models when applicable, there is not much existing theory for this acceleration in the derivative-free setting. In this paper, we propose the first derivative free optimization method with importance sampling and derive new improved complexity results on non-convex, convex and strongly convex functions. We conduct extensive experiments on various synthetic and real LIBSVM datasets confirming our theoretical results. We test our method on a collection of continuous control tasks on MuJoCo environments with varying difficulty. Experiments show that our algorithm is practical for high dimensional continuous control problems where importance sampling results in a significant sample complexity improvement.

Multilevel Strategies Improve History Matching of Complex Reservoir Models

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193895, “Multilevel Strategies and Geological Parameterizations for History Matching Complex Reservoir Models,” by Yimin Liu, SPE, and Louis J. Durlofsky, SPE, Stanford University, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, 10–11 April. The paper has not been peer reviewed. The complete paper explores the use of multilevel derivative-free optimization for history matching, with model properties described using principal component analysis (PCA) -based parameterization techniques. The parameterizations applied are optimization-based PCA (O-PCA) and convolutional-neural-network-based PCA (CNN-PCA). Mesh adaptive direct search (MADS), a pattern search method that parallelizes naturally, is used for the optimizations required to generate posterior models. The use of PCA-based parameterization reduces considerably the number of variables that must be determined during history matching, but the optimization problem can still be computationally demanding. The multilevel strategy addresses this issue by reducing the number of simulations that must be performed at each MADS iteration. History-matching results demonstrate that substantial uncertainty reduction is achieved in all cases considered and that the multilevel strategy is effective in reducing the number of simulations required. Overview Parameterization has two key advantages in history matching: Far fewer parameters must be determined, which simplifies greatly the minimization in some cases. Posterior (history-matched) geomodels will be consistent with the geological scenario or training image for which the parameterization was constructed. PCA is the foundation for many geological-dimension-reduction parameterization methods. PCA is based on the eigen-decomposition of the prior geomodel covariance matrix and, thus, honors only two-point spatial statistics. History-matching algorithms largely can be classified as either optimization-based or ensemble-based procedures. Optimization-based algorithms generate one history-matched model at a time, while ensemble-based algorithms update a large set of models simultaneously. The resulting ensemble of posterior models is used to quantify uncertainty. In this study, only optimization-based history matching is considered, though the parameterizations applied also can be used with ensemble-based methods. Optimization-based history-matching algorithms can be classified further into gradient-based and derivative-free optimization (DFO) methods. Gradient-based algorithms often are combined with adjoint procedures that provide the required gradient efficiently. Unlike adjoint-based procedures, DFO algorithms (which are considered in this work) are nonintrusive. They treat the reservoir simulator as a so-called “black box,” and, as a result, they are much easier to implement and can be applied with any simulator. In this study, MADS, a pattern-search DFO, is applied for history matching. In pattern-search (or stencil-based) algorithms, the number of simulations required at each iteration scales with the number of parameters to be determined. Because the latter typically is much smaller than the number of grid-blocks in the model, geological parameterization leads to large computational savings when a pattern search, or other DFO, is used for history matching. The performance of DFO for history matching with non-Gaussian models, a primary topic in the complete paper, has not been studied extensively. The authors devise a multilevel strategy, applicable for PCA-based parameterization methods, to further reduce the computational cost of history matching using DFO. A multilevel strategy lends itself naturally to PCA-based parameterizations because the PCA representation can be ordered from the most-important to the least-important principal component. Thus, PCA parameters can be determined sequentially, level by level, in groups, rather than all at once.

Inference of the two-parameter Lindley distribution based on progressive type II censored data with random removals

In many practical problems relate to progressively Type-II censored sampling plans, not only an experiment process determines inevitably to use random removals but also a fixed removals assumption may be cumbersome to analyze some results of statistical inference. This paper investigates the estimation problem when lifetimes are the two-parameter Lindley distributed and are collected under two removal patterns based on the uniform discrete distribution and the binomial distribution. The maximum likelihood estimations (MLEs) of parameters are obtained by a derivative-free optimization method and without applying the logarithm of the likelihood function. Furthermore, we propose a method for starting values of optimization to obtain the MLEs and compare numerically their bias, variance, covariance and mean squared error under the two different removal plans. Then, the expected times are discussed and compared numerically under the two approaches of generating random removals. Finally, the optimal progressive Type-II censoring scheme is provided based on the measure of the smallest expected experiment time.

Multilevel Strategies and Geological Parameterizations for History Matching Complex Reservoir Models

Summary In this study, we explore using multilevel derivative-free optimization (DFO) for history matching, with model properties described using principal-component-analysis (PCA) -based parameterization techniques. The parameterizations applied in this work are optimization-based PCA (O-PCA) and convolutional-neural-network (CNN) -based PCA (CNN-PCA). The latter, which derives from recent developments in deep learning, is able to accurately represent models characterized by multipoint spatial statistics. Mesh adaptive direct search (MADS), a pattern-search method that parallelizes naturally, is applied for the optimizations required to generate posterior (history-matched) models. The use of PCA-based parameterization considerably reduces the number of variables that must be determined during history matching (because the dimension of the parameterization is much smaller than the number of gridblocks in the model), but the optimization problem can still be computationally demanding. The multilevel strategy introduced here addresses this issue by reducing the number of simulations that must be performed at each MADS iteration. Specifically, the PCA coefficients (which are the optimization variables after parameterization) are determined in groups, at multiple levels, rather than all at once. Numerical results are presented for 2D cases, involving channelized systems (with binary and bimodal permeability distributions) and a deltaic-fan system using O-PCA and CNN-PCA parameterizations. O-PCA is effective when sufficient conditioning (hard) data are available, but it can lead to geomodels that are inconsistent with the training image when these data are scarce or nonexistent. CNN-PCA, by contrast, can provide accurate geomodels that contain realistic features even in the absence of hard data. History-matching results demonstrate that substantial uncertainty reduction is achieved in all cases considered, and that the multilevel strategy is effective in reducing the number of simulations required. It is important to note that the parameterizations discussed here can be used with a wide range of history-matching procedures (including ensemble methods), and that other derivative-free optimization methods can be readily applied within the multilevel framework.

Well posedness and convergence analysis of the ensemble Kalman inversion

The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various areas of application. We present a complete analysis of the ensemble Kalman inversion with perturbed observations for a fixed ensemble size when applied to linear inverse problems. The well-posedness and convergence results are based on the continuous time scaling limits of the method. The resulting coupled system of stochastic differential equations allows one to derive estimates on the long-time behaviour and provides insights into the convergence properties of the ensemble Kalman inversion. We view the method as a derivative free optimization method for the least-squares misfit functional, which opens up the perspective to use the method in various areas of applications such as imaging, groundwater flow problems, biological problems as well as in the context of the training of neural networks.