One method to solve expensive black-box optimization problems is to use a surrogate model that approximates the objective based on previous observed evaluations. The surrogate, which is cheaper to evaluate, is optimized instead to find an approximate solution to the original problem. In the case of discrete problems, recent research has revolved around surrogate models that are specifically constructed to deal with discrete structures. A main motivation is that literature considers continuous methods, such as Bayesian optimization with Gaussian processes as the surrogate, to be sub-optimal (especially in higher dimensions) because they ignore the discrete structure by, e.g., rounding off real-valued solutions to integers. However, we claim that this is not true. In fact, we present empirical evidence showing that the use of continuous surrogate models displays competitive performance on a set of high-dimensional discrete benchmark problems, including a real-life application, against state-of-the-art discrete surrogate-based methods. Our experiments on different discrete structures and time constraints also give more insight into which algorithms work well on which type of problem.
Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian i…
The cross-entropy (CE) method is a popular stochastic method for optimization due to its simplicity and effectiveness. Designed for rare-event simulations where the probability of a target event occurring is relatively small, the CE-method relies on enough objective function calls to accurately estimate the optimal parameters of the underlying distribution. Certain objective functions may be computationally expensive to evaluate, and the CE-method could potentially get stuck in local minima. This is compounded with the need to have an initial covariance wide enough to cover the design space of…
Johns Hopkins University（约翰斯·霍普金斯大学）；Idaho National Laboratory（爱达荷国家实验室）
Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. This paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework …
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adaptively construct training designs by maximizing the expected improvement in fit of the Gaussian process model to the noisy observational data. Numerical experiments on model problems with synthetic data demonstrate the effectiveness of the obtained adaptive designs compared to the…
Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate models are used to accelerate studies. Deep learning has been used in past to generate surrogates, but such models often fail to quantify prediction uncertainty and are not interpretable. In this work, beta-VAE based regression is proposed to generate simulation surrogates for use in optimization workflow. beta-VAE enables interpretable, factorized representatio…
Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA（航空航天工程学院，佐治亚理工学院，亚特兰大，GA）；School of Computational Science & Engineering, Georgia Institute of Technology, Atlanta, GA（计算科学与工程学院，佐治亚理工学院，亚特兰大，GA）；Air Force Research Lab, Wright-Patterson AFB, Dayton, Ohio（空军研究实验室，威格伍德-帕特森空军基地，代顿，俄亥俄）
Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks
College of Engineering and Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；The Ohio State University（俄亥俄州立大学）；Singapore University of Technology and Design（新加坡科技设计大学）
MATSuMoTo is the MATLAB Surrogate Model Toolbox for computationally expensive, black-box, global optimization problems that may have continuous, mixed-integer, or pure integer variables. Due to the black-box nature of the objective function, derivatives are not available. Hence, surrogate models are used as computationally cheap approximations of the expensive objective function in order to guide the search for improved solutions. Due to the computational expense of doing a single function evaluation, the goal is to find optimal solutions within very few expensive evaluations. The multimodalit…
EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions
School of Industrial Engineering, Eindhoven University of Technology（埃因霍温理工大学工业工程学院）；Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology（代尔夫特理工大学电气工程、数学与计算机科学学院）
Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationall…
McGill University（麦吉尔大学）；Hydro-Québec’s Research Institute（魁北克水电公司研究院）
We consider computationally expensive blackbox optimization problems and present a method that employs surrogate models and concurrent computing at the search step of the mesh adaptive direct search (MADS) algorithm. Specifically, we solve a surrogate optimization problem using locally weighted scatterplot smoothing (LOWESS) models to find promising candidate points to be evaluated by the blackboxes. We consider several methods for selecting promising points from a large number of points. We conduct numerical experiments to assess the performance of the modified MADS algorithm with respect to …
This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work proposes different uncertainty measures when using ensembles of surrogates. The resulting combination of an ensemble of surrogates with our measures behaves as a stochastic model and allows the use of efficient Bayesian optimization tools. The method is incorporated in t…
Target-based Surrogates for Stochastic Optimization
University of British Columbia（不列颠哥伦比亚大学）；Simon Fraser University（西蒙弗雷泽大学）；Samsung - SAIT AI Lab（三星综合技术院人工智能实验室）；Canada CIFAR AI Chair (Amii)（加拿大高等研究院人工智能讲席（阿尔伯塔机器智能研究所））；Microsoft Research（微软研究院）；Canada CIFAR AI Chair (MILA)（加拿大高等研究院人工智能讲席（蒙特利尔学习算法研究所））
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. The method is derivative-free in the sense that neither need derivative information be available for the expensive objectives nor are gradients approximated using repeated function evaluations as is the case in finite-difference methods. Instead, a multiobjective trust region approach is used that works similarly to …
Studying complex phenomena in detail by performing real experiments is often an unfeasible task. Virtual experiments using simulations are usually used to support the development process. However, numerical simulations are limited by their computational cost. Metamodeling techniques are commonly used to mimic the behavior of unknown solver functions, especially for expensive black box optimizations. If a good correlation between the surrogate model and the black box function is obtained, expensive numerical simulations can be significantly reduced. The sampling strategy, which selects a subset…
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop an algorithm based on entropy reduction of a probabilistic belief about the optimum. The algorithm provides an efficient way of estimating the computationally intractable surrogate objective in the general Entropy Search algorithm by leveraging a sampled belief model and designing a metric that measures the information value of any search point.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based "zoom strategy" to improve the efficiency of the algorithm. We prove that if ProSRS is run for sufficiently long, with probability converging to one there will be at least one point among all the evaluations that will be arbitrarily close to the global minimum. We compare our algorithm to several state-of-the-art Bayesian optimization algorithms on a suite of s…
A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate-based algorithms are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate-based algorithm that uses a linear combination of rectified linear units, d…
Significant effort has been made to solve computationally expensive optimization problems in the past two decades, and various optimization methods incorporating surrogates into optimization have been proposed. Most research focuses on either exploiting the surrogate by defining a utility optimization problem or customizing an existing optimization method to use one or multiple approximation models. However, only a little attention has been paid to generic concepts applicable to different types of algorithms and optimization problems simultaneously. Thus this paper proposes a generalized proba…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven mechanism to construct low dimensional surrogate models. These surrogate models reduce the computational time for solution of the complex optimization problems by using training instances derived from the evaluations of the true objective functions. The surrogate models are constructed using combination of proper orthogonal decomposition and radial basis functions…
Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation optimization is concerned with developing efficient sampling schemes -- subject to a computational budget -- to solve such optimization problems. To mitigate the computational burden, surrogates are often constructed using simulation outputs to approximate the response surface of the simulation model. In this tutorial, we provide an up-to-date overview of s…
The central task in modeling complex dynamical systems is parameter estimation. This task involves numerous evaluations of a computationally expensive objective function. Surrogate-based optimization introduces a computationally efficient predictive model that approximates the value of the objective function. The standard approach involves learning a surrogate from training examples that correspond to past evaluations of the objective function. Current surrogate-based optimization methods use static, predefined substitution strategies that decide when to use the surrogate and when the true obj…
Design optimization under uncertainty is notoriously difficult when the objective function is expensive to evaluate. State-of-the-art techniques, e.g, stochastic optimization or sampling average approximation, fail to learn exploitable patterns from collected data and require an excessive number of objective function evaluations. There is a need for techniques that alleviate the high cost of information acquisition and select sequential simulations optimally. In the field of deterministic single-objective unconstrained global optimization, the Bayesian global optimization (BGO) approach has be…
Cornell University（康奈尔大学）；Uber AI Labs（优步人工智能实验室）；National University of Singapore（新加坡国立大学）
This paper describes Plumbing for Optimization with Asynchronous Parallelism (POAP) and the Python Surrogate Optimization Toolbox (pySOT). POAP is an event-driven framework for building and combining asynchronous optimization strategies, designed for global optimization of expensive functions where concurrent function evaluations are useful. POAP consists of three components: a worker pool capable of function evaluations, strategies to propose evaluations or other actions, and a controller that mediates the interaction between the workers and strategies. pySOT is a collection of synchronous an…
Gradient-free optimization methods, such as surrogate based optimization (SBO) methods, and genetic (GAs), or evolutionary (EAs) algorithms have gained popularity in the field of constrained optimization of expensive black-box functions. However, constraint-handling methods, by both classes of solvers, do not usually guarantee strictly feasible candidates during optimization. This can become an issue in applied engineering problems where design variables must remain feasible for simulations to not fail. We propose a constraint-handling method for computationally inexpensive constraint function…
