Black-box and preference-based optimization algorithms are global optimization procedures that aim to find the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons as possible. In the black-box case, the analytical expression of the objective function is unknown and it can only be evaluated through a (costly) computer simulation or an experiment. In the preference-based case, the objective function is still unknown but it corresponds to the subjective criterion of an individual. So, it is not possible to quantify such criterion in a reliable and consistent way. Therefore, preference-based optimization algorithms seek global solutions using only comparisons between couples of different samples, for which a human decision-maker indicates which of the two is preferred. Quite often, the black-box and preference-based frameworks are covered separately and are handled using different techniques. In this paper, we show that black-box and preference-based optimization problems are closely related and can be solved using the same family of approaches, namely surrogate-based methods. Moreover, we propose the generalized Metric Response Surface (gMRS) algorithm, an optimization scheme that is a generalization of the popular MSRS framework. Finally, we provide a convergence proof for the proposed optimization method.
Czech Technical University（捷克技术大学）；Charles University in Prague（布拉格查理大学）；Czech Academy of Sciences（捷克科学院）
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 relationship between the predictive accuracy of surrogate models and features of the black-box function landscape. We also study properties of features for landscape analysis in the context of different transformations and ways of selecting the input data. We perform the landscape analysis of a large set of data generated using runs of a surrogate-assisted version of the Covariance Matrix Adaptation Evolution Strategy on the …
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…
IMT School for Advanced Studies Lucca（卢卡高等研究院）；Dalle Molle Institute for Artificial Intelligence - USI/SUPSI（达勒·莫勒人工智能研究所）
This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as "this is better than that" between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. The surrogate is fit by means of radi…
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…
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）
PMBO: Enhancing Black-Box Optimization through Multivariate Polynomial Surrogates
CASUS – Center for Advanced Systems Understanding（CASUS——高级系统理解中心）；Helmholtz-Zentrum Dresden-Rossendorf e.V. (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心）；California Institute of Technology（加州理工学院）；University of Wrocław（弗罗茨瓦夫大学）
DT-PBO: an Interpretable Tree-based Surrogate Model for Preferential Bayesian Optimization
Data Science Center of Excellence, Faculty of Military Sciences, Breda, NL（数据科学卓越中心，军事科学学院，荷兰布雷达）；NLR - Royal Netherlands Aerospace Centre, Amsterdam, NL（NLR-荷兰航空航天研究中心，荷兰阿姆斯特丹）；Departement Intelligent Systems, Tilburg University, Tilburg, NL（智能系统部门，蒂尔堡大学，荷兰蒂尔堡）
Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research -- unimportant input variables and inefficient treatment of uncertainty associated with the black-box output. We first design a new flexible non-interpolating parsimonious surrogate model using a partitioning-based multivariate adaptive regression splines approach, Tree Knot MARS (TK-MARS). The proposed model is specifically designed for optimization by capturing the structure of the function, be…
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…
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 (es…
Modelling human function learning has been the subject of in-tense research in cognitive sciences. The topic is relevant in black-box optimization where information about the objective and/or constraints is not available and must be learned through function evaluations. In this paper we focus on the relation between the behaviour of humans searching for the maximum and the probabilistic model used in Bayesian Optimization. As surrogate models of the unknown function both Gaussian Processes and Random Forest have been considered: the Bayesian learning paradigm is central in the development of a…
Preference-based global optimization algorithms minimize an unknown objective function only based on whether the function is better, worse, or similar for given pairs of candidate optimization vectors. Such optimization problems arise in many real-life examples, such as finding the optimal calibration of the parameters of a control law. The calibrator can judge whether a particular combination of parameters leads to a better, worse, or similar closed-loop performance. Often, the search for the optimal parameters is also subject to unknown constraints. For example, the vector of calibration par…
Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investig…
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…
