A classification approach to efficient global optimization in presence of non-computable domains

Abstract

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the noncomputable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

Efficient Exploration of Microstructure-Property Spaces via Active Learning

“…In fact, the described extension is similar to Bayesian optimization approaches that account for unknown constraints using classification methods, see for example Sacher et al (2018), Heese et al (2019) and Tran et al (2019).…”

Sequential model based optimization of partially defined functions under unknown constraints

“…Second, the organization of SVM-CBO in two consecutive phases allows to preliminary solve the so-called feasibility determination problemproviding useful information about the behaviour of the simulation software or real-life system to be optimized-and then exploit this information for improving effectiveness and efficiency of the optimization process (i.e., phase 2). Moreover, instead of using the "probability of feasibility", which is basically a penalization factor in [44] and [31], SVM-CBO works by constraining the acquisition function, namely LCB, to the current estimate of the feasibility region. This results in a more effective sampling of the new point, as also reported in [44] when probability of feasibility is used to constrain-in probabilistic terms-the acquisition function (i.e., EI) instead of penalize it.…”

“…A joint GP model for classification of the inputs (failure or success) and for regression of the objective function is proposed. Another definition is non-computable domains, as introduced in [31], referring to situations occurring when the search space encompasses points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. The set of evaluated points is split into two subsets corresponding to computable and non-computable points, respectively (aka, feasible/infeasible).…”

“…In [44] a Probabilistic SVM (PSVM) is used to calculate the "probability of feasibility" and the optimization scheme alternates between (i) a global search for the optimal solution, depending on both this probability and the estimated value of the objective function-modelled through a GP-and (ii) a local refinement of the PSVM through an adaptive local sampling scheme. A similar approach was proposed in [31] in which a Least-Square SVM (LS-SVM) is used instead of a PSVM. The output of the LS-SVM is used, as for PSVM, to provide a "probability of feasibility".…”

Gaussian process optimization with failures: classification and convergence proof

“…A typical example of failure might be a computational fluid dynamics (CFD) solver that does not converge. This convergence failure could be caused by an overly large time-step yielding an instability in the numerical scheme and a divergence, or by an inadequate mesh close to the boundary of the domain (see also the discussions in [28]). Another typical example of failure is when f (x) provides the numerical performance (e.g.…”