Real-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust... Show moreReal-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust counterpart, e.g., by taking an average of the function values over different perturbations to a specific input. Solving the robust counterpart instead of the original problem can significantly increase the associated computational cost, which is often overlooked in the literature to the best of our knowledge. Such an extra cost brought by robust optimization might depend on the problem landscape, the dimensionality, the severity of the uncertainty, and the formulation of the robust counterpart.This paper targets an empirical approach that evaluates and compares the computational cost brought by different robustness formulations in Kriging-based optimization on a wide combination (300 test cases) of problems, uncertainty levels, and dimensions. We mainly focus on the CPU time taken to find robust solutions, and choose five commonly-applied robustness formulations: `"mini-max robustness'', "mini-max regret robustness'', "expectation-based robustness'', ``dispersion-based robustness'', and "composite robustness'' respectively. We assess the empirical performance of these robustness formulations in terms of a fixed budget and a fixed target analysis, from which we find that "mini-max robustness'' is the most practical formulation w.r.t.~the associated computational cost. Show less
Saha, S.; de Jesus de Araujo Rios, T.; Minku, L.L.; Stein, B. van; Wollstadt, P.; Yao, X.; ... ; Menzel, S. 2022
A new acquisition function is proposed for solving robust optimization problems via Bayesian Optimization. The proposed acquisition function reflects the need for the robust instead of the nominal... Show moreA new acquisition function is proposed for solving robust optimization problems via Bayesian Optimization. The proposed acquisition function reflects the need for the robust instead of the nominal optimum, and is based on the intuition of utilizing the higher moments of the improvement. The efficacy of Bayesian Optimization based on this acquisition function is demonstrated on four test problems, each affected by three different levels of noise. Our findings suggest the promising nature of the proposed acquisition function as it yields a better robust optimal value of the function in 6/12 test scenarios when compared with the baseline. Show less
deJesus de Araujo Rios, T.; Stein, B. van, Wollstadt, P.; Bäck, T.H.W.; Sendhoff, B.; Menzel, S. 2021
Automated machine learning (AutoML) aims to automatically produce the best machine learning pipeline, i.e., a sequence of operators and their optimized hyperparameter settings, to maximize the... Show moreAutomated machine learning (AutoML) aims to automatically produce the best machine learning pipeline, i.e., a sequence of operators and their optimized hyperparameter settings, to maximize the performance of an arbitrary machine learning problem. Typically, AutoML based Bayesian optimization (BO) approaches convert the AutoML optimization problem into a Hyperparameter Optimization (HPO) problem, where the choice of algorithms is modeled as an additional categorical hyperparameter. In this way, algorithms and their local hyper-parameters are referred to as the same level. Consequently, this approach makes the resulting initial sampling less robust. In this study, we describe a first attempt to formulate the AutoML optimization problem as its nature instead of transfer it into a HPO problem. To take advantage of this paradigm, we propose a novel initial sampling approach to maximize the coverage of the AutoML search space to help BO construct a robust surrogate model. We experiment with 2 independent scenarios of AutoML with 2 operators and 6 operators over 117 benchmark datasets. Results of our experiments demonstrate that the performance of BO significantly improved by using our sampling approach. Show less
The imbalanced classification problem is very relevant in both academic and industrial applications. The task of finding the best machine learning model to use for a specific imbalanced dataset is... Show moreThe imbalanced classification problem is very relevant in both academic and industrial applications. The task of finding the best machine learning model to use for a specific imbalanced dataset is complicated due to a large number of existing algorithms, each with its own hyperparameters. The Combined Algorithm Selection and Hyperparameter optimization (CASH) has been introduced to tackle both aspects at the same time. However, CASH has not been studied in detail in the class imbalance domain, where the best combination of resampling technique and classification algorithm is searched for, together with their optimized hyperparameters. Thus, we target the CASH problem for imbalanced classification. We experiment with a search space of 5 classification algorithms, 21 resampling approaches and 64 relevant hyperparameters in total. Moreover, we investigate performance of 2 well-known optimization approaches: Random search and Tree Parzen Estimators approach which is a kind of Bayesian optimization. For comparison, we also perform grid search on all combinations of resampling techniques and classification algorithms with their default hyperparameters. Our experimental results show that a Bayesian optimization approach outperforms the other approaches for CASH in this application domain. Show less
de Jesus de Araujo Rios, T.; Stein, B., van; Bäck, T.H.W.; Sendhoff, B.; Menzel, S. 2021
Geometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network... Show moreGeometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network models on geometric input requires considerable computational effort. Even more so, if one considers typical problem sizes found in application domains such as engineering tasks, where geometric data are often orders of magnitude larger than the inputs currently considered in GDL literature. Hence, an assessment of the scalability of the training task is necessary, where model and data set parameters can be mapped to the computational demand during training. The present paper therefore studies the effects of data set size and the number of free model parameters on the computational effort of training a Point Cloud Autoencoder (PC-AE). We further review pre-processing techniques to obtain efficient representations of high-dimensional inputs to the PC-AE and investigate the effects of these techniques on the information abstracted by the trained model. We perform these experiments on synthetic geometric data inspired by engineering applications using computing hardware with particularly recent graphics processing units (GPUs) with high memory specifications. The present study thus provides a comprehensive evaluation of how to scale geometric deep learning architectures to high-dimensional inputs to allow for an application of state-of-the-art deep learning methods in real-world tasks. Show less
Rios, T.; Sendhoff, B.; Menzel, S.; Bäck, T.H.W.; Stein, B. van 2019
A crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off... Show moreA crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off between exploring feasible solutions in the design space and maintaining admissible computational effort. In order to achieve such balance in optimization problems with Computer Aided Engineering (CAE) models, the conventional constructive geometric representations are substituted by deformation methods, e.g. free form deformation, where the position of a few control points might be capable of handling large scale shape modifications. In light of the recent developments in the field of geometric deep learning, autoencoders have risen as a promising alternative for efficiently condensing high-dimensional models into compact representations. In this paper, we present a novel perspective on geometric deep learning models by exploring the applicability of the latent space of a point cloud autoencoder in shape optimization problems with evolutionary algorithms. Focusing on engineering applications, a target shape matching optimization is used as a surrogate to the computationally expensive CAE simulations required in engineering optimizations. Through the quality assessment of the solutions achieved in the optimization and further aspects, such as shape feasibility, point cloud autoencoders showed to be consistent and suitable geometric representations for such problems, adding a new perspective on the approaches for handling high-dimensional models to optimization tasks. Show less
