Abstract
Black-box optimization concerns the optimization of functions that can be evaluated only through numerical simulation and in which partial derivatives are either not known or not de?ned. This means that traditional optimization methods cannot be applied, and the opti-mization can only be carried out using the information obtained through function evaluations. One approach that has been gaining attention from researchers in the last few years con-sists of using the function evaluations to build and re?ne a surrogate model for the objective function of the problem and then use this model to drive the optimization. This model-based approach is very e?ective but it is typically computationally expensive, becoming impractical when the number of variables in the problem is greater than just a few dozens. Moreover, it usually considers only problems with bound-constrained feasible regions, i.e., hyperrectangles. These two aspects prevent this approach to be used on many relevant optimization problems. The objective of this thesis is to overcome to some extent these limitations through the introduction of innovative algorithms and methodologies, ultimately promoting the usage of model-based black-box optimization algorithms for high dimensional problems with bounded mixed-integer feasible regions. In particular, we ?rst present a new sampling method called Constrained Latin Hypercube Sampling (CLHS) that let us generate well-distributed samples (also called space-?lling designs) within mixed-integer feasible regions. Next, we discuss an e?cient implementation of a model-based approach based on Radial Basis Functions (RBFs). The resulting algorithm can handle black-box optimization problems with up to few thousands variables de?ned on bounded mixed-integer feasible regions. RBF approximation methods are e?ective and scalable, but they usually need at least K+1 function evaluations (where K is the dimension of the problem) to build a surrogate model. This becomes an issue when the function evaluation is computationally expensive. In fact, it is not uncommon for black-box problems to require hours or even days to complete a single evaluation. We present an early optimization methodology that tries to deal with this limitation and that lets us build and exploit a RBF model before the K+1 threshold. Finally, we apply our model-based black-box optimization algorithm to the feature selec-tion problem and the in?uence maximization problem. To the best of our knowledge, this is the ?rst time that this kind of algorithm has been applied to such di?cult problems. In the context of feature selection we report results comparable to those of popular feature selection algorithms. We also study the in?uence maximization problem in complex networks using structural controllability tools, proposing a new heuristic and comparing it with a black-box approach. By exploiting the structural properties of the networks, heuristics unsurprisingly perform better than the general-purpose black-box method on this problem. Overall, we think that our algorithm is the ?rst step towards the application of model-based black-box optimization algorithms to large-scale problems with expensive function eval-uations and constrained feasible regions.