Uncertainty and noise are frequently-encountered obstacles in real-world applications of numerical optimization. The practice of optimization that deals with uncertainties and noise is commonly... Show moreUncertainty and noise are frequently-encountered obstacles in real-world applications of numerical optimization. The practice of optimization that deals with uncertainties and noise is commonly referred to as robust optimization. This thesis concentrates on robust optimization w.r.t the parametric uncertaintiesin the search variables. These parametric uncertainties are assumed to be structurally symmetric, additive in nature, and can be modeled in a deterministic or aprobabilistic fashion. This dissertation empirically studies the models, algorithms, and techniques utilized for surrogate-assisted robust optimization in this context. Based on the studies performed in the dissertation, we conclude that Kriging, SVM, and Polynomial Regression are useful modeling techniques to solve robust optimization problems. We also validate the applicability of Autoencoders and PCA for addressing high-dimensional problems. Lastly, we find that mini-max robustness is the most efficient robustness formulation technique in practical scenarios. Show less
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
