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
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
Real-world (black-box) optimization problems often involve various types of uncertainties and noise emerging in different parts of the optimization problem. When this is not accounted for,... Show moreReal-world (black-box) optimization problems often involve various types of uncertainties and noise emerging in different parts of the optimization problem. When this is not accounted for, optimization may fail or may yield solutions that are optimal in the classical strict notion of optimality, but fail in practice. Robust optimization is the practice of optimization that actively accounts for uncertainties and/or noise. Evolutionary Algorithms form a class of optimization algorithms that use the principle of evolution to find good solutions to optimization problems. Because uncertainty and noise are indispensable parts of nature, this class of optimization algorithms seems to be a logical choice for robust optimization scenarios. This thesis provides a clear definition of the term robust optimization and a comparison and practical guidelines on how Evolution Strategies, a subclass of Evolutionary Algorithms for real-parameter optimization problems, should be adapted for such scenarios. Show less
