Distributionally Robust Optimization For Design Under Partially Observable Uncertainty

Distributionally Robust Optimization for Design Under Partially Observable Uncertainty

Deciding how to represent and manage uncertainty is a vital part of designing complex systems. Widely used is a probabilistic approach: assigning a probability distribution to each uncertain parameter. However, this presents the designer with the task of assuming these probability distributions or estimating them from data, tasks which are inevitably prone to error. This thesis addresses this challenge by formulating a distributionally robust design optimization problem, and presents computationally efficient algorithms for solving the problem. In distributionally robust optimization (DRO) methods, the designer acknowledges that they are unable to exactly specify a probability distribution for the uncertain parameters, and instead specifies a so-called ambiguity set of possible distributions. This work uses an acoustic horn design problem to explore how the error incurred in estimating a probability distribution from limited data affects the realized performance of designs found using traditional approaches to optimization under uncertainty, such as multi-objective optimization. It is found that placing some importance on a risk reduction objective results in designs that are more robust to these errors, and thus have a better mean performance realized under the true distribution than if the designer were to focus all efforts on optimizing for mean performance alone. In contrast, the DRO approach is able to uncover designs that are not attainable using the multi-objective approach when given the same data. These DRO designs in some cases significantly outperform those designs found using the multi-objective approach.

Optimal Operation of Integrated Energy Systems Under Uncertainties

Optimal Operation of Integrated Energy Systems Under Uncertainties: Distributionally Robust and Stochastic Models discusses new solutions to the rapidly emerging concerns surrounding energy usage and environmental deterioration. Integrated energy systems (IESs) are acknowledged to be a promising approach to increasing the efficiency of energy utilization by exploiting complementary (alternative) energy sources and storages. IESs show favorable performance for improving the penetration of renewable energy sources (RESs) and accelerating low-carbon transition. However, as more renewables penetrate the energy system, their highly uncertain characteristics challenge the system, with significant impacts on safety and economic issues. To this end, this book provides systematic methods to address the aggravating uncertainties in IESs from two aspects: distributionally robust optimization and online operation. - Presents energy scheduling, considering power, gas, and carbon markets concurrently based on distributionally robust optimization methods - Helps readers design day-ahead scheduling schemes, considering both decision-dependent uncertainties and decision-independent uncertainties for IES - Covers online scheduling and energy auctions by stochastic optimization methods - Includes analytic results given to measure the performance gap between real performance and ideal performance

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