State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits

Assessment Of Blackbox Optimization Methods For Efficient Calibration Of Computationally Intensive Hydrological Models

Many studies have shown the effectiveness of blackbox optimization algorithms for the calibration of lumped conceptual hydrological models. Among these algorithms, the « Shuffled Complex Evolution method developed at the University of Arizona » (SCE-UA) is a very popular one. However, when it comes to calibrating distributed and/or physically-based models, computational efficiency becomes an issue. A single simulation with this type of model may take several minutes and the optimization process may require more than thousands of simulations. To alleviate this problem, two recently developed optimization methods, « Dynamically Dimensioned Search » (DDS) and « Nonsmooth Optimization by Mesh Adaptive Direct search » (NOMAD), adapt their search strategy based on the available budget of simulations. This work aims to verify the computational efficiency of DDS and NOMAD for the calibration of the HYDROTEL model (distributed and physically-based). Two versions of the model are used, one with 10 parameters and one with 19 parameters, and they are both applied to two different watersheds located in the province of Quebec (Canada). A second, lumped conceptual, model (HSAMI) is also applied to both watersheds to examine the impact of model structure on the results. Each combination of model-watershed is calibrated with each one of the optimization algorithms: DDS and NOMAD. SCE-UA is also used as the benchmark for comparison. The objective function uses the Nash-Sutcliffe Efficiency criterion, and is computed between simulated and observed streamflows. For every combination of model-watershed-algorithm, calibrations are repeated 32 times and the mean results are shown. This research sheds a better light and understanding on the efficiency of the three optimization algorithms for computationally intensive calibration problems, and on the model-related characteristics of the optimization problem