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Root Finding and Optimization
Published in James P. Howard, Computational Methods for Numerical Analysis with R, 2017
With hill climbing, the decision on which neighborhood point to evaluate is left to the implementor. Different selection processes lead to different variants of the algorithm. This implementation selects an input variable at random, xi $ x_i $ . The change in that variable then is drawn randomly from a uniform distribution with mean of xi $ x_i $ and standard deviation of h, the implied step size. This is a form of stochastic hill climbing, which are hill climbing implementations where the direction is selected at random. Another option for direction selection is to change each input variable and evaluate to see which is closest and jumping to it.
Introduction
Published in Jun Ma, Xiaocong Li, Kok Kiong Tan, Advanced Optimization for Motion Control Systems, 2020
Jun Ma, Xiaocong Li, Kok Kiong Tan
Stochastic hill climbing algorithm (Mondal, Dasgupta, and Dutta 2012): Stochastic hill climbing algorithm is a variant of the gradient method, but the steepest climbing direction is determined by searching the neighborhood. Similar to the gradient method, this algorithm is likely to trap in a local minimum. Since the problem of looping exists by using such an algorithm, the algorithm needs to be executed several times with a variety of random initial values, and then the best result among them is chosen.
Predicting pedestrian crash occurrence and injury severity in Texas using tree-based machine learning models
Published in Transportation Planning and Technology, 2023
Bo Zhao, Natalia Zuniga-Garcia, Lu Xing, Kara M. Kockelman
XBART is a variant of the Bayesian additive regression tree (BART) model with improved computational efficiency (He, Yalov, and Hahn 2018). Conceptually, BART is a Bayesian nonparametric approach that fits a parameter-rich model using a strongly influential prior distribution (Chipman, George, and McCulloch 2012). BART is similar to GBT models, i.e. XGBoost and LightGBM, in that they all sum the contribution of sequential weak learners. However, BART weakens the individual trees using a prior, instead of multiplying each sequential tree by a small constant, i.e. the learning rate, as in GBT models. Additionally, BART performs the iterative fitting by using the back-fitting Monte Carlo Markov Chain (MCMC) algorithm rather than using gradient descent algorithms. The Bayesian perspective yields a number of practical advantages of BART, including the robustness to hyperparameter settings, more accurate predictions, and the inherent Bayesian measure of uncertainties. On the other side, the incorporation of the MCMC algorithm also imposes severe computational demands, especially in the application of high-dimensional large datasets. XBART improves the computational efficiency by adopting the novel stochastic hill-climbing algorithms, which follow the Gibbs update framework in BART but replace the Metropolis-Hasting updates of each tree with a novel grown-from-root back-fitting strategy (He, Yalov, and Hahn 2018). XBART is shown to yield very similar results to BART, but with a much higher computational efficiency (He, Yalov, and Hahn 2018).
Mixcoatl Software (Part 1): Coupled Thermal Physics and Mechanics for Efficient Engineering Design
Published in Nuclear Science and Engineering, 2023
CORTES ran a stochastic hill climbing algorithm to independently optimize each hole within the assembly to improve the thermal performance while ensuring the reactor stays critical. All boundary conditions were held constant, and only the hole diameters were modified for each simulation. Figure 7 displays the final result of the Mixcoatl optimization, which exhibits a greater than 300 K decrease in maximum temperature. The centermost hole diameter of the assembly was decreased as expected. All hole diameters, except for the centermost hole, were increased in order to decrease the distance between holes and thus reduce maximum temperature. The middle hole was disproportionately increased relative to other holes due to the geometry causing larger solid regions around the hole. An unexpected result is that the orificing has been reversed from the original design. Flow is now diverted to the centermost hole, and the orificing size is now quite uniform for all other holes in the assembly.
A model-based systems engineering approach for developing modular system architectures
Published in Journal of Engineering Design, 2022
Benjamin W. Stirgwolt, Thomas A. Mazzuchi, Shahram Sarkani
One widely used algorithm is the Idicula-Gutierrez-Thebeau Algorithm (IGTA), which was progressively developed and refined by Idicula (1995), Gutierrez Fernandez (1998), and Thebeau (2001). The stochastic, hill-climbing optimisation algorithm is used to select which cluster is best for each element. Borjesson and Hölttä-Otto (2012) further evolved the IGTA with the creation of IGTA+, with the objective of improving the algorithm’s speed by (1) disallowing elements to belong to more than one cluster, and (2) generating a record of elements that have not yet been tried for a better fit in another cluster. More recently, the IGTA and IGTA+ have been utilised to cluster elements into modules while also considering design constraints (Sinha, Han, and Suh 2020; Sanaei et al. 2016). Sinha, Han, and Suh (2020) use a penalty function-based approach to account for design constraints such as maintenance, packaging, and thermal constraints.