Optimization

Abstract

Process optimization plays a crucial role in process and system transformation; in the manufacturing process, for instance, it increases efficiency and reduces production costs through process improvement. In machine learning, on the other hand, optimization is used to improve the accuracy of a machine learning model by minimizing the degree of error and, hence, enhancing their learning to make accurate predictions. Furthermore, as we saw in previous chapters, data analytics and machine learning are fundamental to redefining process prediction and control, which will ultimately align with optimization. In this Chapter, we introduce simple optimization algorithms used for process engineers, such as grid search, random search, and gradient search, followed by a different generation of techniques, including evolutionary algorithms, particle swarm, and Bayesian inference and optimization. Moreover, we explore multi-objective optimization, a must tool engineers employ to improve decision-making in solving design and monitoring problems.

Appendices

Data Disclosure

The data was generated, maintaining the described problem's physical meaning of the analyzed phenomenon or process.

Problems

• 5.1 Review, run, compare, and discuss all the previous examples using different optimization algorithms. Is there a metric (or set of metrics) to effectively compare these algorithms?

• 5.2 Perform sensitivity analyses on each optimization algorithm's tuning parameters to evaluate their impact on the found solutions.

Resources

GA documentation: https://www.rdocumentation.org/packages/GA/versions/3.2.3/topics/ga

PSO documentation: https://cran.r-project.org/web/packages/pso/pso.pdf

NSGA-II documentation: https://cran.r-project.org/web/packages/nsga2R/nsga2R.pdf

Bayesian Optimization I: https://cran.r-project.org/web/packages/rBayesianOptimization/rBayesianOptimization.pdf

Bayesian Optimization II: https://www.rdocumentation.org/packages/ParBayesianOptimization/versions/1.2.6/topics/bayesOpt

R-codes and data repository: https://github.com/CHE408UofT/DGSD_UofT

Recommended Readings

Boyd, S. P., & Vandenberghe, L. (2011). Convex optimization. Cambridge Univ. Pr.

Chaves, I.D.G., López, J.R.G., Zapata, J.L.G., Robayo, A.L., Niño, G.R. (2016). Process Optimization in Chemical Engineering. In: Process Analysis and Simulation in Chemical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-14812-0_7

Deb, K., Pratap, A. Agarwal, S. Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. https://doi.org/10.1109/4235.996017.

Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for optimization. The Mit Press.

Edgar, T. F., Himmelblau, D. M., & Lasdon, L. S. (2201). Optimization of Chemical Processes. McGraw-Hill.

Simon, D. (2013). Evolutionary optimization algorithms: Biologically-inspired and population-based approches to computer intelligence. Wiley-Blackwell.

Yu, X., & Gen, M. (2013). Introduction to evolutionary algorithms. Springer London.