Differential evolution - simulated annealing (DESA) optimization algorithm, its mechanical frameworks, convergence properties and applications - Addawe, Rizavel C.
Abstract (A significant challenge of dealing with high-dimensional data such as mixture models, nonlinear regression, and response surface methodology is to find the best fit that the model can achieve by maximizing the goodness of fit measures. In cases where a model has failed to provide a good fit to the data is primarily because the fitting procedures has failed to find the optimal parameters. There is, therefore, a need for robust methods that consistently obtain the optimal fit to the data. The primary goal of this dissertation is the development of the DESA algorithm, a combination of Differential Evolution and Simulated Annealing optimizing algorithms from a theoretical perspective and its application as an alternative search technique for real-world statistical problems. The (DE/rand/1/bin) mutation scheme of the classical DE algorithm allows diversity of the optimal region and the SA-like selection component of the DESA allows it to escape from a local minimum. The DESA algorithm is developed for both continuous and discrete domains. The theoretical foundation explains the behaviors of DESA through the proofs of convergence and stability. The analysis of the discrete DESA-population is treated based on a Markov model and its convergence with probability one is derived in the Markovian framework. The analysis of the continuous DESA-population, on the other hand, is modeled in the global random search framework. The asymptotic stability of the population dynamics system is asymptotically stable. Moreover, the system defined by the DESA-population is stable in the sense of Lyapunov. The SA-like selection operator of DESA increases its learning rate and momentum. Hence, DESA has faster convergence than the classical DE. Based on several test cases, the DESA algorithm has the potential to improve the quality and success rate of DE without loss of robustness. It is a promising tool to use in the search for a more efficient algorithm for the problem of fitting high-dimensional functions to data. The mathematical formulations of DESA to fitting finite mixture (FMM), nonlinear regression, and optimization of the response surface methodology (RSM) to data can serve as prototypes for other high-dimensional problems in which the DESA acts as the parameter optimization strategy. This study also demonstrates applications of DESA algorithm in the optimization of seasonal autoregressive integrated moving average (SARIMA) models to forecast monthly dengue incidence among the young and adult population of Baguio City. The experiments on DESA for multiple sequence alignments (MSAs) demonstrates applications in the optimization of single and multi-objective functions).
July 2018
Dissertation (Ph.D. Statistics)--University of the Philippines, Diliman.
Keywords: Differential evolution - simulated annealing; Optimization algorithm