Continuous Optimization using Evolutionary Computing: Advancements in Differential Evolution Algorithm for Function Optimization and Data Classification

Abstract

Evolutionary computing algorithms have been implemented successfully for optimization problems. Differential Evolution (DE) is one of the evolutionary global optimization algorithm which has enjoyed considerable interest by many researchers in the recent years. Due to intensive study of DE algorithm by researchers; a number of mutation variants have been established for this algorithm. These mutation variants make DE algorithm more applicable, but due to the random development of these variants have created inconsistencies such as naming and formulation. Therefore, this research work also aims to identify inconsistencies and propose solution to make them consistent. Most of the inconsistencies exist because of the uncommon nomenclature used for these variants. In this research a comprehensive study is carried out to identify inconsistencies in the nomenclature of mutation variants that does not match each other. Their proper and consistent names are proposed which provide significant contribution to the literature. The proposed names are assigned for conflicting variants that is based on the name of the variant, total number of vectors used to generate the trial vector and the order of the vectors to form the equation of these mutation variants. For effective conflict analysis of mutation strategies, trial vector generation mechanism of each variant is illustrated graphically. The consistent set of mutation variants will prove to be a valuable addition to DE literature. A number of variants have been proposed to improve the performance of DE. However, most of the variants suffer from the problems of convergence speed and local optima. A novel tournament based parent selection mutation strategy of DE algorithm (TSDE) is proposed in this research. The proposed mutation strategy enhances searching capability in terms of fitness and improves convergence speed of the DE algorithm in terms of number of function calls. This research work also presents statistical comparison of existing DE mutation variants, which categorizes these variants in terms of their overall performance. The proposed mutation strategy is tested for standard benchmark functions and validated to train the artificial neural network for data classification problem. This thesis also introduces random controlled pool base differential evolution algorithm (RCPDE). A mutation strategy pool and a control parameter pool are used in RCPDE. The mutation strategy pool contains mutations strategies having diverse characteristics and control parameter pool contains varying nature pairs of control parameter values. The author has also observed that addition of rarely used control parameter values in the parameter pool and mutation strategy in the strategy pool is helpful to enhance the average fitness value and the number of function call performance parameters of DE algorithm. The proposed mutation strategies pool and control parameters pool in RCPDE are helpful in improving the solution quality and convergence speed of DE algorithm. RCPDE algorithm is tested over a test set of multi dimensional (N-dimensional) benchmark functions that shows significant performance of the proposed algorithm over many state of the art DE algorithms. To validate the performance of RCPDE algorithm; it has been used to train artificial neural network for data classification problem. Through experimental studies it is proved that proposed TSDE achieved better performance than other mutation strategies of DE algorithm. Similarly random controlled mutation strategies pool and control parameter pool based DE algorithm (RCPDE) also shows significant performance in the experimental studies as compared to other well known state of the art algorithms such as jDE, EPSDE, CoDE and standard DE algorithm.