Statistics and Numerical Methods

The chapter gives an outline of some statistical and numerical methods that will be applied in later chapters. The first section deals with the minimization of functions. Several gradient-based methods and a popular non-gradient method are discussed. The following section discusses statistical models and the estimation of model parameters. The basics of linear and nonlinear regression models and state space models are presented, including least-squares estimation and the (extended) Kalman filter. The final section gives a brief overview of clustering and different types of clustering algorithms.

A Metaheuristic-Based Tool for Function Minimization

During the last decade, metaheuristic algorithms have occupied an important place in the field of optimization. Function minimization is of importance to researchers since many real-world problems can be modeled mathematically and be solved effectively through metaheuristic algorithms. Due to the growing scientific interest in the field of optimization and the good performances shown by the algorithms on function minimization, the practical and quick implementation concept is necessary to select the most appropriate algorithms on function minimization, and to assist researchers in analyzing the performance of the algorithms. In this study, a tool is developed to minimize user-defined functions in a specified range according to the chosen metaheuristic algorithms, which allows analyzing the algorithms in the general experimental environment. The tool, which has a user-friendly interface, can provide single and comparative solutions by simultaneously executing the algorithms. Each solution and computational time obtained by the algorithms is given numerically, and the convergence behavior of the algorithms is shown graphically in the tool interface. Minimization of functions can be made fast, easily and effectively through the developed tool.