OPTIMIZATION INSPIRED BY SPIRAL MAPPING AND ITS APPLICATION

• Main Author: Kania, Adhe
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/37046
• Institution: Institut Teknologi Bandung

Spiral mapping always converges to its center point. Because of its covergency, using spiral mapping as a basis for the optimization method is very interesting. In addition to the global optimization problem, spiral optimization method also can be used to find a root of the system of non-linear equations. However, in this case only one root is able to obtained for each time the program running. In order to obtain (all) the roots of the system of non-linear equations for each time the program running, grouping technique is developed in this thesis. By combining the spiral optimization method and grouping technique, many roots, even all the roots of the system of non-linear equations can be obtained, just with a single running of the program. Not only real roots, but the complex roots also can be obtained by running in a complex scheme. Furthermore, by utilizing the derivative function, this grouping technique can also be used to find the extreme points of a multimodal function, just with a single running of the program. For non-differentiable functions, in this thesis also developed a technique to obtain extreme points with using the grouping technique that has been developed previously. The combination of spiral optimization method and the grouping technique which developed in this thesis has been successfully tested on some benchmark functions and some applications of the real problems, either on global