A multi-objective Spiral Dynamic algorithm and its application for PD design

This paper presents a novel multi-objective Spiral Dynamic Optimization (MOSDA) algorithm. It is an extended version of a single objective type SDA. A Non-dominated sorting (NS) approach from Non-dominated Sorting Genetic Algorithm II (NSGAII) is adopted into SDA to develop its multi-objective (MO) type algorithm. SDA has a good elitism strategy and a simple structure. On the other hand, NS is a fast strategy to develop good Pareto Front (PF) characteristics for MO type algorithm. The proposed algorithm is tested with various benchmark functions used to test a newly developed MO algorithm. A PF graph is presented as a result of the test. Moreover, it is adopted to optimize parameters of Proportional-Derivative (PD) controller for an Inverted Pendulum (IP) system. Time-domain response of the IP is presented to show performance of the optimized controller. Result presented in this paper shows that MOSDA has a better performance in terms of finding PF and solution spread when tested with benchmark functions compared to NSGAII. In terms of its application in solving a real problem, both algorithms successfully optimize the PD and control the system very well. IP controlled by MOSDA-based PD shows better rise time.