AN ANALYSIS OF MIGRATION MODELS FOR LINEARIZED BIOGEOGRAPHY-BASED OPTIMIZATION APPLIED FOR PID TUNING PROBLEM

Abstract

: Linearized Biogeography-Based Optimization (LBBO) is a new version of Biogeography-Based Optimization (BBO). BBO is an evolutionary optimization algorithm based on the mathematical model of organism distribution of Biological systems. BBO permits a recombination for the features of candidate solutions (habitats) by means of emigration and immigration. This paper presents a new migration model based on the sigmoid function (S curve) to be one of the nonlinear migration models. This paper also presents an analysis of three linear and three nonlinear different migration models, including the sigmoid model, in LBBO and tests their performance with the non-noisy 23 benchmark functions that have been accepted for 2005 Congress on Evolutionary Computation (CEC). Another test with seven transfer functions is carried out and the performance study explores that sigmoid migration model has the best performance between the different models that will be discussed. The proposed LBBO algorithm with the sigmoid migration function (LBBO-S) had been tested with 23 benchmarks and then compared with the 20 algorithms that have been accepted for 2005 CEC. The proposed algorithm achieved advanced rank between them and it gave better results and lower variance, which proved to have competitive performance with state-of-the-art evolutionary algorithms. An application of the proposed sigmoid model is applied here to tune Proportional Integral Derivative (PID) controller, which is widely used in ind