Comparison of particle swarm optimization and firefly algorithm in parameter estimation of Lotka-Volterra

Abstract

Lotka-Volterra competition model has been applied in life sciences including competition between species, predicting the Aeromonas hydrophila growth on fish surface. The competition model also has been used in social sciences, including competition in the Korean stock market and competition between two types of bank, namely commercial bank and rural bank in Indonesia. It is well-known that the analytical solution of the Lotka-Volterra is unknown. Here gradient-base methods such as Newton method and Levenberg-Marquardt are difficult to be implemented to estimate paramaters of the model. In order to estimate parameters in the model, one need to use heuristic method such as genetic algorithm, particle swarm optimization, firefly algorithm or other heuristic methods. In this paper, we compared performance of particle swarm optimization and firefly algorithm in parameter estimation of Lotka-Volterra type competition model. Here we used the profit data of commercial bank and rural bank, where the data cited from literature. We found the mean absolute percentage error (MAPE) of firefly algorithm is a little bit smaller than the error of particle swarm optimization method. We also found variance of the error of firefly algorithm is lower than the particle swarm optimization method. Hence, for parameter estimation of Lotka-Volterra competition model, firefly algorithm is more beneficial than the particle swarm optimization method.