Applying Firefly Algorithm to Data Fitting for the Van der Waals Equation of State with Bézier Curves

The Van der Waals equation is an equation of state that generalizes the ideal gas law. It involves two characteristic curves, called binodal and spinodal curves. They are usually reconstructed through standard polynomial fitting. However, the resulting fitting models are strongly limited in several ways. In this paper, we address this issue through least-squares approximation of the set of 2D points by using free-form Bezier curves. This requires to perform data parameterization in addition to computing the poles of the curves. This is achieved by applying a powerful swarm intelligence method called the firefly algorithm. Our method is applied to real data of a gas. Our results show that the method can reconstruct the characteristic curves with good accuracy. Comparative work shows that our approach outperforms two state-of-the-art methods for this example.