ISSN 1810-2328, Journal of Engineering Thermophysics, 2016, Vol. 25, No. 2, pp. 216–226. c  Pleiades Publishing, Ltd., 2016. Application of Particle Swarm+Ant Colony Optimization to Calculate the Interaction Parameters on Phase Equilibria J. A. Lazz ´ us * , M. Rivera, I. Salfate, G. Pulgar-Villarroel, and P. Rojas Departamento de F ´ ısica, Universidad de La Serena, Casilla 554, La Serena, Chile Received January 2, 2014 Abstract—In this study, a hybrid particle swarm+ant colony optimization (PSO+ACO) was applied to solve the vapor–liquid phase equilibrium. The NRTL activity coefficient model was optimized with this new algorithm and the binary interaction parameters of twenty mixtures were obtained. The results were compared with the Levenberg–Marquardt algorithm, and show that the PSO+ACO algorithm is a good method to describe the vapor–liquid equilibrium of any binary system. DOI: 10.1134/S1810232816020065 1. INTRODUCTION The accurate prediction of physical properties on phase equilibrium can be considered one of the most important applications in thermodynamic processes [1]. The most common way to face this task is to fit the experimental data to a thermodynamic model and use the obtained model with fitted parameters for predicting properties at other conditions. The existing methods to solve phase equilibrium systems obtain only local solutions. It has been demonstrated that for several cases, the optimum values of the interaction parameters depend on the searching interval and on the initial value of used interaction parameters [2]. Then, the parameter optimization procedures are very important for development of mathematical models obtained from experimental data [3]. The aim of optimization is to determine the best-suited solution to a problem under a given set of constraints. Mathematically, an optimization problem involves a fitness function describing the problem, under a set of constraints representing the solution space for the problem. The optimization problem, nowadays, is represented as an intelligent search problem, where one or more agents are employed to determine the optimum on a search landscape [4]. Modern optimization techniques have aroused great interest among the scientific and technical community in a wide variety of fields, because of their ability for solving problems with nonlinear and nonconvex dependence of design parameters [5]. Thus, the use of heuristic optimization methods, such as particle swarm optimization [6] and ant colony optimization [7], for the parameter estimation is very promising [2]. These biologically- derived methods represent an excellent alternative for finding a global optimum for phase equilibrium calculations [3]. In this work, twenty binary vapor–liquid phase systems were evaluated using a hybrid algorithm based on particle swarm optimization and ant colony optimization. The complete program was used for calculating the binary interaction parameters of these mixtures by minimization of the difference between calculated and experimental data. * E-mail: jlazzus@dfuls.cl 216