Research Article On the Effectiveness of Nature-Inspired Metaheuristic Algorithms for Performing Phase Equilibrium Thermodynamic Calculations Seif-Eddeen K. Fateen 1 and Adrian Bonilla-Petriciolet 2 1 Department of Chemical Engineering, Cairo University, Giza 12316, Egypt 2 Department of Chemical Engineering, Aguascalientes Institute of Technology, 20256 Aguascalientes, AGS, Mexico Correspondence should be addressed to Seif-Eddeen K. Fateen; fateen@eng1.cu.edu.eg Received 27 March 2014; Accepted 30 April 2014; Published 20 May 2014 Academic Editor: Xin-She Yang Copyright © 2014 S.-E. K. Fateen and A. Bonilla-Petriciolet. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. he search for reliable and eicient global optimization algorithms for solving phase stability and phase equilibrium problems in applied thermodynamics is an ongoing area of research. In this study, we evaluated and compared the reliability and eiciency of eight selected nature-inspired metaheuristic algorithms for solving diicult phase stability and phase equilibrium problems. hese algorithms are the cuckoo search (CS), intelligent irely (IFA), bat (BA), artiicial bee colony (ABC), MAKHA, a hybrid between monkey algorithm and krill herd algorithm, covariance matrix adaptation evolution strategy (CMAES), magnetic charged system search (MCSS), and bare bones particle swarm optimization (BBPSO). he results clearly showed that CS is the most reliable of all methods as it successfully solved all thermodynamic problems tested in this study. CS proved to be a promising nature-inspired optimization method to perform applied thermodynamic calculations for process design. 1. Introduction Applied thermodynamic calculations in chemical engineer- ing oten involve the repeated solution of phase stability and phase equilibrium problems as their solutions are needed during the design of several equipment and separation pro- cesses. hese problems can be formulated as minimization problems, for which the global minimum represents the required result. hese calculations are challenging due to the high nonlinearity of thermodynamic models used to describe the equilibrium phases, the potential nonconvexity of the thermodynamic functions used as objective, and the presence of trivial solutions in the feasible search space. hus, the solution of this type of problems via global optimization algorithms remains to be an active area of research. hese problems generally feature local minima that are comparable to the global minimum, which accentuates the need for reliable global optimizers [1, 2]. For example, the features of reactive phase equilibrium calculations increase the dimen- sionality and complexity of the optimization problem because the objective functions are required to satisfy the chemical equilibrium constraints [1, 2]. he global stochastic optimization methods show high probabilities to locate the global minimum within reasonable computational costs, and thus they ofer a desirable balance between reliability and eiciency for inding the global optimum solution. Moreover, stochastic methods do not require any assumptions for the optimization problem at hand, are more capable of addressing the nonlinearity and nonconvexity of the objective function, and are relatively easier to program and implement, among other advantages [3]. he application of stochastic global optimization meth- ods for solving phase equilibrium thermodynamic problems has grown considerably during last years. To date, the most popular stochastic global optimization methods have been used and applied for solving phase equilibrium thermody- namic problems, for example, simulated annealing, genetic algorithms, tabu search, diferential evolution, particle swarm optimization, and ant colony optimization (ACO) [4–15]. Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 374510, 12 pages http://dx.doi.org/10.1155/2014/374510