Cuckoo Search (CS), which is a nature-inspired stochastic optimization method, has been successfully applied for estimating binary interaction parameters of universal quasichemical (UNIQUAC) and nonrandom two-liquid (NRTL) activity coefficient models for liquid liquid ternary systems involving 12 imidazolium and phosphonium ionic liquids (ILs). Thirty-nine ternary systems, comprising 371 experimental tie-lines, were correlated by the UNIQUAC and NRTL models. The results, expressed by deviations between experimental and calculated mole fractions, are very satisfactory, with global deviation values of 0.0053 (UNIQUAC) and 0.0072 (NRTL), which are 63% and 45% better than literature reported values. Three quaternary systems and one quinary system were taken from literature to compare the capability of CS algorithm with genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The global % root-mean-square deviation (RMSD) value obtained with CS algorithm was similar to 0.14-0.85% as compared to similar to 1.0-2.0% with GA and PSO algorithms. This shows a higher efficiency for the CS algorithm in solving global optimization problems involved in the thermodynamic modeling of multicomponent systems.