Optimizing UNIQUAC model parameters using an enhanced evolutionary algorithm: applications in vapor–liquid equilibrium modeling

• A new improved OPDE (IOPDE) algorithm is proposed in this work • IOPDE improves convergence and robustness using an adaptive generation jumping mechanism • Performance of DE, OPDE, and IOPDE is demonstrated to VLE modeling for binary, ternary, and quaternary systems • Delivers low % AAPE and AARD %, ensuring close match with experimental data • IOPDE outperforms DE and OPDE with 100% success rate Parameter estimation in thermodynamic models is challenging due to nonlinearity, flat objective functions near optima, poorly scaled models, and nondifferential terms. This study introduces an enhanced algorithm, the Improved Opposite Point-based Differential Evolution (IOPDE), building on the previously developed OPDE algorithm. IOPDE incorporates generation jumping guided by an adaptive Jumping Rate ( JR ) strategy to improve convergence speed, solution diversity, and robustness. The performance of Differential Evolution (DE), OPDE, and IOPDE is evaluated on vapor-liquid equilibrium (VLE) modeling problems involving binary, ternary, and quaternary systems. The least-squares approach is used for objective function minimization to estimate interaction parameters for the UNIQUAC model. Algorithm performance is assessed using metrics such as the number of function evaluations ( NFE ), success rate ( SR ), and overall acceleration rate ( AR ). Meanwhile, the quality of parameter estimation is evaluated via average absolute percentage error (% AAPE ) and average absolute relative deviation ( AARD %). Results indicate that the estimated parameters and % AAPE values either match or exceed those found in previous studies. The AARD % values indicate excellent agreement between calculated and experimental pressures in most cases. The best coefficient of determination ( R 2 ) is observed for the ternary system acetone(1) + chloroform(2) + methanol(3), confirming an excellent fit. IOPDE consistently shows high convergence speed, robustness, and a 100% success rate in most cases, excelling in high-dimensional problems. Compared to DE and OPDE, IOPDE achieves AR s of 6.19% and 2.67%, respectively. Overall, IOPDE emerges as a promising approach for robust and efficient parameter estimation in complex thermodynamic models.