A constrained grey prediction evolution algorithm for calculating two-phase equilibria at given volume, temperature, and moles

Traditional methods for solving phase equilibrium problems at given volume, temperature, and moles (NVT-flash) exhibit sensitivity to initial values and require complex derivative calculations. In contrast, emerging constrained methods based on heuristic algorithms overcome these drawbacks. However, computational efficiency becomes a significant concern when applying heuristic algorithms to an optimization problem. To address this challenge, this paper proposes a more efficient constrained grey prediction evolution algorithm (CGPE), which adds the constraints handling of the NVT-flash problem to the original operation of the grey predictive algorithm. This algorithm takes the moles vector and volume of a certain phase as the decision variables and aims to minimize the total Helmholtz free energy. A direct search method and an exterior point method are adopted to deal with the constraints of the NVT-flash problem. The effectiveness of CGPE in solving the NVT-flash problem is demonstrated on various numerical tests of pure substances, binary and ternary mixtures. The competitiveness of CGPE in handling the NVT-flash problem is demonstrated through comparative data analysis with other advanced algorithms. The success of CGPE can inspire the development of more efficient heuristic algorithms to tackle the NVT-flash problem, thereby promoting advancements in the phase equilibria computation domain.