A numerical Optimization of an Evaporative in HDH Desalination System: A Comparative Analysis of ADMM and Quadratic Programming

Evaporative systems play a crucial role in various industrial and environmental applications, offering energy-efficient cooling and humidification solutions. Optimizing these systems can significantly improve their performance and sustainability. This study compares the Alternating Direction Method of Multipliers (ADMM) and Quadratic Programming (QP) for optimizing key parameters in an evaporative system, including heat exchanger dimensions, airflow rates, water distribution, and operating temperatures. Results highlight the effectiveness of ADMM in managing complex, multi-variable constrained optimization problems, while QP provides faster convergence for specific quadratic formulations. The QP method ensures accuracy, whereas ADMM offers flexibility in handling real-world constraints. This research aims to provide insights into selecting the most suitable optimization techniques for enhancing evaporative system design and efficiency