Stochastic bi-objective optimization for closed wet cooling tower systems based on a simplified analytical model

Zhiyong Wu, Zhibin Lu, Bingjian Zhang, Chang He (Corresponding Author), Qinglin Chen (Corresponding Author), Haoshui Yu, Jingzheng Ren

Research output: Journal article publicationJournal articleAcademic researchpeer-review


A fast and accurate representation of the complex heat and mass transfer processes of closed-wet cooling tower (CWCT) systems for optimal design and management is challenging, especially considering the impact of weather variability. This study develops a systematic approach for the stochastic bi-objective optimization of CWCT systems based on a simplified analytical model. The analytical model is constructed by using the effectiveness-number of transfer unit method, which is embedded in a stochastic non-linear programming model for optimizing two competing objectives, namely the specific area and the coefficient of performance. A decomposition strategy is proposed to convert the original problem into multiple bi-objective optimization sub-problems by sequentially discretizing the design and uncertain spaces. Each bi-objective optimization sub-problem is solved using an augmented e-constraint method. The resulting solutions are finally processed by an efficient multi-criteria decision-making method, namely the Technique for Order Preference by Similarity to Ideal Solution to select the preferred Pareto solution. From an illustrative case study, it is found that the stochastic approach outperforms the deterministic approach since it allows for a certain design margin of heat exchanger area to reduce the impact of the variability in weather and to avoid the risks of abnormal running cases.
Original languageEnglish
Article number123703
Publication statusPublished - 1 Jul 2022


  • Closed-wet cooling towers
  • Stochastic bi-objective optimization
  • Simplified analytical model
  • Stochastic non-linear programming
  • Decomposition strategy

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