A master–slave solving method with adaptive model reformulation technique for water network synthesis using MINLP

A unified mixed-integer nonlinear programming (MINLP) model is developed for process synthesis of integrated water networks, where water-using processes and treatment operations are combined in a single network. Pump and pipe costs and different treatment technologies can also be included in the unified MINLP model. A master–slave solving method is proposed along with a heuristic method dealing with integer variables in the outer loop and a gradient-based method optimizing nonlinear programming (NLP) in the inner loop. An adaptive model reformulation module is developed in the middle layer to bridge the inner and outer loops. By exploiting the structure knowledge of the MINLP model for the water network (WN) synthesis, this module automatically simplifies the NLP model in both dimensionality and complexity. It helps to generate the most concise NLP model for the inner loop optimization. Good performance of the proposed method is demonstrated through examples.

► We model the water network synthesis as a unified mixed-integer nonlinear programming. ► We propose a master–slave solving method with adaptive model reformulation for WN synthesis. ► The most concise sub-NLPs can be generated by using the adaptive model reformulation technique.