Adaptive Partition Linearization Global Optimization Algorithm and Its Application on the Simultaneous Heat Exchanger Network and Organic Rankine Cycle Optimization

The simultaneous optimization problem of the heat exchanger network and organic Rankine cycle (HEN-ORC) poses significant challenges due to its highly nonconvex and nonlinear equations. We develop an adaptive partition linearization global optimization algorithm which is suitable for a wide range of mixed integer nonlinear programming (MINLP) problems and specially customized for HEN-ORC. The algorithm identifies convex equations of the logarithmic mean temperature function and the power function within the HEN-ORC model, which are relaxed by the first Taylor expansion and piecewise linearization. A multilevel McCormick relaxation is applied for the bilinear/multilinear functions derived from the HEN-ORC energy balance equations. The algorithm achieves global optimality by solving mixed integer linear programming and NLP submodels iteratively, enhancing the lower bound adaptively. Tested on seven heat exchanger networks and waste heat power generation cases, it outperforms two mainstream MINLP global optimization solvers (Baron and Couenne). The current best solutions are obtained for both a HEN and a HEN-ORC case, respectively.