Optimization of a heat exchanger network superstructure using nonlinear programming

A heat exchanger network design for a particular set of hot and cold stream duties requires multiple stream splits for minimum energy use. A modern NLP solver, FilterSQP, is applied to minimize a total cost function that takes account of capital and energy costs. The best solution contains fewer exchangers than the initial network. There are multiple local optima at various cost levels. They contain different subsets of exchangers of the initial design, which constitutes a partial superstructure for the problem. Several optimization alternatives are examined: for the model formulation, leading to problems with different optimum costs, for the way the objective is written, which affects the formal degree of nonlinearity in the equations or objective, and for the way the solver operates. For each combination of options, tests were run using widely different initial values for the Trust Region size, a parameter in the solver. FilterSQP solved the network with impressive reliability and efficiency from several starting guesses, some of which were highly arbitrary. From even the most unpromising initial guesses, the solver converged to a local optimum in nearly all cases.