Design of double pipe heat exchanger structures using linear models and smart enumeration

The design of double pipe heat exchanger hairpin-based structures has been presented in the form of a mixed-integer nonlinear model (MINLM). While some metaheuristics/stochastic methods can provide good answers, the only way to guarantee global solutions of this model is by using mixed-integer nonlinear programming (MINLP). Our novel contribution focuses on globally optimal solutions obtained robustly, that is, without convergence and initialization issues. For that purpose, as an alternative to the direct solution of the original nonlinear mathematical model, we propose the use of a rigorous linear reformulation of a MINLM to a linear model (MILM). Because the reformulation is rigorous, the global optimum of the original nonlinear model is obtained using a MILP approach. Smart enumeration procedures, applicable after parametrization of the search space are applied to overcome computational obstacles associated with solving the reformulation resultant MILP. Our approach presents various novelties: parametrization, calculation of lower bounds, and Smart Enumeration, a recently introduced technique, extendable to the solution of other problems. Numerical examples illustrate the corresponding performances.