  Optimization of the refrigerant circuitry can improve a heat exchanger's
performance. Design engineers currently choose the refrigerant circuitry
according to their experience and heat exchanger simulations. However, the
design of an optimized refrigerant circuitry is difficult. The number of
refrigerant circuitry candidates is enormous. Therefore, exhaustive search
algorithms cannot be used and intelligent techniques must be developed to
explore the solution space efficiently. In this paper, we formulate refrigerant
circuitry design as a binary constrained optimization problem. We use
CoilDesigner, a simulation and design tool of air to refrigerant heat
exchangers, in order to simulate the performance of different refrigerant
circuitry designs. We treat CoilDesigner as a black-box system since the exact
relationship of the objective function with the decision variables is not
explicit. Derivative-free optimization (DFO) algorithms are suitable for
solving this black-box model since they do not require explicit functional
representations of the objective function and the constraints. The aim of this
paper is twofold. First, we compare four mixed-integer constrained DFO solvers
and one box-bounded DFO solver and evaluate their ability to solve a difficult
industrially relevant problem. Second, we demonstrate that the proposed
formulation is suitable for optimizing the circuitry configuration of heat
exchangers. We apply the DFO solvers to 17 heat exchanger design problems.
Results show that TOMLAB/glcDirect and TOMLAB/glcSolve can find optimal or
near-optimal refrigerant circuitry designs after a relatively small number of
circuit simulations.
