A system for designing a circuitry configuration of heat-exchanger units includes an interface to acquire design parameters the heat-exchanger units, a memory to store computer-executable programs including a relaxed decision diagram formation module, and a processor, in connection with the memory, configured to perform the computer-executable programs. The computer-executable programs include steps of providing a configuration of the heat-exchanger units, providing the design parameters of the heat-exchanger units acquired via the interface, generating a relaxed decision diagram based on the design parameters, creating constraints with respect to connections of the heat-exchanger units according to the relaxed decision diagram, and generating feasible configurations of the heat-exchanger units by a mixed-integer-programing method using the constraints.