The power consumption of a single mixed-refrigerant process (PRICO (R)) for natural gas liquefaction was minimized using four different constraint formulations to handle the trade-off between investment and operating costs. Aspen HYSYS (R) VR was used for process simulation, while a sequential quadratic programming algorithm (NLPQLP) was used for optimization. The results confirm that optimal utilization of the heat exchanger area is only obtained with a constraint based on a maximum heat exchanger conductance (UA). The minimum temperature difference constraint commonly used in process design gives a significant energy penalty as it is incapable of accounting for the distribution of driving forces with respect to temperature, the nonlinearity of the composite curves and the trade-off between driving forces and cooling load. The results also indicate that the maximum UA constraint leads to increased complexity of the optimization problem, and that the success rate of the optimization method used therefore is reduced. (C) 2016 American Institute of Chemical Engineers AIChE J, 62: 3598-3610, 2016