Performance optimization of heat transfer systems with consideration of both heat transfer and flow resistances is critical for energy conservation. This paper compares two different optimization strategies to trade off heat transfer enhancement and flow resistance reduction. One is to convert multiple objectives to a single one by some individual optimization criteria, such as minimization of entropy generation and other dimensionless entropy generation-based numbers, and the other is to select the maximum heat transfer rate or the minimum flow resistance as the objective directly and adapt the others as constraints by Pareto Optimality. After optimizing a practical multi-loop heat exchanger network (HXN), the optimized results by the former strategy with individual optimization criteria are probably unsuitable for practical operations. Nevertheless, it needs the energy conservation and heat transfer equations of all heat exchangers as the constraints, which makes the optimization more complex. Oppositely, the latter strategy provides a series of maximum heat transfer rates with different flow resistances, i.e. Pareto front, which can be applied according to different practical requirements. The equivalent thermal circuit diagram offers the systematical constraint without involving any intermediate fluid temperatures. The systematic constraint shows advantages and convenience to optimize HXN with consideration of heat transfer and flow resistance, which is pivotal and general for the synergy of heat transfer enhancement and flow resistance reduction in heat transfer system optimization. (C) 2017 Elsevier Ltd. All rights reserved.