Controllability reflects the ease that a process can be controlled in practical operating environment. However, an unclear influence between the HEN synthesis and the control structure selection has been not investigated for the work of controllability of heat exchanger network (HEN). To address this challenge, this paper proposes a multi-objective optimization method by considering both the quantitative measures of economic and controllability, i.e., minimizing the total annual cost (TAC) and the relative gain array number (RGAn). This method is developed using a HEN synthesis procedure where a model-based superstructure is employed to involve the set of the network configuration alternatives and all the potential control structures. The effects of minimum approach temperature (ΔTmin) on the multi-objective optimization problem are investigated to distinguish the consistent and opposite variations of TAC and RGAn. The consistent change enables us to solve the single objective optimization problem for economical HEN design as well as for taking controllability into account. The opposite change prompts the Pareto front of the two objectives in order to develop a trade-off strategy. Results indicate that this method helps in the determination of the relationship-based nature between network configuration and control structure to yield a HEN design with economic and controllability considerations.