For the fixed total raw material cost and based on constructal theory and finite time thermodynamics, a BFIM (blast furnace iron-making) process is optimized by taking a complex function as optimization objective. The complex function is integrated with HM (hot metal) yield and useful energy of the BF (blast furnace). The optimal cost distribution of raw materials (namely "generalized optimal construct") is obtained. The effects of some parameters, such as oxygen enrichment, blast temperature and pulverized coal dosage, on the optimization results are analyzed. The results show that the HM yield, useful energy and complex function are, respectively, increased by 3.13%, 2.66% and 2.90% after generalized constructal optimization. The utilization efficiencies of the BFG (blast furnace gas) and slag are 41.3% and 57.1%, respectively, which means that the utilization potentials of the BFG and slag can be further exploited. Increasing pulverized coal dosage and decreasing the agglomerate ratio can increase the complex function. The performance the BFIM process can be improved by adjusting the oxygen enrichment, blast temperature, blast dosage, pressure ratio of the Brayton cycle's air compressor and relative pressure drop of the air compressor inlet to their optimal values, respectively, which are new findings of this paper. (C) 2016 Elsevier Ltd. All rights reserved.