“…(10), (11), where HFCP ex and CFCP ex are heat-flow capacities (the multiplication between heat capacity and flow-rate) of hot stream and cold stream in exchanger ex, and variables of heat transfer differences (HBA ex and HBB ex ) should be small and the objective function will be formulated to minimize the sum of this infeasibility in energy balances HBA ex P HFCP ex  ðHTI ex À HTO ex Þ À EXA ex  U ex  LMTD 0 ex ; 8ex 2 EX ð10Þ HBB ex P EXA ex  U ex  LMTD 0 ex À HFCP ex  ðHTI ex À HTO ex Þ; 8ex 2 EX ð11Þ Eqs. (12)- (15) show the differences of energy balances in exchangers, where AEB ex and BEB ex are positive and should be small, EX ec&sh is the set of all economisers and superheaters, EX ev is the set of all evaporators, CF ex is flow rate of cold stream in an evaporator, and CHI ex and CHO ex are enthalpy of inlet and outlet cold streams in an evaporator. AEB ex P HFCP ex  ðHTI ex À HTO ex Þ À CFCP ex  ðCTO ex À CTI ex Þ; 8ex 2 EX ec&sh ð12Þ BEB ex P CFCP ex  ðCTO ex À CTI ex Þ À HFCP ex  ðHTI ex À HTO ex Þ; 8ex 2 EX ec&sh ð13Þ AEB ex P HFCP ex  ðHTI ex À HTO ex Þ À CF ex  ðCHO ex À CHI ex Þ; 8ex 2 EX ev ð14Þ BEB ex P CF ex  ðCHO ex À CHI ex Þ À HFCP ex  ðHTI ex À HTO ex Þ;…”