The maximization of the energy (steam) efficiency of a multi-stage evaporator system used for concentrating the black liquor in pulp and paper mills carries immense significance in today's scenario. The nonlinear mathematical models of heptads' effect backward feed flow with various energy saving schemes namely, steam-split, feed-split, feed-preheating and their hybrid operations have been developed. The steam economy as a cost function translates the problem into a nonlinear optimal search problem. The mass and heat balance equations act as nonlinear equality constraints while vapor temperatures and liquor flows appear as inequality constraints. The formulated optimal problem has been solved efficiently using Interior-Point Method which demonstrates advantages of convergence and less sensitivity towards initial values versus conventional algorithms. The simulation results indicate that a hybrid of steam-split, feed-split and feed-preheating process arrangements with backward feed flow could provide the highest heat transfer across evaporator effects with optimum of steam economy of similar to 6.49 and consumption of similar to 1.97 kg/s. (C) 2017 Elsevier Ltd. All rights reserved.