The mathematical model of complex countercurrent multi-effect evaporation with condensed water flash is established

which aims at minimum annual cost (including cost of fresh vapor

vacuum pump power

evaporator

maintenance and depreciation).Based on such decisive variables as the pressure of fresh vapor

the pressure of condenser and heat-transfer mean temperature difference of vari-effect

the model is solved by the complex method

Lagrangian multiplier method

iteration method and matrix method.The practical example indicates that the influence of the pressure of fresh vapor

the pressure of condenser and flash of condensed water on the optimum design results is notable.The annual cost calculated by the optimum method is decreased by about 11% against that calculated by the conventional method.The new algorithm increases the convergence speed and stability.