There is an infeasible structure in heat exchanger network optimization in which matching temperatures of cold and hot streams are crossed. Replacing matching by internal utilities is a way to deal with infeasible structure and its solution domain can be expanded. This approach introduces additional fixed investment costs in total annual cost which may be accepted in weaker solutions, which may cause a decrease of optimization efficiency. Therefore, we analyze firstly probable bad influence caused by internal utilities and propose an evolutionary strategy for internal utilities. Total annual cost of the solution which has internal utilities are punished to reduce the accepting probability. If the solution with internal utilities still exist, then heat loads of internal utility exchangers are forced to evolve to optimize the heat load and improve its structure. Effectiveness of the strategy is verified with two examples.

Based on the fifth order dissipative compact spatial finite difference scheme(DCS5) and the seven stage Runge-Kutta time integration scheme, with the principle that numerical amplification factor approaches the real amplification factor optimally, an optimal methodology for time integration scheme is proposed and a seven stage fifth order LDDRK scheme is obtained. Numerical results of onedimensional wave propagation obtained by convection equation and linearized Euler equations show that the proposed LDDRK scheme has lower dissipation than standard Runge-Kutta schemes.