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.

As heat exchange loads are treated as continuous variables to be optimized in heat exchanger network (HEN) problems, temperature cross could be generated in stream matches. Infeasible structures with temperature cross are penalized by penalty function method in literature. However, in random walk algorithm with compulsive evolution (RWCE) algorithm to HEN optimization, structures with temperature cross may be accepted as imperfect solutions due to its mutation operation of accepting imperfect solutions, which may negatively affect optimization process and decrease algorithm efficiency. Hence, temperature cross in HEN is firstly explained. Then negative effects of infeasible structures on optimization process of RWCE is described. A treatment method is proposed: Individuals trapped in infeasible regions are compulsively returned to their original positions in feasible regions to accept re-optimization. It was demonstrated that the proposed method improves algorithm efficiency and achieves better results than reported ones in literature.

Traditional stage-wised superstructure (SWS) of heat exchanger network allowes that utilities are placed at ends of process streams, which restricts flexible development of network structures. Hence, a novel inner utility placement strategy is proposed, in which utilities could be placed at each stream branch in intermediate stages. An improved random walk algorithm with compulsive evolution with structure-protection strategy (SP-RWCE) is employed, in which a pseudo optimum generation strategy is presented to modify SP-RWCE, where pseudo optimums with evolution potentialities could be promoted and generated to accept protection and exploitation by expanding optimal total annual cost of individuals in long-term evolution stagnation. Optimization results of three benchmark cases are superior to reported values, all of them include inner utilities. It indicates that the modified SWS enlarges solution space, the improved SP-RWCE has stronger search ability, and the placement of inner utility could effectively reduce heat exchange areas.

Individual gathering could cause decline of search ability as heuristic methods are applied to heat exchanger network (HEN) optimization. An evaluation methodology for HEN structure diversity was designed to measure degree of individual structure gathering, and guided algorithm improvement. Firstly, group division of population was performed, individuals of a certain scale with a common structure were classified as a group to get individual structure distribution. Then dispersal search strategy was proposed to give perturbation to heat exchangers randomly selected from common structure of individuals in each group except the best one, which aimed at dispersing individual structures in groups. Concentration search strategy was then proposed to enhance exploitation for excellent structure by making other individuals accept a common structure of the optimal group. Finally, two cases involving nine and fifteen streams proved that dispersal search strategy strengthened global search ability and concentration search strategy strengthened local search ability. It obtained results decreased by 7 008 $·a^-1 and 17 973 $·a^-1, respectively, compared to those obtained by original algorithm. They are superior to results in literature.