Considering that differential evolution algorithm (DE) is sensitive to the selection of control parameters and population diversity's decrease leads to the loss of power as DE is applied in heat exchanger network (HEN), a weighted differential evolution algorithm (WDE) is applied in this study. Effectiveness of the algorithm has been proved in continuous variable optimization. This study applies it in mixed integer nonlinear programming problems of HEN without controlling parameters. Three cases ranging from small to medium testify the effectiveness of WDE. By setting up equal mutation factor and analyzing its distribution, we explore WDE's optimization mechanism which provides reference for algorithm improvements.

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.

To avoid the problem of being disturbed by stochastic acceptance of imperfect solution for evolution process of individual optimal solution existing in optimization of heat exchanger network by random walk algorithm with compulsive evolution, an improved RWCE based on trilevel protection strategy is proposed. Individuals in population are divided into three levels. The lower-level is optimized by basic RWCE to protect global search ability of individuals. The middle-level reads historical optimal solution of the lower-level's individuals, and optimized by RWCE with fine tuning to protect evolution process of each individual's optimal solution from disruption. All individuals in the upper-level are initialized by solution of the best individuals in the middle-level, and optimized by RWCE with automatic fine search to ensure that the best individuals are fully searched. Finally, result of the upper-level is passed to corresponding individual at the lower-level. Two cases are optimized by using the algorithm,and results are better than those in literature. Evolution process of individual optimal solution is protected while accepting imperfect solution, therefore, both global search ability and local search ability are realized.

Optimization in random walking algorithm with compulsive evolution (RWCE) for heat exchanger network synthesis (HENS) turns to slow down in late evolution as heat load of all heat exchangers are optimized simultaneously. A random walk algorithm with compulsive evolution combined with restrictive-evolution strategy for heat unit (RS-RWCE) is proposed, in which number of evolved heat units in HEN is restricted in each random walk evolution to keep fast convergence of total annual cost in early evolution process and fine search in late evolution process. Specific examples are applied to verify high computational efficiency and accuracy of the strategy. It gives consideration to integer variable and continuous variable. The results are encouraging.

Particle swarm optimization (PSO) algorithm has strong ability to explore global optimal region for heat exchanger networks synthesis. However, particles may trap into local optima and converge prematurely in late evolution. Therefore, an improved particle swarm optimization algorithm based on diversity feedback and real-time updating strategy is proposed. Firstly, index of population health degree is established to evaluate population diversity during evolution. Secondly, a random perturbation strategy and a centrifugal strategy are combined respectively with PSO algorithm to enrich population diversity and enhance global search ability. Furthermore, gradient search strategy is applied to search efficiently local optima and improve computational efficiency of PSO algorithm. Finally, a feedback mechanism of population health degree is proposed to real-time monitor health status of population and further to adopt different update strategies for keeping particles healthy during evolution. The method was applied to several cases taken from literature and results are encouraging. They are better than those of other improvements for PSO.

Generally, differential evolution (DE) algorithm is easily stuck into local optima as well as suffers from low convergence accuracy when employed for optimization of heat exchanger network. To solve these issues, an opposition-based multi-population parallel differential evolution algorithm is proposed. Firstly, opposite population is built by using initial population. Then, new generation of individuals are generated through information exchange, which is produced by mutated operation between opposite population and its original correspondence. The final step is to retain evolution of multi-population in parallel by applying multi-round opposites, so that the population is enable to keep current solution information and search new solutions in a larger space as well. Computing results of improved DE algorithm on 9sp and 15sp suggests that the method improves population diversity, jumps out local optima and at the same time achieves higher speed and accuracy.