As random walk algorithm with compulsive evolution is used to optimize heat exchange network, the structure with lower annual cost in continuous variable evolution stage is destroyed by integer variable evolution operation. As a result, the structure formed after the evolution of continuous variables can not play its full advantages, which restricts the evolution of continuous variables. We propose an optimization strategy of separating continuous variables and integers to protect the effective structure, thereby, protecting structures with development potential and reducing the combined annual cost further. In example study our result is better than that in literature. Precision of the algorithm is improved, and validity of the strategy is verified.

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.

As nodes-based nonstructural model with stream splits (NNM-SS) applied in heat exchanger network synthesis, optimization may be trapped in local optima due to the difficult in generating suitable structures with stream splits. Structural perturbation strategy is proposed and is added into random walk algorithm with compulsive evolution (RWCE-SS). During optimization, a heat exchanger without stream splits is chosen under a certain probability, and then generating a new substream structure on its position to add the number of stream splits in the network. Optimization results obtained by retrofitted algorithm are better than those in literatures.

To solve the problem that the forced evolutionary random walk algorithm (RWCE) falls into local optimization and reduces search ability in the later stage of optimization,a strategy of combining periodic dominance structure extraction with search path enhancement is proposed. Firstly,population of the system is preliminarily optimized,and the dominant individuals are extracted in certain period.Then these dominant individuals are replicated by multiple paths to other individuals. Finally,according to the search mechanism,they are spread all over the whole solution domain. It shows that the multi-path search strategy centered on dominant individuals improves accuracy of local optimization,increases diversity of population,enhances global search ability,and improves efficiency and quality of optimization.

As node-wise non-structural superstructure model is applied to heat exchanger network optimization, heat exchanger crossover may appear. It is found that crossover structure causes an increase of total heat transfer area for heat exchange unit with same heat loads. At the same time, it reduces obviously computational efficiency of the algorithm. A vertical node-wise non-structural superstructure model is established. Compared with node-wise non-structural superstructure, the vertical node-wise non-structural superstructure model reduces computational complexity in the optimization process and eliminates adverse effects of crossover structure, which improves efficiency and accuracy of optimization. Finally, optimization performance of RWCE algorithm based on vertical non-structural superstructure model is analyzed in two examples. The results are superior to those in literature.

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.

In view of structural evolution difficulty caused by integer variables in heat exchanger network with fixed investment cost, a fixed investment cost relaxation strategy is proposed. It simplifies mathematical model of the problem by relaxing fixed investment cost. As heat exchanger is very small, fixed investment cost is almost zero. With increase of heat exchanger, fixed investment cost is gradually increased with a certain slope, and finally equals to the actual value. Controlling the change slope by the relaxation strength coefficient, on the basis of ensuring reliability of optimization results, heat exchangers with structural evolutionary obstacles are guided to generate or eliminate. The strategy is used to two cases in the literature, and effect of this strategy on generation or elimination of heat exchanger under different relaxation strength is investigated. Finally, a random walk algorithm with compulsive evolution based on fixed investment cost relaxation strategy is proposed. The algorithm is applied to a heat transfer network case. The result is superior to existing literature.

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.

Aiming at popularing diversity is disappared or other reasons in the later stage of optimiging heat exchanger network synthesis problem, it is difficult to find direction of evolution which makes total annual cost further reduce in optimization. A coupling evolution strategy of heat exchanger was proposed. In later stage of heuristic algorithm optimization, heat exchangers with no heat load are taken into coupled evolution by a certain probability distribution, to find coupling match to reduce cost. It shows that the strategy is effective. The strategy was combined with RWCE algorithm to form a hybrid algorithm. Firstly, RWCE algorithm was used to explore solution domain to find potential solutions by its strong global searching ability. Secondly, the coupled evolution strategy is applied to further optimize for these explored solutions. Thirdly, the further optimized solutions are fed back to RWCE algorithm after mutated. The hybrid algorithm is applied to 10SP2 and 15SP, and better optimization results are obtained.

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.

Due to non-convex and non-continuous complexity of MINLP problems, heuristic methods are subject to numerous local optima. A novel random walking algorithm with compulsive evolution (RWCE) is an efficient global optimization method for HENS, where probability δ of accepting imperfect network is able to keep population diversity and jump out of local optima effectively during evolution process. In this paper, strong ability of parameter δ to detect promising structure is proved. Structure of evolution process is compared and analyzed under different parameters. Furthermore, a strategy for accepting imperfect network oriented with number of heat exchangers is proposed to improve computational time and evolution ability of optimization. The strategy was applied to several cases taken from literature. It shows better performance of global optimization.

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.

An improved chaotic ant swarm algorithm, which synthesizes simultaneously heat exchanger network well, is proposed. Organization variables update strategy and novel dynamic neighborhood topology are introduced to enhance global search ability and local search ability of the algorithm. Two strategies of integer variables are proposed to optimize integer variables represented by heat exchangers. Two heat exchanger network problems with different scale are selected to test the algorithm. Obtained solutions are better than solutions published in literature, which indicates robustness and effectiveness of the algorithm.

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.

For optimization problem of heat integration system, serious nonlinear and non-convex heat exchanger network belonging to multi-extremum and multi-dimensional problems are considered. Dynamic multi-agent differential evolution algorithm is provided to solve the problem. It makes use of sensing capability of multi-agent with dynamic update strategy, which improves formation mechanism of population and mutation mechanism of differential evolution algorithm and globle searching ability in large scale nonlinear system. The algorithm was applied to 10SP2 and 9SP1 cases of heat exchanger network problems. Better total annual cost is obtained, which indicates better globle searching ability of the algorithm.

By analyzing mechanism of premature phenomenon in particle swarm optimization (PSO), we found nature of premature convergence and proposed a "leap" strategy to jump out of local minimum, making halted particles "renewed" when they are trapped into a local optimum. The strategy is applied to nonlinear programming and results are encouraging. The improved PSO solves efficiently premature convergence of the algorithm applying in nonlinear optimizations and improves global search ability of PSO.

In a one-dimensional radiation transfer model, energy distribution and spectral absorption mechanism of greenhouse effect under Pre-Industrial and current atmospheric compositions were analyzed. Coupling mechanism between greenhouse effect and surface temperature was investigated on the basis of greenhouse gas concentrations at current level. It shows that warm environment before Industrial Revolution is mainly due to three strong absorption bands of greenhouse gases, which are (100-370)cm^-1, (640-710)cm^-1 and (1370-2000)cm^-1 respectively. However, current global warming is originated from weak absorption bands of greenhouse gases, that is, radiation absorptions by (370-640)cm^-1 and (710-1370)cm^-1. Contributions to greenhouse effect increment of these weak bands after Industrial Revolution are 25% and 55% respectively. With rising temperature, contribution of right side of the earth's radiation peak wavenumber to total greenhouse effect shows positive change, while contribution of left side shows negative change.