一种应用于换热网络综合的阻尼优化方法

doi:10.11949/0438-1157.20211681

摘要/Abstract

摘要：

针对启发式方法优化换热网络在优化后期易陷入局部极值的问题，提出一种阻尼优化方法，即通过引入延缓概率的概念，以一定的概率不接受费用下降的结构，延缓该结构形成固定匹配，避免因连续变量优化过快导致整型变量优化不充分而陷入局部最优。通过探讨不同阶段的优化特点及优化陷入局部极值的成因，进而提出分阶段延缓策略，合理调控延缓条件以及延缓概率的取值，从而提高算法的全局搜索能力。最后采用四个不同规模的算例进行验证，结果表明该方法可有效地跳出局部最优解，促进结构的进一步优化。

关键词: 换热网络, 优化, 局部极值, 延缓, 结构进化, 模型, 计算机模拟

Abstract:

Aiming at the problem that the heat exchange network optimized by the heuristic method is easy to fall into the local extreme value in the later stage of optimization, a damping optimization method is proposed, that is, by introducing the concept of delay probability, the structure with a certain probability will not accept the cost reduction, the structure will be delayed from forming a fixed structure match, and will avoid falling into local optimum due to insufficient optimization of integer variables due to too fast optimization of continuous variables. By discussing the optimization characteristics of different stages and the causes of optimization falling into local extreme, a phased delay strategy is proposed to reasonably adjust the delay conditions and the value of delay probability, to improve the global search ability of the algorithm. Finally, four different scale examples are used to verify the results. The results show that the method can effectively jump out of the local optimal solution and promote the further optimization of the structure.

Key words: heat exchanger network, optimization, local extreme, delay, structural variation, model, computer simulation

中图分类号:

TK 124

刘薇薇, 崔国民, 张璐, 肖媛, 杨其国, 张冠华. 一种应用于换热网络综合的阻尼优化方法[J]. 化工学报, 2022, 73(5): 2060-2072.

Weiwei LIU, Guomin CUI, Lu ZHANG, Yuan XIAO, Qiguo YANG, Guanhua ZHANG. Damping optimization method for heat exchange network synthesis[J]. CIESC Journal, 2022, 73(5): 2060-2072.

图/表 19

图1 有分流节点非结构模型示意图

Fig.1 Structure of nodes-based non-structural model with stream splitting

图2 RWCE算法优化流程

Fig.2 Flow chart of RWCE algorithm

图3 当前解及历史最优解的费用变化曲线

Fig.3 Cost variation of current solution and historical optimal solution

图4 TAC优化过程中的延缓机理

Fig.4 Delay mechanism in TAC optimization

图5 阻尼RWCE算法优化流程

Fig.5 Optimization process of DS-RWCE

图6 不同延缓概率下的费用变化曲线

Fig.6 Cost variation curves under different delay probabilities

表1 分阶段延缓策略在不同优化阶段延缓概率的取值

Table 1 Values of delay probability of phased delay strategy in different optimization stages

Case	it∈[0, 5×10⁷]	it∈(5×10⁷, 2×10⁸]	it∈(2×10⁸, 8×10⁸]	TAC/(USD/a)
DS2-1	η=0.6	η=0.2	η=0	1497798
DS2-2	η=0.6	η=0.2	η=0.2	1504171
DS2-3	η=0.4	η=0.2	η=0.2	1511764
DS2-4	η=0.4	η=0.2	η=0	1495453
DS2-5	η=0.2	η=0.2	η=0.2	1509360
DS2-6	η=0.2	η=0.2	η=0	1496393

表2 9SP在不同优化阶段延缓概率的取值

Table 2 Value of delay probability （η） of 9SP in different optimization stages

Case	it∈[0, 5×10⁷]	it∈(5×10⁷, 2×10⁸]	it∈(2×10⁸, 8×10⁸]	TAC/(USD/a)
RWCE	—	—	—	2898422
DS1	η=0.2	η=0.2	η=0.2	2893376
DS2	η=0.5	η=0.2	η=0	2892210

图7 9SP算例RWCE算法优化结果（TAC=2898422 USD/a）

Fig.7 Optimization results of RWCE algorithm in 9SP (TAC=2898422 USD/a)

图8 分阶段延缓策略优化9SP最优结果（TAC=2892210 USD/a）

Fig.8 9SP optimal results of phased delay strategy optimization （TAC=2892210 USD/a）

表3 9SP算例优化结果对比

Table 3 Comparison of results for 9SP

References	Method	Formulation	Units	Q_CU/MW	Q_HU/MW	TAC/(USD/a)
Linnhoff等^[30]	Pinch	—	13	33.02	25.31	2.96 × 10⁶
Fieg等^[31]	GA	NIM-SWS	14	31.34	23.62	2922298^①
霍兆义等^[32]	GA-PSO	NIM-SWS	13	31.94	24.22	2922585^①
孙涛等^[25]	RWCE	NIM-SWS	16	31.26	23.53	2920246^①
Pav?o等^[4]	SA-RFO	NIM-SWS	14	32.48	24.76	2909906^①
鲍中凯等^[33]	RWCE	IU-SWS	18	32.31	24.28	2906286^①
图7	DS1-RWCE	NNM-SS	20	31.54	23.87	2898422^①
图8	DS2-RWCE	NNM-SS	19	31.51	23.79	2892210^①

图9 20SP算例RWCE算法优化结果(TAC=1721621 USD/a)

Fig.9 Optimization results of RWCE algorithm in 20SP （TAC=1721621 USD/a）

表4 20SP在不同优化阶段延缓概率的取值

Table 4 Value of delay probability （η） of 20SP in different optimization stages

Case	it∈[0, 5×10⁷]	it∈(5×10⁷, 2×10⁸]	it∈(2×10⁸, 8×10⁸]	TAC/(USD/a)
RWCE	—	—	—	1721621
DS1	η=0.15	η=0.15	η=0.15	1717208
DS2	η=0.5	η=0.15	η=0	1714524

图10 分阶段延缓策略优化20SP最优结果(TAC=1714524 USD/a)

Fig.10 20SP optimal results of phased delay strategy optimization （TAC=1714524 USD/a)

表5 20SP算例优化结果对比

Table 5 Comparison of results for 20SP

References	Method	Formulation	Units	Q_CU/MW	Q_HU/MW	TAC/(USD/a)
陈帅等^[21]	SAA-QPSO	NS-SWS	23	4.89	9.04	1753110
韩正恒等^[27]	RWCE	NW-NSS	22	5.01	9.16	1727637
Rathjens等^[22]	HGA-SIR	NIM-SWS	24	4.38	8.53	1715088^①
图9	DS1-RWCE	NNM-SS	24	4.49	8.64	1721621^①
图10	DS2-RWCE	NNM-SS	22	4.27	8.42	1714524^①

图11 分阶段延缓策略优化16SP最优结果（TAC=6651937 USD/a）

Fig.11 16SP optimal results of phased delay strategy optimization（TAC=6651937 USD/a）

表6 16SP算例优化结果对比

Table 6 Comparison of results for 16SP

References	Method	Formulation	Units	Q_CU/MW	Q_HU/MW	TAC/(USD/a)
Huo等^[34]	GA-PSO	Mixed NS and NIM-SWS	16	442.37	38.80	7361190^①
Feyli等^[23]	GA	MQLP	17	437.77	34.21	7128522
Bao等^[35]	OP-RWCE	NW-RWCE	19	413.61	10.04	6869610^①
Pav?o等^[5]	SA-RFO	NIM-SWS	18	413.07	9.50	6712551^①
Rathjens等^[22]	HGA-SIR	NIM-SWS	18	413.02	9.70	6657080^①
图11	DS2-RWCE	NNM-SS	18	413.08	9.52	6651937^①

图12 分阶段延缓策略优化39SP最优结果（TAC=1877898 USD/a）

Fig.12 39SP optimal results of phased delay strategy optimization(TAC=1877898 USD/a)

表7 39SP算例优化结果对比

Table 7 Comparison of results for 39SP

References	Method	Formulation	Units	Q_CU/MW	Q_HU/MW	TAC/(USD/a)
Zhang等^[36]	PPSO	NS-SWS	47	11.45	8.15	1939149
孙涛等^[25]	RWCE	NIM-SWS	44	11.87	8.56	1933752^①
Nemet等^[37]	GUROBI-DICOPT	TransHEN	44	10.65	7.35	1.9288×10^6①
Pav?o等^[17]	SA-RFO	NIM-SWS	42	—	—	1900614^①
图12	DS2-RWCE	NNM-SS	40	11.02	7.72	1877898^①

参考文献 37

1	Masso A H, Rudd D F. The synthesis of system designs (Ⅱ): Heuristic structuring[J]. AIChE Journal, 1969, 15(1): 10-17.
2	Yee T F, Grossmann I E, Kravanja Z. Simultaneous optimization models for heat integration (Ⅰ): Area and energy targeting and modeling of multi-stream exchangers[J]. Computers & Chemical Engineering, 1990, 14(10): 1151-1164.
3	Yee T F, Grossmann I E. Simultaneous optimization models for heat integration (Ⅱ): Heat exchanger network synthesis[J]. Computers & Chemical Engineering, 1990, 14(10): 1165-1184.
4	Pavão L V, Costa C B B, Ravagnani M A S S. An enhanced stage-wise superstructure for heat exchanger networks synthesis with new options for heaters and coolers placement[J]. Industrial & Engineering Chemistry Research, 2018, 57(7): 2560-2573.
5	Pavão L V, Costa C B B, Ravagnani M A S S. A new stage-wise superstructure for heat exchanger network synthesis considering substages, sub-splits and cross flows[J]. Applied Thermal Engineering, 2018, 143: 719-735.
6	Zamora J M, Hidalgo-Muñoz M G, Pedroza-Robles L E, et al. Optimization and utilities relocation approach for the improvement of heat exchanger network designs[J]. Chemical Engineering Research and Design, 2020, 156: 209-225.
7	Xiao Y, Kayange H A, Cui G M. Heat integration of energy system using an integrated node-wise non-structural model with uniform distribution strategy[J]. International Journal of Heat and Mass Transfer, 2020, 152: 119497.
8	徐玥, 崔国民. 基于节点配置策略的有分流换热网络优化性能探析[J]. 化工进展, 2021, 40(7): 3608-3616.
	Xu Y, Cui G M. Analyzing optimization performance of heat exchanger network synthesis based on nodes' adjustment strategy[J]. Chemical Industry and Engineering Progress, 2021, 40(7): 3608-3616.
9	Dolan W B, Cummings P T, LeVan M D. Process optimization via simulated annealing: application to network design[J]. AIChE Journal, 1989, 35(5): 725-736.
10	Yerramsetty K M, Murty C V S. Synthesis of cost-optimal heat exchanger networks using differential evolution[J]. Computers & Chemical Engineering, 2008, 32(8): 1861-1876.
11	Silva A P, Ravagnani M A S S, Biscaia E C. Particle swarm optimisation in heat exchanger network synthesis including detailed equipment design[J]. Computer Aided Chemical Engineering, 2008, 25: 713-718.
12	Biyanto T R, Gonawan E K, Nugroho G, et al. Heat exchanger network retrofit throughout overall heat transfer coefficient by using genetic algorithm[J]. Applied Thermal Engineering, 2016, 94: 274-281.
13	肖媛, 崔国民, 李帅龙. 一种新的用于换热网络全局优化的强制进化随机游走算法[J]. 化工学报, 2016, 67(12): 5140-5147.
	Xiao Y, Cui G M, Li S L. A novel random walk algorithm with compulsive evolution for global optimization of heat exchanger networks[J]. CIESC Journal, 2016, 67(12): 5140-5147.
14	Zhang S, Luo Y Q, Ma Y J, et al. Simultaneous optimization of nonsharp distillation sequences and heat integration networks by simulated annealing algorithm[J]. Energy, 2018, 162: 1139-1157.
15	Patel J L, Rana P B, Lalwani D I. Optimization of five stage cantilever beam design and three stage heat exchanger design using amended differential evolution algorithm[J]. Materials Today: Proceedings, 2020, 26: 1977-1981.
16	Silva G P, Miranda C B, Carvalho E P, et al. A simultaneous approach for the synthesis of multiperiod heat exchanger network using particle swarm optimization[J]. The Canadian Journal of Chemical Engineering, 2018, 96(5): 1142-1155.
17	Pavão L V, Costa C B B, Ravagnani M A S S, et al. Large-scale heat exchanger networks synthesis using simulated annealing and the novel rocket fireworks optimization[J]. AIChE Journal, 2017, 63(5): 1582-1601.
18	Aguitoni M C, Pavão L V, Ravagnani M A S S. Heat exchanger network synthesis combining simulated annealing and differential evolution[J]. Energy, 2019, 181: 654-664.
19	Thuy N T P, Pendyala R, Rahmanian N, et al. Heat exchanger network optimization by differential evolution method[J]. Applied Mechanics and Materials, 2014, 564: 292-297.
20	王世豪, 田一彤, 李绍军. 基于双层优化策略的柔性换热网络同步优化方法[J]. 高校化学工程学报, 2021, 35(5): 905-914.
	Wang S H, Tian Y T, Li S J. A simultaneous synthesis based on a bi-level optimization strategy for flexible heat exchanger network[J]. Journal of Chemical Engineering of Chinese Universities, 2021, 35(5): 905-914.
21	陈帅, 罗娜. 基于抽样平均近似的双层改进粒子群算法的无分流换热网络综合[J]. 高校化学工程学报, 2018, 32(3): 620-627.
	Chen S, Luo N. Sample average approximation based double-layer improved particle swarm optimization for heat exchanger network synthesis without split streams[J]. Journal of Chemical Engineering of Chinese Universities, 2018, 32(3): 620-627.
22	Rathjens M, Fieg G. A novel hybrid strategy for cost-optimal heat exchanger network synthesis suited for large-scale problems[J]. Applied Thermal Engineering, 2020, 167: 114771.
23	Feyli B, Soltani H, Hajimohammadi R, et al. A reliable approach for heat exchanger networks synthesis with stream splitting by coupling genetic algorithm with modified quasi-linear programming method[J]. Chemical Engineering Science, 2022, 248: 117140.
24	陈子禾, 崔国民, 徐玥, 等. 基于控制参数动态协调策略的换热网络优化研究[J]. 工程热物理学报, 2020, 41(4): 957-965.
	Chen Z H, Cui G M, Xu Y, et al. Study of heat exchanger network optimization based on dynamic coordination strategy of control parameters[J]. Journal of Engineering Thermophysics, 2020, 41(4): 957-965.
25	孙涛, 崔国民, 陈家星. 一种大步长激励的结构进化策略应用于换热网络优化[J]. 化工学报, 2018, 69(7): 3135-3148.
	Sun T, Cui G M, Chen J X. A structure evolution strategy motivated by large step size for optimization of heat exchanger network[J]. CIESC Journal, 2018, 69(7): 3135-3148.
26	鲍中凯, 崔国民, 陈家星. 采用结构保护策略的强制进化随机游走算法优化换热网络[J]. 化工学报, 2017, 68(9): 3522-3531.
	Bao Z K, Cui G M, Chen J X. Optimization of heat exchanger network by random walk algorithm with compulsive evolution with structure-protection strategy[J]. CIESC Journal, 2017, 68(9): 3522-3531.
27	韩正恒, 崔国民, 肖媛. 采用结构融合策略优化换热网络[J]. 化工学报, 2019, 70(12): 4730-4740.
	Han Z H, Cui G M, Xiao Y. Optimization of heat exchanger network by structure-fusion strategy[J]. CIESC Journal, 2019, 70(12): 4730-4740.
28	韩正恒, 崔国民, 赵倩倩, 等. RWCE算法中采用单元重构策略激励换热网络结构优化[J]. 化工学报, 2021, 72(6): 3316-3327.
	Han Z H, Cui G M, Zhao Q Q, et al. Impelling structural optimization of heat exchanger network by unit-reconfiguration strategy in RWCE algorithm[J]. CIESC Journal, 2021, 72(6): 3316-3327.
29	Pavão L V, Costa C B B, Ravagnani M A S S, et al. Costs and environmental impacts multi-objective heat exchanger networks synthesis using a meta-heuristic approach[J]. Applied Energy, 2017, 203: 304-320.
30	Linnhoff B, Ahmad S. Cost optimum exchanger networks (1): Minimum energy and capital using simple methods for capital cost[J]. Computer Chemical Engineering. 1990, 14: 729-750.
31	Fieg G, Luo X, Jeżowski J. A monogenetic algorithm for optimal design of large-scale heat exchanger networks[J]. Chemical Engineering and Processing: Process Intensification, 2009, 48(11/12): 1506-1516.
32	霍兆义, 尹洪超, 赵亮. 有分流换热网络同步综合[J]. 大连理工大学学报, 2013, 53(1): 45-50.
	Huo Z Y, Yin H C, Zhao L. Simultaneous synthesis of heat exchanger network with stream splits[J]. Journal of Dalian University of Technology, 2013, 53(1): 45-50.
33	鲍中凯, 崔国民, 曹冲, 等. 基于公用工程内置策略的换热网络优化[J]. 计算物理, 2019, 36(6): 707-718.
	Bao Z K, Cui G M, Cao C, et al. Heat exchanger network optimization based on inner utility placement strategy[J]. Chinese Journal of Computational Physics, 2019, 36(6): 707-718.
34	Huo Z Y, Zhao L, Yin H C, et al. Simultaneous synthesis of structural‐constrained heat exchanger networks with and without stream splits[J]. The Canadian Journal of Chemical Engineering, 2013, 91(5): 830-842.
35	Bao Z K, Cui G M, Chen J X, et al. A novel random walk algorithm with compulsive evolution combined with an optimum-protection strategy for heat exchanger network synthesis[J]. Energy, 2018, 152: 694-708.
36	Zhang C W, Cui G M, Chen S. An efficient method based on the uniformity principle for synthesis of large-scale heat exchanger networks[J]. Applied Thermal Engineering, 2016, 107: 565-574.
37	Nemet A, Isafiade A J, Klemeš J J, et al. Two-step MILP/MINLP approach for the synthesis of large-scale HENs[J]. Chemical Engineering Science, 2019, 197: 432-448.

[1]	杨欣, 王文, 徐凯, 马凡华. 高压氢气加注过程中温度特征仿真分析[J]. 化工学报, 2023, 74(S1): 280-286.
[2]	宋嘉豪, 王文. 斯特林发动机与高温热管耦合运行特性研究[J]. 化工学报, 2023, 74(S1): 287-294.
[3]	连梦雅, 谈莹莹, 王林, 陈枫, 曹艺飞. 地下水预热新风一体化热泵空调系统制热性能研究[J]. 化工学报, 2023, 74(S1): 311-319.
[4]	金正浩, 封立杰, 李舒宏. 氨水溶液交叉型再吸收式热泵的能量及分析[J]. 化工学报, 2023, 74(S1): 53-63.
[5]	刘远超, 关斌, 钟建斌, 徐一帆, 蒋旭浩, 李耑. 单层XSe₂（X=Zr/Hf）的热电输运特性研究[J]. 化工学报, 2023, 74(9): 3968-3978.
[6]	李科, 文键, 忻碧平. 耦合蒸气冷却屏的真空多层绝热结构对液氢储罐自增压过程的影响机制研究[J]. 化工学报, 2023, 74(9): 3786-3796.
[7]	何松, 刘乔迈, 谢广烁, 王斯民, 肖娟. 高浓度水煤浆管道气膜减阻两相流模拟及代理辅助优化[J]. 化工学报, 2023, 74(9): 3766-3774.
[8]	王浩, 王振雷. 基于自适应谱方法的裂解炉烧焦模型化简策略[J]. 化工学报, 2023, 74(9): 3855-3864.
[9]	陈哲文, 魏俊杰, 张玉明. 超临界水煤气化耦合SOFC发电系统集成及其能量转化机制[J]. 化工学报, 2023, 74(9): 3888-3902.
[10]	齐聪, 丁子, 余杰, 汤茂清, 梁林. 基于选择吸收纳米薄膜的太阳能温差发电特性研究[J]. 化工学报, 2023, 74(9): 3921-3930.
[11]	邢雷, 苗春雨, 蒋明虎, 赵立新, 李新亚. 井下微型气液旋流分离器优化设计与性能分析[J]. 化工学报, 2023, 74(8): 3394-3406.
[12]	于旭东, 李琪, 陈念粗, 杜理, 任思颖, 曾英. 三元体系KCl + CaCl₂ + H₂O 298.2、323.2及348.2 K相平衡研究及计算[J]. 化工学报, 2023, 74(8): 3256-3265.
[13]	张曼铮, 肖猛, 闫沛伟, 苗政, 徐进良, 纪献兵. 危废焚烧处理耦合有机朗肯循环系统工质筛选与热力学优化[J]. 化工学报, 2023, 74(8): 3502-3512.
[14]	诸程瑛, 王振雷. 基于改进深度强化学习的乙烯裂解炉操作优化[J]. 化工学报, 2023, 74(8): 3429-3437.
[15]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.