Parallel evolutionary and mass-heat analogy optimization method of mass exchange network

doi:10.11949/0438-1157.20241337

Abstract

Abstract:

Based on the analogy between mass and heat exchange processes, devices and networks, the mass-energy network analogy optimization can be used to analogize the mass exchange network with small-scale characteristics to the generalized heat exchange network, effectively expanding the solution domain and improving the global optimization quality. However, this method has not yet fully considered the optimal network structures of different individuals of the generalized heat exchange network in different evolutionary periods, and there is still much room for improvement of its global and local optimization performance. To this end, a synchronous analogy and parallel evolution strategy for the generalized heat exchange network and the mass exchange network was established to achieve the real-time regression of the local optimal structure of the generalized heat exchange network to the mass exchange network, and further global and local optimization was implemented in the parallel evolution layer. The analysis of the results of phenol removal and ammonia removal shows that the mass-heat analogy and parallel evolution can give full play to the global search capability of the generalized heat exchanger network in a larger solution domain, and take into account the local optimum accuracy through parallel evolution, providing a more effective method for mass exchange network synthesis.

Key words: mass exchange network, mass-heat analogy, generalized heat exchanger network, global optimization

摘要：

基于质量和能量交换过程、设备和网络的比拟关系，采用质-能网络比拟优化可将小尺度特征的质量交换网络比拟为广义换热网络，有效地扩大求解域，提升全局优化质量。然而，该方法尚未充分考虑广义换热网络的不同个体在不同进化时期的最优网络结构，其全局和局部优化性能仍有较大的提升空间。为此，建立了广义换热网络和质量交换网络的同步比拟和平行进化策略，实现广义换热网络的局部最优结构实时回归至质量交换网络，并至平行进化层实施进一步的全局和局部优化。空气除氨和废水脱酚算例的应用结果表明，质-能系统比拟与平行进化可充分发挥广义换热网络在更大求解域内的全局搜索能力，并通过平行进化兼顾局部最优精度，为质量交换网络综合提供更有效的方法。

关键词: 质量交换网络, 质-能比拟, 广义换热网络, 全局优化

CLC Number:

TQ 021.8

Yi CHEN, Yuan XIAO, Guomin CUI. Parallel evolutionary and mass-heat analogy optimization method of mass exchange network[J]. CIESC Journal, 2025, 76(6): 2755-2769.

陈怡, 肖媛, 崔国民. 质量交换网络的质-能系统比拟与平行进化[J]. 化工学报, 2025, 76(6): 2755-2769.

Figures/Tables 24

Fig.1 Mass exchange network diagram

Fig.2 Mass transfer process inside a mass exchanger

Table 1 The analogy of different mass transfer equipment

传质设备	比拟关系Ⅰ	比拟关系Ⅱ
填料塔	$\frac{A}{a m_{p}} = \frac{1}{ρ} C_{1}$	$K_{m, p} = \frac{K_{w}}{a}$
板式塔	$\frac{A}{μ_{0} N} = \frac{1}{ρ} C_{1}$	$K_{m, t} = \{\begin{matrix} \frac{G_{i} L_{j} l n (\frac{L_{j}}{m_{i, j} G_{i}})}{(L_{j} - m_{i, j} G_{i}) μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} \neq 1 \\ \frac{G_{i}}{μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} = 1 \end{matrix}$

Table 1 The analogy of different mass transfer equipment

传质设备	比拟关系Ⅰ	比拟关系Ⅱ
填料塔	$\frac{A}{a m_{p}} = \frac{1}{ρ} C_{1}$	$K_{m, p} = \frac{K_{w}}{a}$
板式塔	$\frac{A}{μ_{0} N} = \frac{1}{ρ} C_{1}$	$K_{m, t} = \{\begin{matrix} \frac{G_{i} L_{j} l n (\frac{L_{j}}{m_{i, j} G_{i}})}{(L_{j} - m_{i, j} G_{i}) μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} \neq 1 \\ \frac{G_{i}}{μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} = 1 \end{matrix}$

Table 2 Stream data in case R5S3

流股	流量上限/ (kg/s)	入口浓度/ (kg/kg)	出口浓度/ (kg/kg)	m_i,j	b_i,j	C₀_j
K_w=0.02 kg NH₃/(s∙kg)；f_C,p=139.05；α=0.66
R1	2.00	0.0050	0.0010	—	—	—
R2	4.00	0.0050	0.0025	—	—	—
R3	3.50	0.0110	0.0025	—	—	—
R4	1.50	0.0100	0.0050	—	—	—
R5	0.50	0.0080	0.0025	—	—	—
S1	1.80	0.0017	0.0071	1.20	0	0
S2	1.00	0.0025	0.0085	1.00	0	0
S3	∞	0	0.0170	0.50	0	0.001

Table 3 Stream data and analogy data in case H5C3

流股		热容流率上限/[J/(kg/s)]	入口温度/ ℃	出口温度/℃
H1		20.00	200.00	40.00
H2		40.00	200.00	100.00
H3		35.00	440.00	100.00
H4		15.00	400.00	200.00
H5		5.00	320.00	100.00
C1		18.00	81.60	340.80
C2		10.00	100.00	340.00
C3		50.00	0	340.00
比拟参数
C_max	T_max	a	c_p	ρ	C₀
0.0100	400.00	100	10	1000	1.4

Table 4 The parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g_,X	δ	NP
GHEN	Q	100.0000	5.00000	0.2850	100.000	0.001	0.010	10
	SP	0.0300	0.01000	0.0150	1.000
	Fc_p	0.0500	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.001	10
	SPM	0.0300	0.01000	0.0600	1.000
	L	0.0300	0.02000	0.1000	0.500

Fig.3 The structure diagram of mass exchange network

Fig.4 Comparison of optimization results for the same individuals at different iteration steps

Fig.5 The structure diagram of mass exchange network

Fig.6 Comparison of optimization results at the same number of iteration steps for different individuals

Fig.7 The structure diagram of mass exchange network

Fig.8 The conceptual diagram of mass-heat analogy and parallel evolution method

Fig.9 Mass-heat analogy and parallel evolution method flowchart

Table 5 Stream data in case R2S3

流股	流量上限/ (kg/s)	入口浓度/ (kg/kg)	出口浓度/ (kg/kg)	m_i.j	b_i.j	C₀_j
f_C,N=4552 USD/(块·a)
R1	2.00	0.0500	0.0100	—	—	—
R2	1.00	0.0300	0.0060	—	—	—
S1	5.00	0.0050	0.0150	2.00	0	0
S2	3.00	0.0100	0.0300	1.53	0	0
S3	∞	0.0013	0.0150	0.71	0.001	0.010

Table 6 Stream data and analogy data in case H2C3

流股	热容流率上限/(J/(kg·s))	入口温度/℃		出口温度/℃
H1	20.00	1000.00		200.00
H2	10.00	600.00		120.00
C1	50.00	200.00		600.00
C2	30.00	306.00		918.00
C3	10.00	38.46		233.00
比拟参数
C_max	T_max	μ₀	c_p	ρ	C₀
0.0100	200.00	10000	10	1000	0.8

Table 7 Parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g,_X	δ
GHEN	Q	100.0000	10.00000	0.4000	100.000	0.005	0.020
	SP	0.0300	0.01000	0.1000	1.000
	$F C_{p N_{S}}$	0.5000	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.002
	SPM	0.0300	0.01000	0.0600	1.000
	$L_{N_{S}}$	0.0500	0.02000	0.0001	0.500

Table 7 Parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g,_X	δ
GHEN	Q	100.0000	10.00000	0.4000	100.000	0.005	0.020
	SP	0.0300	0.01000	0.1000	1.000
	$F C_{p N_{S}}$	0.5000	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.002
	SPM	0.0300	0.01000	0.0600	1.000
	$L_{N_{S}}$	0.0500	0.02000	0.0001	0.500

Fig.10 The structure diagram of mass exchange network

Table 8 Comparison results of case R2S3

文献	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)
[24]	6	28	345416
[8]	7	28	338168
[25]	7	28	333300
[18]	7	21	329503
[21]	6	24	321800
本文（图11）	6	21	318362
本文（图10）	6	22	317013

Table 8 Comparison results of case R2S3

文献	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)
[24]	6	28	345416
[8]	7	28	338168
[25]	7	28	333300
[18]	7	21	329503
[21]	6	24	321800
本文（图11）	6	21	318362
本文（图10）	6	22	317013

Table 9 Comparison of optimization results for case R2S3 at different population sizes

算例	种群规模	C $_{T A}^{M, t}$ /(USD/a)	单元个数	总塔板数	迭代次数/步
R2S3	10	321086	6	22	4.17×10⁷
	20	321623	6	22	2.78×10⁷
	40	321766	7	27	1.39×10⁷
	60	325406	7	22	9.43×10⁶
	80	318362	6	21	6.88×10⁶
	100	334429	6	24	4.92×10⁶

Table 9 Comparison of optimization results for case R2S3 at different population sizes

算例	种群规模	C $_{T A}^{M, t}$ /(USD/a)	单元个数	总塔板数	迭代次数/步
R2S3	10	321086	6	22	4.17×10⁷
	20	321623	6	22	2.78×10⁷
	40	321766	7	27	1.39×10⁷
	60	325406	7	22	9.43×10⁶
	80	318362	6	21	6.88×10⁶
	100	334429	6	24	4.92×10⁶

Fig.11 The structure diagram of mass exchange network

Table 10 The optimization results for R2S3 case study with different accepting imperfect solution

δ_M	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)	优化时间/s
0	5	24	334660	431764
0.100	7	22	321536	436478
0.010	6	23	319785	434416
0.001	6	24	321136	430204
0.002	6	22	317073	374296

Table 10 The optimization results for R2S3 case study with different accepting imperfect solution

δ_M	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)	优化时间/s
0	5	24	334660	431764
0.100	7	22	321536	436478
0.010	6	23	319785	434416
0.001	6	24	321136	430204
0.002	6	22	317073	374296

Fig.12 The optimal TAC decline curve for MEN optimization process with different accepting imperfect solution

Fig.13 The structure diagram of mass exchange network

Table 11 Comparison results of case R5S3

文献	单元数	C $_{T O}^{M, p}$ /(USD/a)	C $_{T C}^{M, p}$ /(USD/a)	C $_{T A}^{M, p}$ /(USD/a)
[27]	8	85203	48797	134000
[8]	7	82410	50913	133323
[28]	9	—	—	132101
[29]	9	81301	48599	129900
[30]	8	73350	47367	120717
[26]	9	77508	50299	127807
本文（图7）	9	78338	47823	126161
本文（图13）	9	78338	47773	126148

Table 11 Comparison results of case R5S3

文献	单元数	C $_{T O}^{M, p}$ /(USD/a)	C $_{T C}^{M, p}$ /(USD/a)	C $_{T A}^{M, p}$ /(USD/a)
[27]	8	85203	48797	134000
[8]	7	82410	50913	133323
[28]	9	—	—	132101
[29]	9	81301	48599	129900
[30]	8	73350	47367	120717
[26]	9	77508	50299	127807
本文（图7）	9	78338	47823	126161
本文（图13）	9	78338	47773	126148

References 30

[1]	裴宏斌, 陈理, 都健, 等. 进出口流率变化的多组分质量交换网络综合方法研究[J]. 大连理工大学学报, 2008, 48(6): 793-799.
	Pei H B, Chen L, Du J, et al. Study of multi-component mass exchange network synthesis with variable flowrates of inlet and outlet[J]. Journal of Dalian University of Technology, 2008, 48(6): 793-799.
[2]	杨友麒. 质量交换网络[J]. 化工进展, 2007, 26(2): 284-289.
	Yang Y Q. Mass exchange networks[J]. Chemical Industry and Engineering Progress, 2007, 26(2): 284-289.
[3]	Linnhoff B, Hindmarsh E. The pinch design method for heat exchanger networks[J]. Chemical Engineering Science, 1983, 38(5): 745-763.
[4]	El-Halwagi M M, Manousiouthakis V. Synthesis of mass exchange networks[J]. AIChE Journal, 1989, 35(8): 1233-1244.
[5]	Gadalla M A. A new graphical-based approach for mass integration and exchange network design[J]. Chemical Engineering Science, 2015, 127: 239-252.
[6]	Yanwarizal, Oladosu W A, Wan Alwi S R, et al. A new graphical approach for simultaneous targeting and design of mass exchange networks[J]. Computers & Chemical Engineering, 2020, 142: 107061.
[7]	Papalexandri K, Pistikopoulos E, Floudas A. Mass exchange networks for waste minimization: a simultaneous approach: process design[J]. Chemical Engineering Research & Design, 1994, 72: 279-294.
[8]	Isafiade A J, Fraser D M. Interval based MINLP superstructure synthesis of mass exchange networks[J]. Chemical Engineering Research and Design, 2008, 86(8): 909-924.
[9]	谢会, 史彬, 鄢烈祥, 等. 列队竞争算法综合质量交换网络[J]. 计算机与应用化学, 2010, 27(12): 1617-1620.
	Xie H, Shi B, Yan L X, et al. Mass exchange networks synthesis using line-up competition algorithm[J]. Computers and Applied Chemistry, 2010, 27(12): 1617-1620.
[10]	李绍军, 阳永荣. 利用改进的遗传算法进行质量交换网络的最优综合[J]. 化工学报, 2002, 53(1): 60-65.
	Li S J, Yang Y R. Mass exchanger networks synthesis using genetic-alopex algorithms[J]. Journal of Chemical Industry and Engineering (China), 2002, 53(1): 60-65.
[11]	Chen C L, Hung P S. Simultaneous synthesis of mass exchange networks for waste minimization[J]. Computers & Chemical Engineering, 2005, 29(7): 1561-1576.
[12]	都健, 高志辉, 陈理, 等. 采用浓度差同步优化的质量交换网络设计[J]. 化工学报, 2007, 58(7): 1768-1775.
	Du J, Gao Z H, Chen L, et al. Mass exchange network design using simultaneous optimization of composition differences[J]. Journal of Chemical Industry and Engineering (China), 2007, 58(7): 1768-1775.
[13]	Zhou Z Q, Cui G M, Xiao Y. A novel node-based non-structural model for mass exchanger network synthesis using a stochastic algorithm[J]. Journal of Cleaner Production, 2022, 376: 134227.
[14]	薛东峰. 废物最小化为目标的质量集成方法研究[D]. 大连: 大连理工大学, 2001.
	Xue D F. Study on mass integration for waste minimization[D]. Dalian: Dalian University of Technology, 2001.
[15]	都健, 李秀峰, 陈理, 等. 超结构法分步综合热集成的质量交换网络[J]. 化工学报, 2010, 61(10): 2636-2643.
	Du J, Li X F, Chen L, et al. Synthesis of heat integrated mass exchanger networks using step-wise approach based on superstructure[J]. CIESC Journal, 2010, 61(10): 2636-2643.
[16]	刘琳琳. 多组分体系质量-热量联合交换网络综合研究[D]. 大连: 大连理工大学, 2013.
	Liu L L. Study on combined mass and heat exchange networks synthesis for multi-component systems[D]. Dalian: Dalian University of Technology, 2013.
[17]	Xu Y, Cui G M, Shen S Q, et al. An efficient two-step optimization method for mass exchanger network synthesis[J]. Chemical Engineering Science, 2023, 273: 118631.
[18]	Xiao Y, Cui G M, Xu Y, et al. An efficient and random synthesis method for mass exchange networks with multi-component using a node-based vertical non-structural model[J]. Journal of Cleaner Production, 2023, 416: 137951.
[19]	易智康, 崔国民, 周志强, 等. 棋盘模型同步优化质量交换网络[J]. 计算物理, 2023, 40(4): 500-510.
	Yi Z K, Cui G M, Zhou Z Q, et al. A chessboard model for simultaneous optimization of mass exchange networks[J]. Chinese Journal of Computational Physics, 2023, 40(4): 500-510.
[20]	Xiao Y, Cui G M. A novel mass-heat exchange network analogy, regression, and synthesis method for mass exchanger networks[J]. Heliyon, 2023, 9(10): e20574.
[21]	肖媛, 陈怡, 刘思琪, 等. 基于广义换热网络的质量交换网络质能比拟及全局优化[J]. 化工进展, 2025, 44(1): 121-134.
	Xiao Y, Chen Y, Liu S Q, et al. Mass-heat analogy and global optimization of mass exchange network based on generalized heat exchanger network[J]. Process in Chemistry, 2025, 44(1): 121-134.
[22]	Hallale N, Capital cost targets for the optimum synthesis of mass exchange networks[D]. Cape Town: University of Cape Town, 1998.
[23]	Hallale N, Fraser D M. Capital and total cost targets for mass exchange networks(part 2): Detailed capital cost models[J]. Computers & Chemical Engineering, 2000, 23(11/12): 1681-1699.
[24]	Hallale N, Fraser D M. Capital and total cost targets for mass exchange networks(part 1): Simple capital cost models[J]. Computers & Chemical Engineering, 2000, 23(11/12): 1661-1679.
[25]	Comeaux R. Synthesis of MENs with minimum total cost[D]. Manchester, UK: UMIST, 2000.
[26]	杨岭, 崔国民, 周志强, 等. 精细搜索策略应用于质量交换网络综合[J]. 化工学报, 2022, 73(7): 3145-3155.
	Yang L, Cui G M, Zhou Z Q, et al. Fine search strategy applied to mass exchange network synthesis[J]. CIESC Journal, 2022, 73(7): 3145-3155.
[27]	Szitkai Z, Farkas T, Lelkes Z, et al. Fairly linear mixed integer nonlinear programming model for the synthesis of mass exchange networks[J]. Industrial & Engineering Chemistry Research, 2006, 45(1): 236-244.
[28]	Isafiade A J, Fraser D M. Extended interval-based mixed integer nonlinear programming superstructure synthesis of heat and mass exchanger networks[J]. Industrial & Engineering Chemistry Research, 2010, 49(1): 166-179.
[29]	Azeez O S, Isafiade A J, Fraser D M. Supply-based superstructure synthesis of heat and mass exchange networks[J]. Computers & Chemical Engineering, 2013, 56: 184-201.
[30]	高志辉. 费用最小的质量交换网络综合研究[D]. 大连: 大连理工大学, 2007.
	Gao Z H. Study on synthesis of mass exchange network targeting minimum cost[D]. Dalian: Dalian University of Technology, 2007.