Influence analysis and enhancement strategy of infeasible solutions for heat exchanger network optimization with RWCE

doi:10.16085/j.issn.1000-6613.2019-0595

Abstract

Abstract:

In optimization of heat exchanger network (HEN), the exterior penalty method was usually used to deal with the constraints, which gave a large penalty value to the infeasible solutions that violated the constraints. When random walk algorithm with compulsive evolution (RWCE) was applied to the HEN optimization, the infeasible solutions maybe accepted with a certain probability due to the non-greedy search mechanism of RWCE, thus changing the global optimization process. In this paper, the influence of infeasible solutions on the optimization process was analyzed firstly, revealing that the infeasible solutions with small offset could promote structure evolution. Then, a dynamic adjustment strategy of the acceptance probability of bad solutions was proposed aiming to reasonably utilize the positive effect of the infeasible solutions to enhance the structure evolution. Finally, considering that most of the above optimization results were infeasible solutions with relatively small offset, a feasible strategy was proposed. Through the application of the piecewise penalty index technique and two-population optimization technique, the infeasible solutions with evolution potential were enabled to rapidly return to the feasible regions, the optimization quality could also be improved. The modified algorithm combining the two reinforcement strategies and RWCE was applied to the cases involving 16 streams and 15 streams, whose results respectively saved 0.35% and 0.48% as compared to the optimums in literature, indicating that the global search ability of the modified algorithm was significantly improved compared with the original algorithm.

Key words: heat exchanger network, penalty function method, infeasible solutions, random walk algorithm with compulsive evolution(RWCE), structure evolution

摘要：

换热网络优化问题常以外罚函数法处理约束，赋予违反约束的不可行解较大的罚值。强制进化随机游走算法(RWCE)优化换热网络时，其非贪婪搜索机制使不可行解以一定概率被保留，从而改变全局寻优过程。本文首先分析不可行解对优化进程的影响，揭示偏移量较小的不可行解对结构进化的促进作用；然后提出差解概率动态调整策略，合理利用不可行解的正面作用，强化结构进化能力；最后，鉴于上述优化结果中偏移量较小的不可行解居多，提出一种可行化策略，通过分段罚指数和双种群优化技术促使过程中有潜力的不可行解快速返回可行域，并提升优化质量。将结合两条强化策略的改进算法应用于16股流与15股流算例，优化结果较文献最优解分别节省了0.35%、0.48%，表明改进后的算法较原算法全局搜索能力得到了显著提升。

关键词: 换热网络, 外罚函数法, 不可行解, 强制进化随机游走算法, 结构进化

CLC Number:

TK124

Geman SU,Guomin CUI,Zhongkai BAO,Yuan XIAO,Aowei JIANG. Influence analysis and enhancement strategy of infeasible solutions for heat exchanger network optimization with RWCE[J]. Chemical Industry and Engineering Progress, 2020, 39(1): 14-25.

苏戈曼,崔国民,鲍中凯,肖媛,蒋奥炜. RWCE优化换热网络的不可行解影响分析及强化策略[J]. 化工进展, 2020, 39(1): 14-25.

Figures/Tables 19

References 30

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流股	进口温度 /℃	出口温度 /℃	热容流率/kW·℃^-1	换热系数/kW·m^-2·℃^-1
H1	327	40	100	0.5
H2	220	160	160	0.4
H3	220	60	60	0.14
H4	160	45	400	0.3
C1	100	300	100	0.35
C2	35	164	70	0.7
C3	85	138	350	0.5
C4	60	170	60	0.14
C5	140	300	200	0.6
HU	330	250	—	0.5
CU	15	30	—	0.5
换热器费用=2000+70A USD·a^-1(A的单位为m²)
热公用工程费用=60USD·kW^-1·a^-1
冷公用工程费用=6USD·kW^-1·a^-1

流股	进口温度 /℃	出口温度 /℃	热容流率/kW·℃^-1	换热系数/kW·m^-2·℃^-1
H1	327	40	100	0.5
H2	220	160	160	0.4
H3	220	60	60	0.14
H4	160	45	400	0.3
C1	100	300	100	0.35
C2	35	164	70	0.7
C3	85	138	350	0.5
C4	60	170	60	0.14
C5	140	300	200	0.6
HU	330	250	—	0.5
CU	15	30	—	0.5
换热器费用=2000+70A USD·a^-1(A的单位为m²)
热公用工程费用=60USD·kW^-1·a^-1
冷公用工程费用=6USD·kW^-1·a^-1

偏移量大小	u₁	u₂	(u₂/u₁)×100%/%
0.00～0.25	10537	1778	16.9
0.25～0.50	5260	771	14.7
0.50～0.75	2468	325	13.2
0.75～1.00	1285	151	11.8
1.00～1.25	700	70	10.0
1.25～1.50	331	36	10.9
1.50～1.75	200	14	7.0
1.75～2.00	103	10	9.7
2.00～2.25	53	5	9.4
2.25～2.50	25	2	8.0
2.50～2.75	14	0	0.0
2.75～3.00	4	0	0.0
3.00～3.25	1	0	0.0
3.25～3.50	3	0	0.0

偏移量大小	u₁	u₂	(u₂/u₁)×100%/%
0.00～0.25	10537	1778	16.9
0.25～0.50	5260	771	14.7
0.50～0.75	2468	325	13.2
0.75～1.00	1285	151	11.8
1.00～1.25	700	70	10.0
1.25～1.50	331	36	10.9
1.50～1.75	200	14	7.0
1.75～2.00	103	10	9.7
2.00～2.25	53	5	9.4
2.25～2.50	25	2	8.0
2.50～2.75	14	0	0.0
2.75～3.00	4	0	0.0
3.00～3.25	1	0	0.0
3.25～3.50	3	0	0.0

偏移量大小	u₁	u₂	(u₂/u₁)×100%/%
0.00～0.25	51229	10584	20.7
0.25～0.50	9654	1693	17.5
0.50～0.75	1690	258	15.3
0.75～1.00	377	65	17.2
1.00～1.25	68	6	8.8
1.25～1.50	16	1	6.3
1.50～1.75	3	0	0
1.75～2.00	2	0	0
2.00～2.25	0	0	0
2.25～2.50	0	0	0
2.50～2.75	0	0	0
2.75～3.00	0	0	0
3.00～3.25	0	0	0
3.25～3.50	0	0	0