VLSI中高性能X结构多层总体布线器

刘耿耿; 庄震; 郭文忠; 陈国龙

doi:10.16383/j.aas.c170714

VLSI中高性能X结构多层总体布线器

doi: 10.16383/j.aas.c170714

刘耿耿^1,2,3,,
庄震^1,,
郭文忠^1,2,3, ,,
陈国龙^1,

1.
福州大学数学与计算机科学学院福州 350116
2.
福建省网络计算与智能信息处理重点实验室福州 350116
3.
空间数据挖掘与信息共享教育部重点实验室福州 350116

基金项目:

国家重点基础研究发展计划(973计划) 2011CB808000

国家自然科学基金 61877010

国家自然科学基金 11501114

福建省自然科学基金 2019J01243

福建省科技创新平台项目 2014H2005

福建省科技创新平台项目 2009J1007

详细信息

作者简介:
刘耿耿福州大学数学与计算机科学学院副教授. 2015年获得福州大学应用数学博士学位.主要研究方向为计算智能及超大规模集成电路物理设计算法研究. E-mail:liugenggeng@fzu.edu.cn

庄震福州大学数学与计算机科学学院硕士研究生.主要研究方向为超大规模集成电路物理设计算法研究.E-mail:zhuang_zhen@126.com

陈国龙福州大学数学与计算机科学学院教授. 2002年获得西安交通大学计算机科学博士学位.主要研究方向为计算智能及其应用. E-mail: fzucgl@163.com

通讯作者:
郭文忠福州大学数学与计算机科学学院教授. 2010年获得福州大学通信与信息系统博士学位.主要研究方向为计算智能及其应用.本文通信作者.E-mail: fzugwz@163.com

计量
- 文章访问数: 1887
- HTML全文浏览量: 456
- PDF下载量: 108
- 被引次数: 0
出版历程
- 收稿日期: 2017-12-21
- 录用日期: 2018-04-16
- 刊出日期: 2020-01-21

A High Performance X-architecture Multilayer Global Router for VLSI

LIU Geng-Geng^{1,2,3
,},
ZHUANG Zhen^1
,,
GUO Wen-Zhong^{1,2,3
, ,},
CHEN Guo-Long^1
,

1.
College of Mathematics and Computer Sciences, Fuzhou University, Fuzhou 350116
2.
Key Laboratory of Network Computing and Intelligent Information Processing, Fujian Province, Fuzhou 350116
3.
Key Laboratory of Spatial Data Mining & Information Sharing, Ministry of Education, Fuzhou 350116

Funds:

National Basic Research Program of China (973 Program) 2011CB808000

National Natural Science Foundation of China 61877010

National Natural Science Foundation of China 11501114

Natural Science Foundation of Fujian Province 2019J01243

Technology Innovation Platform Project of Fujian Province 2014H2005

Technology Innovation Platform Project of Fujian Province 2009J1007

More Information

Author Bio:
LIU Geng-Geng Associate professor at the College of Mathematics and Computer Science, Fuzhou University. He received his Ph. D. degree from Fuzhou University in 2015. His research interest covers computational intelligence and very large scale integration physical design.)

ZHUANG Zhen Master student at the College of Mathematics and Computer Science from Fuzhou University. His research interest covers very large scale integration physical design.)

CHEN Guo-Long Professor at the College of Mathematics and Computer Science, Fuzhou University. He received his Ph. D degree in Computer Science from Xi\begin{document}$'$\end{document}an Jiaotong University in 2002. His research interest covers computation intelligence.)

Corresponding author: GUO Wen-Zhong Professor at the College of Mathematics and Computer Science, Fuzhou University. He received his Ph. D degree in Communication and Information System from Fuzhou University in 2010. His research interest covers computational intelligence and its application. Corresponding author of this paper.)

摘要

摘要: X结构带来物理设计诸多性能的提高, 该结构的引入和多层工艺的普及, 使得总体布线算法更复杂.为此, 在XGRouter布线器的基础上, 本文设计了三种有效的加强策略, 包括: 1)增加新类型的布线方式; 2)粒子群优化(Particle swarm optimization, PSO)算法与基于新布线代价的迷宫布线的结合; 3)初始阶段中预布线容量的缩减策略, 继而引入了多层布线模型, 简化了XGRouter的整数线性规划模型, 最终构建了一种高性能的X结构多层总体布线器, 称为ML-XGRouter.在标准测试电路的仿真实验结果表明, ML-XGRouter相对其他各类总体布线器, 在多层总体布线中最重要的优化目标——溢出数和线长总代价两个指标上均取得最佳.
- X结构 /
- 多层布线 /
- 超大规模集成电路 /
- 总体布线 /
- 粒子群优化
Abstract: The introduction of X-architecture can improve many performance standards of the chip in physical design. The proposed X-architecture and pervasive multilayer technology make the global routing problem more complex. For this reason, this paper presents the following enhancements based on XGRouter: 1) the introduction of some new types of routing; 2) the combination of particle swarm optimization (PSO) algorithm and maze routing with new routing cost; 3) a reduction strategy of routing capacity in the initial stage. Then the multilayer routing model is introduced and the integer linear programming model of XGRouter is simplified. Finally, a high performance X-architecture multilayer global router, namely ML-XGRouter, is proposed. The experimental results on benchmark circuits have shown that our proposed ML-XGRouter is effective and superior to state-of-the-art multilayer routing algorithms on overflows and the total cost of wirelength, which are the two most important optimization goals for the multilayer global routing problem.
- X-architecture /
- multilayer routing /
- very large scale integration (VLSI) /
- global routing /
- particle swarm optimization (PSO)
Recommended by Associate Editor WANG Ding
注释:

1) 本文责任编委王鼎

HTML全文

图 1 总体布线图

Fig. 1 The design graph of global routing

下载: 全尺寸图片幻灯片

图 2 初始布线阶段由于布线容量约束造成未能直接连线的4种情况

Fig. 2 The four cases of the failure to connect directly due to the limitation of routing capacity in the initial stage

下载: 全尺寸图片幻灯片

图 3 E1策略

Fig. 3 E1 Strategy

下载: 全尺寸图片幻灯片

图 4 E2策略

Fig. 4 E2 Strategy

下载: 全尺寸图片幻灯片

图 5 E3策略

Fig. 5 E3 Strategy

下载: 全尺寸图片幻灯片

图 6 ML-XGRouter的算法流程

Fig. 6 The flow chart of ML-XGRouter

下载: 全尺寸图片幻灯片

图 7 总体布线问题的实例

Fig. 7 An instance for the global routing problem

下载: 全尺寸图片幻灯片

图 8 图 7(b)中布线实例的编码图

Fig. 8 The encoding for the routing instance in Fig. 7 (b)

下载: 全尺寸图片幻灯片

图 9 本文的两种操作算子

Fig. 9 Two operators in this paper

下载: 全尺寸图片幻灯片

表 1 未采用和采用E1策略(E2策略)的布线结果对比

Table 1 Comparison of routing results without and with E1 strategy (E2 strategy)

基准	E0		E1		减少率(%)		E2		减少率(%)
电路	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL
11	85	46.7	85	46.9	0	-0.43	0	47.9	100	-2.57
12	75	45.9	70	45.8	6.67	0.22	0	46.6	100	-1.53
13	44	127.1	34	127.2	22.73	-0.08	0	128.9	100	-1.42
14	12	110.8	7	110.9	41.67	-0.09	0	111	100	-0.18
15	32	130.8	29	131.4	9.38	-0.46	0	130.3	100	0.38
16	2	33.9	1	33.9	50	0	0	33.9	100	0
17	0	63.4	0	63.3	0	0.16	0	63.5	0	-0.16
18	3 779	80	3 682	80	2.57	0	3 170	80.8	16.12	-1
AVG					16.63	-0.09			77.01	-0.81

下载: 导出CSV

表 2 在E1策略(E2策略)的基础上未采用和采用E3策略的布线结果对比

Table 2 Comparison of routing results without and with E3 strategy, on the basis of E1 strategy (E2 strategy)

基准	E1		E1+E3		减少率(%)		E2		E2+E3		减少率(%)
电路	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL
11	85	46.9	68	46.4	20	1.07	0	47.9	0	47.5	0	0.84
12	70	45.8	49	44.4	30	3.06	0	46.6	0	45.6	0	2.15
13	34	127.2	27	123.7	20.59	2.75	0	128.9	0	127.4	0	1.16
14	7	110.9	7	110.2	0	0.63	0	111	0	110.7	0	0.27
15	29	131.4	13	127.7	55.17	2.82	0	130.3	0	129.8	0	0.38
16	1	33.9	1	33.9	0	0	0	33.9	0	34	0	-0.3
17	0	63.3	0	63	0	0.47	0	63.5	0	64.2	0	-1.1
18	3 682	80	3 226	80.5	12.38	-0.63	3 170	80.8	3 165	81	0.16	-0.25
AVG					17.27	1.27					0.02	0.39

下载: 导出CSV

表 3 在E1和E2策略共同作用的基础上未采用和采用E3策略的布线结果对比

Table 3 Comparison of routing results without and with E3 strategy, on the basis of E1 and E2 strategies

基准	E1+E2		E1+E2+ E3		减少率(%)
电路	TOF	TWL	TOF	TWL	TOF	TWL
11	0	47.8	0	47	0	1.67
12	0	46.5	0	45	0	3.23
13	0	128.8	0	124.6	0	3.26
14	0	110.9	0	110.1	0	0.72
15	0	130.2	0	126.8	0	2.61
16	0	33.9	0	33.9	0	0
17	0	63.4	0	63.1	0	0.47
18	3 106	80.8	2 762	81.1	11.08	-0.37
AVG					1.38	1.45

下载: 导出CSV

表 4 在ISPD98测试电路的属性及初始布线的结果

Table 4 ISPD98 benchmark circuits and the results of the initial stage

基准电路初始布线情况
名称	网格大小	线网数	bf.nets	af.nets	Ratio (%)
ibm01	64 $\times$ 64	11 507	25 698	20 127	78.32
ibm02	80 $\times$ 64	18 429	55 739	39 871	71.53
ibm03	80 $\times$ 64	21 621	43 272	30 181	69.75
ibm04	96 $\times$ 64	26 163	49 821	34 193	68.63
ibm06	128 $\times$ 64	33 354	75 912	59 812	78.79
ibm07	192 $\times$ 64	44 394	97 391	69 123	70.97
ibm08	192 $\times$ 64	47 944	121 912	89 134	73.11
ibm09	256 $\times$ 64	50 393	115 871	91 268	78.77
ibm10	256 $\times$ 64	64 227	169 391	113 459	66.98
AVG					72.98

下载: 导出CSV

表 5 在ISPD07测试电路的属性及初始布线的结果

Table 5 ISPD07 benchmark circuits and the results of the initial stage

基准电路初始布线情况
名称	网格大小	线网数	bf.nets	af.nets	e3.af.nets	Ratio (%)	e3.Ratio (%)
11	324 $\times$ 324	219 794	560 406	430 376	428 383	76.8	76.44
12	424 $\times$ 424	260 159	600 317	452 931	450 048	75.45	74.97
13	774 $\times$ 779	466 295	1 093 066	829 270	825 112	75.87	75.49
14	774 $\times$ 779	515 304	1 075 147	783 478	782 257	72.87	72.76
15	465 $\times$ 468	867 441	1 664 608	1 319 629	1 307 906	79.28	78.57
16	399 $\times$ 399	331 663	657 467	528 243	527 043	80.35	80.16
17	557 $\times$ 463	463 213	956 459	743 183	738 101	77.7	77.17
18	973 $\times$ 1 256	551 667	936 162	700 745	699 252	74.85	74.69
AVG						76.65	76.28

下载: 导出CSV

表 6 在E3的基础上E1策略或(和) E2策略结合后的优化情况

Table 6 The optimization results with the combination of E1 strategy or (and) E2 strategy based on E3 strategy

基准	EO		E1+E3		E2+E3		E1+E2+E3
电路	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL
11	85	46.7	68	46.4	0	47.5	0	47
12	75	45.9	49	44.4	0	45.6	0	45
13	44	127.1	27	123.7	0	127.4	0	124.6
14	12	110.8	7	110.2	0	110.7	0	110.1
15	32	130.8	13	127.7	0	129.8	0	126.8
16	2	33.9	1	33.9	0	34	0	33.9
17	0	63.4	0	63	0	64.2	0	63.1
18	3 779	80	3 226	80.5	3 165	81	2 762	81.1
Comp.	100	100	67.63	98.91	22.97	100.41	21.64	99.24

下载: 导出CSV

表 7 在ISPD98上与5种总体布线算法的对比

Table 7 Comparison between our algorithm and five global routing algorithms on ISPD98

基准	算法						减少率(%)
电路	[3]	[5]	[2]	[4]	[6]	Ours	[3]	[5]	[2]	[4]	[6]
ibm01	63 332	64 389	62 659	63 720	62 498	58 564	7.53	9.05	6.54	8.09	6.29
ibm02	168 918	171 805	171 110	170 342	169 881	158 383	6.24	7.81	7.44	7.02	6.77
ibm03	146 412	146 770	146 634	147 078	146 458	136 313	6.9	7.12	7.04	7.32	6.93
ibm04	167 101	169 977	167 275	170 095	166 452	153 190	8.32	9.88	8.42	9.94	7.97
ibm06	277 608	278 841	277 913	279 566	277 696	261 606	5.76	6.18	5.87	6.42	5.79
ibm07	366 180	370 143	365 790	369 340	366 133	341 170	6.83	7.83	6.73	7.63	6.82
ibm08	404 714	404 530	405 634	406 349	404 976	379 684	6.18	6.14	6.4	6.56	6.25
ibm09	413 053	414 223	413 862	415 852	414 738	389 281	5.76	6.02	5.94	6.39	6.14
ibm10	578 795	583 805	590 141	585 921	579 870	541 839	6.38	7.19	8.18	7.52	6.56
AVE							6.66	7.47	6.95	7.43	6.61

下载: 导出CSV

表 8 在ISPD07上与2种串行算法的总体布线算法的对比

Table 8 Comparison between our algorithm and two serial global routing algorithms on ISPD07

	算法						减少率(%)
基准	[6]		[8]		Ours		[6]		[8]
电路	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL
11	0	55.9	0	53.5	0	47	0	15.92	0	12.15
12	0	54	0	51.69	0	45	0	16.67	0	12.94
13	0	134.4	0	130.35	0	124.6	0	7.29	0	4.41
14	0	127.8	0	120.67	0	110.1	0	13.85	0	8.76
15	0	157	0	154.7	0	126.8	0	19.24	0	18.03
16	0	48.6	0	45.99	0	33.9	0	30.25	0	26.29
17	0	78.5	0	74.88	0	63.1	0	19.62	0	15.73
18	31 390	94.9	31 454	104.28	2 762	81.1	91.2	14.54	91.22	22.23
AVE							11.4	17.17	11.4	15.07

下载: 导出CSV

表 9 在ISPD07上与2种并行算法的总体布线算法的对比

Table 9 Comparison between our algorithm and two concurrent global routing algorithms on ISPD07

	算法						减少率(%)
基准	[11]		[12]		Ours		[11]		[12]
电路	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL	TOF	TWL
11	0	52.82	0	54.3	0	47	0	11.02	0	13.44
12	0	51.46	0	52.9	0	45	0	12.55	0	14.93
13	0	128.92	0	131	0	124.6	0	3.35	0	4.89
14	0	119.96	0	124	0	110.1	0	8.22	0	11.21
15	0	153.23	0	155	0	126.8	0	17.25	0	18.19
16	228	45.58	228	47	0	33.9	100	25.63	100	27.87
17	0	74.46	0	77.9	0	63.1	0	15.26	0	19
18	31 026	107.22	31 484	108.5	2 762	81.1	91.1	24.36	91.23	25.25
AVE							23.89	14.7	23.9	16.85

下载: 导出CSV

参考文献(37)

[1]	徐宁, 洪先龙.超大规模集成电路物理设计理论与方法.清华大学出版社, 2009. Xu Ning, Hong Xian-Long. Very large scale integration physical design theory and method. Tsinghua University Press, 2009.
[2]	Zhang Y, Xu Y, Chu C. Fastroute 3.0: a fast and high quality global router based on virtual capacity. In: Proceedings of IEEE/ACM International Conference on Computer-Aided Design. New York, USA: IEEE, 2008. 344-349
[3]	Roy A J, Markov I L. High-performance routing at the nanometer scale. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2008, 27(6): 1066-1077 doi: 10.1109/TCAD.2008.923255
[4]	Moffitt M D. Maizerouter: Engineering an effective global router. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2008, 27(11): 2017-2026 doi: 10.1109/TCAD.2008.2006082
[5]	Ozdal M M, Wong M D F. Archer: A history-based global routing algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2009, 28(4): 528-540 doi: 10.1109/TCAD.2009.2013991
[6]	Chang Y J, Lee Y T, Gao J R, Wu P C, Wang T C. NTHU-Route 2.0: A robust global router for modern designs. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2010, 29(12): 1931-1944 doi: 10.1109/TCAD.2010.2061590
[7]	Held S, Muller D, Rotter D, Scheifele R, Traub V, Vygen J. Global routing with timing constraints. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2018, 37(2): 406-419 doi: 10.1109/TCAD.2017.2697964
[8]	Dai K R, Liu W H, Li Y L. NCTU-GR: efficient simulated evolution-based rerouting and congestion-relaxed layer assignment on 3-D global routing. IEEE Transactions on very large scale integration (VLSI) systems, 2012, 20(3): 459-472 doi: 10.1109/TVLSI.2010.2102780
[9]	Wu T H, Davoodi A, Linderoth J T. GRIP: scalable 3D global routing using integer programming. In: Proceedings of ACM/IEEE Design Automation Conference. New York, USA: IEEE, 2009. 320-325
[10]	Cho M, Pan D Z. BoxRouter: A new global router based on box expansion and progressive ILP. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2007, 26(12): 2130-2143 doi: 10.1109/TCAD.2007.907003
[11]	Liu W H, Kao W C, Li Y L, Chao K Y. NCTU-GR 2.0: multithreaded collision-aware global routing with bounded-length maze routing. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2013, 32(5): 709-722 doi: 10.1109/TCAD.2012.2235124
[12]	Han Y, Ancajas D M, Chakraborty K, Roy S. Exploring high-throughput computing paradigm for global routing. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2014, 22(1): 155-167 doi: 10.1109/TVLSI.2012.2234489
[13]	Teig S L. The X architecture: not your father's diagonal wiring. In: Proceedings of International workshop on System-level interconnect prediction. New York, USA: ACM, 2002. 33-37
[14]	Dong J, Zhu H L, Xie M, Zeng X. Graph Steiner tree construction and its routing applications. In: Proceedings of IEEE 10th International Conference on ASIC. New York, USA: IEEE, 2013. 1-4
[15]	Hung J H, Yeh Y K, Lin Y C, Huang H H, Hsieh T M. ECO-aware obstacle-avoiding routing tree algorithm. WSEAS Transactions on Circuits and Systems, 2010, 9(9): 567-576 http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0221981287/
[16]	Liu G G, Chen G L, Guo W Z. DPSO based octagonal steiner tree algorithm for VLSI routing. In: Proceedings of IEEE 5th International Conference on Advanced Computational Intelligence. New York, USA: IEEE, 2012. 383-387
[17]	Ho T Y. A performance-driven X-architecture router based on a novel multilevel framework. Integration, the VLSI Journal, 2009, 42(3): 400-408 doi: 10.1016/j.vlsi.2008.12.002
[18]	Ho T Y. A performance-driven multilevel framework for the X-based full-chip router. In: Proceedings of International Workshop on Power and Timing Modeling, Optimization and Simulation. Berlin, Heidelberg: Springer, 2008. 209-218
[19]	Hu Y, Jing T, Hong X, Hu X, Yan G. A routing paradigm with novel resources estimation and routability models for X-architecture based physical design. In: Proceedings of International Workshop on Embedded Computer Systems. Berlin, Heidelberg: Springer, 2005. 344-353
[20]	Cao Z, Jing T, Hu Y, Shi Y, Hong X, Hu X, Yan G. DraXRouter: Global routing in X-architecture with dynamic resource assignment. In: Proceedings of the 2006 Asia and South Pacific Design Automation Conference. New York, USA: ACM, 2006. 618-623
[21]	Liu G G, Guo W Z, Li R R, Niu Y Z, Chen G L. XGRouter: high-quality global router in X-architecture with particle swarm optimization. Frontiers of Computer Science, 2015, 9(4): 576-594 http://d.old.wanfangdata.com.cn/Periodical/zggdxxxswz-jsjkx201504007
[22]	ISPD 2007 Global Routing Contest [Online], available: http://www.sigda.org/ispd2007/contest.html, 2007
[23]	Liu G G, Huang X, Guo W Z, Niu Y Z, Chen G L. Multilayer obstacle-avoiding X-architecture Steiner minimal tree construction based on particle swarm optimization. IEEE Transactions on Cybernetics, 2015, 45(5): 989-1002 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d6b5eb99a0190723fcec4d0ce6de9cb3
[24]	ISPD 1998 Global Routing Benchmark Suite [Online], available: http://cseweb.ucsd.edu/kastner/research/labyrinth/, 1998
[25]	Kennedy J, Eberhart R C. A discrete binary version of the particle swarm optimization algorithm. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics. New York, USA: IEEE, 1997. 4104-4109
[26]	Parsopoulos K E, Vrahatis M N. Recent approaches to global optimization problems through particle swarm optimization. Natural Computing, 2002, 1(2-3): 235-306
[27]	Pan Q K, Tasgetiren M F, Liang Y C. A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Computers & Operations Research, 2008, 35(9): 2807-2839 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f0ae38a762e2dd59c2fdc4318af860e1
[28]	Guo W Z, Liu G G, Chen G L, Peng S J. A hybrid multi-objective PSO algorithm with local search strategy for VLSI partitioning. Frontiers of Computer Scienceh, 2014, 8(2): 203-216 http://d.old.wanfangdata.com.cn/Periodical/zggdxxxswz-jsjkx201402004
[29]	Huang X, Guo W Z, Liu G G, Chen G L. FH-OAOS: a fast 4-step heuristic for obstacle-avoiding octilinear Steiner tree construction. ACM Transactions on Design Automation of Electronic Systems, 2016, 21(3): 48
[30]	Huang X, Guo W Z, Liu G G, Chen G L. MLXR: multi-layer obstacle-avoiding X-architecture Steiner tree construction for VLSI routing. Science China Information Sciences, 2017, 60(3): 19102 doi: 10.1007/s11432-015-0850-4?slug=abstract
[31]	王东风, 孟丽.粒子群优化算法的性能分析和参数选择.自动化学报, 2016, 42(10): 1552-1561 doi: 10.16383/j.aas.2016.c150774 Wang Dong-Feng, Meng Li. Performance analysis and parameter selection of PSO algorithms. Acta Automatica Sinica, 2016, 42(10): 1552-1561 doi: 10.16383/j.aas.2016.c150774
[32]	吕柏权, 张静静, 李占培, 刘廷章.基于变换函数与填充函数的模糊粒子群优化算法.自动化学报, 2018, 44(1): 74-86 doi: 10.16383/j.aas.2018.c160547 Lv Bai-Quan, Zhang Jing-Jing, Li Zhan-Pei, Liu Ting-Zhang. Fuzzy partical swarm optimization based on filled function and transformation function. Acta Automatica Sinica, 2018, 44(1): 74-86 doi: 10.16383/j.aas.2018.c160547
[33]	Zhang W, Zhang H, Liu J, Li K, Yang D, Tian H. Weather prediction with multiclass support vector machines in the fault detection of photovoltaic system. IEEE/CAA Journal of Automatica Sinica, 2017, 4(3): 520-525 doi: 10.1109/JAS.2017.7510562
[34]	Han Z, Zhao J, Wang W. An optimized oxygen system scheduling with electricity cost consideration in steel industry. IEEE/CAA Journal of Automatica Sinica, 2017, 4(2): 216-222 doi: 10.1109/JAS.2017.7510439
[35]	Tang Y, Luo C, Yang J, He H. A chance constrained optimal reserve scheduling approach for economic dispatch considering wind penetration. IEEE/CAA Journal of Automatica Sinica, 2017, 4(2): 186-194 doi: 10.1109/JAS.2017.7510499
[36]	Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks, 1994, 5(1): 96-101
[37]	Lv H, Zheng J, Wu J, Zhou C, Li K. The convergence analysis of genetic algorithm based on space mating. In: Proceedings of IEEE 5th International Conference on Natural Computation. New York, USA: IEEE, 2009. 557-562