Research on Photomask Defects Path Optimization Based on Ant Colony Algorithm Mixed with 2⁃opt

Zhijun XU; Yateng WANG; Qilong XIONG

doi:10.19453/j.cnki.1005-488x.2021.04.006

Journals >Optoelectronic Technology >Volume 41 >Issue 4 >Page 274 > Article

Optoelectronic Technology
Vol. 41, Issue 4, 274 (2021)

Research on Photomask Defects Path Optimization Based on Ant Colony Algorithm Mixed with 2⁃opt

Zhijun XU¹, Yateng WANG¹, and Qilong XIONG^1,2

Author Affiliations

¹Hefei Qingyi Photomask Ltd., Hefei,2300，CHN

²Shenzhen Qingyi Photomask Ltd., Shenzhen Guangdong,518053，CHN

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DOI: 10.19453/j.cnki.1005-488x.2021.04.006 Cite this Article

Zhijun XU, Yateng WANG, Qilong XIONG. Research on Photomask Defects Path Optimization Based on Ant Colony Algorithm Mixed with 2⁃opt[J]. Optoelectronic Technology, 2021, 41(4): 274 Copy Citation Text

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Fig. 1. Common abnormalities of mask layers

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Fig. 2. Defect path inspected by AOI machine

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Fig. 3. Schematic of searching tactics in 2-opt algorithm

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Fig. 4. Flow chart of ACO mixed with 2-opt algorithm

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Fig. 5. Optimized paths of AOI, basic ACO and 2⁃opt+ACO_DFT

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Fig. 6. Defocus rates of AOI order, X/Y ascending order, Basic ACO and 2-opt+ACO_DFT algorithms (R=100 mm)

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Fig. 7. Optimized paths of four 2-opt+ACO algorithms

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	总行程/mm	优化率/(%)	耗时/s	总行程/mm	优化率/(%)	耗时/s	总行程/mm	优化率/(%)	耗时/s
AOI排序	18 904	0	/	39 282	0	/	53 837	0	/
X升序	17 656	6.6	/	14 203	63.8	/	36 647	31.9	/
Y升序	11 641	38.4	/	32 547	17.1	/	29 044	46.1	/
Basic ACO	6 748	64.3	270	5 027	87.2	656	7 659	85.8	2 044
2⁃opt+ACO_DFT	5 246	72.3	19	5 009	87.3	92	7 160	86.7	194

Table 1. Optimization comparison among AOI order， X/Y ascending order， basic ACO and 2⁃opt+ACO_DFT

	$α$ 、 $β$ 、 $ρ$	蚂蚁数 $m$	循环数 $c$	$n_{a}$	$n_{b}$
2⁃opt+ACO_DFT	$α = 1 、 β = 2$ 、 $ρ$ =0.6	取坐标数 $n$	100	/	/
2⁃opt+ACO_less ant		10	100	/	/
2⁃opt+ACO_acc_1		10	100	20	20
2⁃opt+ACO_acc_2		20	200	20	20

Table 2. Parameter settings of four ACO algorithms mixed with 2⁃opt

	pr299				fl417
	最优解	耗时/s	结果	误差/(%)	最优解	耗时/s	结果	误差/(%)
2⁃opt+ACO_DFT	48 191	1293	49 250	2.2	11 861	4 909	12 052	1.61
2⁃opt+ACO_less ant		44	49 129	1.95		112	12 034	1.46
2⁃opt+ACO_acc_1		4.28	49 030	1.74		8.32	12 032	1.44
2⁃opt+ACO_acc_2		14.96	48 904	1.48		28.26	12 018	1.32

Table 3. Optimization results comparison of four ACO algorithms mixed with 2⁃opt

		2⁃opt+ACO_DFT			2⁃opt+ACO_less ant
序号	耗时/s	行程/mm	失焦率/(%)	优化率/(%)	耗时/s	行程/mm	失焦率/(%)	优化率/(%)
1	1 923	7 954.03	0.31	92.41	52	7 839.32	0.31	92.52
2	1 740	7 768.36	0.62	92.59	53	7 882.88	0.62	92.48
3	1 747	7 806.21	0.31	92.55	52	7 819.07	0.31	92.54
4	1 718	7 846.97	0.62	92.51	53	7 832.07	0.62	92.53
5	1 719	7 708.77	0.31	92.64	53	7 850.98	0.62	92.51
6	1 818	7 847.72	0.31	92.51	53	7 951.2	0.62	92.41
7	1 735	7 802.49	0.31	92.56	52	7 860.31	0.31	92.50
8	1 686	7 779.74	0.31	92.58	53	7 855.55	0.31	92.50
9	1 663	7 850	0.31	92.51	52	7 902.88	0.31	92.46
10	1 718	7 800.7	0.31	92.56	52	7 767.46	0.31	92.59
Ave	1 746.7	7 816.5	0.37	92.54	52.5	7 856.17	0.43	92.50

Table 4. Optimized paths of 2⁃opt+ACO_DFT and 2⁃opt+ACO_less ant

		2⁃opt+ACO_acc_1			2⁃opt+ACO_acc_2
序号	耗时/s	行程/mm	失焦率/(%)	优化率/(%)	耗时/s	行程/mm	失焦率/(%)	优化率/(%)
1	5.59	7 792.38	0.62	92.57	19.22	7 806.15	0.31	92.55
2	5.63	7 801.62	0.31	92.56	19.36	7 738.88	0.62	92.62
3	5.47	7 805.7	0.31	92.55	19.22	7 802.37	0.00	92.56
4	5.66	7 830.86	0.00	92.53	19.23	7 739.23	0.00	92.62
5	5.54	7 823.87	0.00	92.5	19.09	7 786.99	0.31	92.57
6	5.53	7 845.53	0.31	92.51	19.1	7 700.44	0.62	92.65
7	5.64	7 768.19	0.31	92.59	19.29	7 792.98	0.31	92.56
8	5.53	7 836.91	0.31	92.52	19.26	7 813.04	0.31	92.55
9	5.54	7 756.25	0.31	92.60	19.57	7 802.21	0.31	92.56
10	5.59	7 779.59	0.31	92.58	19.7	7 812.41	0.31	92.55
Ave	5.57	7 804.09	0.28	92.55	19.3	7 779.47	0.31	92.58

Table 5. Optimized paths of 2⁃opt+ACO_acc_1 and 2⁃opt+ACO_acc_2

订单号	蚂蚁数 $m$ &循环数 $c$	路径长度/mm		镜头寻点时长/min		节省时长/min
订单号	蚂蚁数 $m$ &循环数 $c$	优化前	优化后	优化前	优化后	节省时长/min
A1960798	$m$ =10& $c$ =100	9 118	5 377	11.3	3.1	8.2
A1960799		16 850	5 521	17.5	5.1	12.4
A1964778		29 518	4 399	29.8	8.9	20.9
A1964136		45 080	7 762	40.0	12.2	27.8
A1964115	$m$ =20& $c$ =200	66 310	7 780	75.9	19.8	56.1
A1964407		77 333	15 088	83.7	24.3	59.4
A1973844		111 524	11 966	102.7	26.7	76
A1972959	$m$ =25& $c$ =250	134 565	12 772	173.3	67.8	105.5

Table 6. Application results of 2⁃opt+ACO_acc algorithm applied in practical production

Zhijun XU, Yateng WANG, Qilong XIONG. Research on Photomask Defects Path Optimization Based on Ant Colony Algorithm Mixed with 2⁃opt[J]. Optoelectronic Technology, 2021, 41(4): 274

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