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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2021, Vol. 16 Issue (2) : 393-409    https://doi.org/10.1007/s11465-020-0613-3
RESEARCH ARTICLE
Ant colony optimization for assembly sequence planning based on parameters optimization
Zunpu HAN1, Yong WANG1,2(), De TIAN1
1. Renewable Energy School, North China Electric Power University, Beijing 102206, China
2. College of Mechanical and Electronic Engineering, Tarim University, Alar 843300, China
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Abstract

As an important part of product design and manufacturing, assembly sequence planning (ASP) has a considerable impact on product quality and manufacturing costs. ASP is a typical NP-complete problem that requires effective methods to find the optimal or near-optimal assembly sequence. First, multiple assembly constraints and rules are incorporated into an assembly model. The assembly constraints and rules guarantee to obtain a reasonable assembly sequence. Second, an algorithm called SOS-ACO that combines symbiotic organisms search (SOS) and ant colony optimization (ACO) is proposed to calculate the optimal or near-optimal assembly sequence. Several of the ACO parameter values are given, and the remaining ones are adaptively optimized by SOS. Thus, the complexity of ACO parameter assignment is greatly reduced. Compared with the ACO algorithm, the hybrid SOS-ACO algorithm finds optimal or near-optimal assembly sequences in fewer iterations. SOS-ACO is also robust in identifying the best assembly sequence in nearly every experiment. Lastly, the performance of SOS-ACO when the given ACO parameters are changed is analyzed through experiments. Experimental results reveal that SOS-ACO has good adaptive capability to various values of given parameters and can achieve competitive solutions.
Keywords assembly sequence planning      ant colony optimization      symbiotic organisms search      parameter optimization     
Corresponding Author(s): Yong WANG   
Just Accepted Date: 15 January 2021   Online First Date: 10 March 2021    Issue Date: 15 June 2021
 Cite this article:   
Zunpu HAN,Yong WANG,De TIAN. Ant colony optimization for assembly sequence planning based on parameters optimization[J]. Front. Mech. Eng., 2021, 16(2): 393-409.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0613-3
https://academic.hep.com.cn/fme/EN/Y2021/V16/I2/393
Fig.1  Flowchart of the hybrid SOS-ACO algorithm.
Fig.2  Explosion model of a wind turbine gearbox.
No. Part name Number of part Connection type Assembly tool
1 Input shaft 1 Key joint T3
2 Left-end cover 1 Threaded connection T2
3 Left-end bearing chock 1 Threaded connection T1
4 First-stage inner gear ring 1 Threaded connection T4
5 First-stage planet gear 3 Interference fit T5
6 First-stage planet gear axle 3 Pin connection T3
7 First-stage planet carrier 1 Key joint T4
8 First-stage solar gear 1 Splined connection T5
9 Box 1 Threaded connection T1
10 Second-stage inner gear ring 1 Threaded connection T4
11 Second-stage planet carrier 1 Splined connection T4
12 Second-stage planet gear 3 Interference fit T5
13 Second-stage planet gear axle 3 Pin connection T3
14 Second-stage solar gear 1 Splined connection T5
15 Spline shaft 1 Splined connection T3
16 Output straight gear 1 Key joint T5
17 Third-stage straight gear 1 Key joint T5
18 Output shaft 1 Key joint T3
19 Output box 1 Threaded connection T1
20 Output bearing end cover 1 Threaded connection T2
21 Bearing end cover 1 Threaded connection T2
Tab.1  Information on the parts of a wind turbine gearbox
Parameter Range
α [1, 5]
β [1, 5]
ρ [0.1, 1]
γ [0.1, 1]
Tab.2  Value range of each parameter
Parameter combination Combination α β ρ γ
Optimal parameter combinations 1 2.79 1.25 0.10 0.21
2 2.71 1.56 0.14 0.37
3 4.20 2.32 0.19 0.39
4 3.41 2.18 0.23 0.28
5 2.29 1.63 0.12 0.34
Random parameter combinations I 1.00 2.00 0.50 0.40
II 2.00 3.00 0.30 0.70
III 3.00 1.00 0.50 0.60
IV 4.00 1.00 0.10 0.20
V 3.00 5.00 0.60 0.20
Tab.3  Optimal and random parameter combinations
Fig.3  Fitness value changes for the ACO parameter combination.
Fig.4  Minimum cost change of the assembly sequence.
Parameter combination Combination Minimum cost Cmin Number of times to find Cmin Average minimum cost Average number of ants to find Cmin Average minimum number of iterations to find Cmin
Optimal parameter combinations 1 41.2 7 41.5 16 17
2 41.2 8 41.4 17 22
3 41.2 8 41.8 15 32
4 41.2 6 42.3 14 17
5 41.2 8 41.5 16 27
Random parameter combinations I 41.6 1 42.8 1 44
II 42.0 3 44.2 2 53
III 41.2 1 43.3 2 48
IV 43.2 2 44.8 19 10
V 45.2 3 46.2 1 65
Tab.4  Comparison of the results of running ACO under different parameter combinations
Part number Assembly direction Assembly tool Assembly stability ?Part ?number Assembly direction Assembly tool Assembly stability
9 +X T1 Yes ?12 −X T5 Yes
3 +X T1 Yes ?14 −X T5 Yes
2 +X T2 Yes ?10 −X T4 Yes
7 −X T4 Yes ?15 −X T3 Yes
4 −X T4 Yes ?17 −X T5 Yes
6 −X T3 Yes ?16 −X T5 Yes
1 −X T3 Yes ?18 −X T3 Yes
5 −X T5 Yes ?19 −X T1 Yes
8 −X T5 Yes ?21 −X T2 Yes
11 −X T4 Yes ?20 −X T2 Yes
13 −X T3 Yes
Tab.5  Information on the optimal assembly sequence
m α β ρ γ Minimum cost Cmin Number of ants to find Cmin Minimum number of iterations to find Cmin
10 2.52 1.21 0.23 0.34 41.2 7 18
20 2.72 1.00 0.21 0.33 41.2 17 24
30 3.13 1.31 0.14 0.34 41.2 24 15
40 3.34 2.21 0.10 0.22 41.2 37 18
50 3.76 1.68 0.10 0.12 41.2 45 34
Tab.6  Experimental results for m
Q α β ρ γ Minimum cost Cmin Number of ants to find Cmin Minimum number of iterations to find Cmin
20 3.26 1.62 0.17 0.19 41.2 17 19
40 2.10 1.23 0.11 0.24 41.2 15 24
60 2.14 2.12 0.21 0.29 41.2 16 20
80 1.81 2.09 0.24 0.27 41.2 13 33
100 1.64 1.78 0.35 0.29 41.2 15 23
Tab.7  Experimental results for Q
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