Using an Improved Differential Evolution for Scheduling Optimization of Dual-Gantry Multi-Head Surface-Mount Placement Machine
Abstract
:1. Introduction
- ♦
- The component height restriction is considered in SMP processing.
- ♦
- The proposed modified differential evolution (MDE) algorithm with two similarity measurement mechanisms using a random-key encoding mapping method is designed for minimizing the number of picks in feeder arrangement.
- ♦
- A combination of nearest-neighbor search (NNS) and 2-opt method is applied to shorten the path in component placing operations.
- ♦
- The experimental results indicate that while using the MDE algorithm for feeder arrangement, at most 30% of the number of picks can be reduced; moreover, when adding a combination of NNS and 2-opt method for component placing sequence, the whole assembly time is decreased at most by 13% using the proposed method.
2. Description of the SMP Machine
- (a)
- Gantry: This moves above the surface-mount machine, allowing the pick-and-place heads to pick components from the correct feeder and then to place the components on the correct position of the PCB.
- (b)
- Pick-and-place head: Every pick-and-place head is equipped with a single nozzle, which is used to pick and place components.
- (c)
- ANC: This is where nozzles are placed and changed.
- (d)
- Nozzle: These are installed on pick-and-place heads for component picking and placing. Different nozzle types are required for different components. Accordingly, the pick-and-place heads move to the ANC for nozzle changes when required.
- (e)
- Feeder: The feeder is used to store and provide components. Every feeder stores only one component.
- (f)
- Feeder station: Feeders for placement operation here.
- (g)
- PCB table: PCBs are fixed and placed here.
- (h)
- Fly vision system: This is used to determine whether a component is damaged or faulty and confirm a component’s loading position by recalibrating the X–Y coordinate.
3. Problem Definition
3.1. Problem Description
- (i)
- Component allocation problem:
- (ii)
- ANC assignment problem:
- (iii)
- Feeder arrangement problem:
- (iv)
- Component height restrictions:
- (v)
- Component pick-and-place sequence:
3.2. Establishment of a Mathematical Model
4. Method
4.1. Component Allocation
4.2. ANC Assignment Using a Quantity Ratio Method
- Step 1:
- Step 2:
- Step 3:
4.3. Feeder Arrangement Using the MDE Algorithm
- (a)
- Initialization
- (b)
- Mutation
- (c)
- Selection
MDE Algorithm
- (a)
- Initialization
- (b)
- Selection
- (c)
- Similarity
- Similarity 1: This method measured the Euclidean distance between an individual and to determine their level of similarity. The mean level of similarity () is the threshold value; individuals with levels of similarity lower than this value are defined as being similar to the position. The equation is presented as follows:
- Similarity 2: Based on the Dice coefficient [23], feeder slots loaded with components are presented in sets to obtain a set-similarity metric function. The equation is presented as follows:
4.4. Determining Placing Sequence Using the Nearest-Neighbor Search and 2-Opt Method
5. Experimental Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Component Allocation | ANC Assignment | Feeder Arrangement | Component Height | Pick-and-Place Sequence | Method | |
---|---|---|---|---|---|---|
Sun et al. [1] | ✓ | ✓ | ✓ | GA | ||
Du and Li [2] | ✓ | ✓ | ✓ | Hybrid GA | ||
Ashayeri et al. [3] | ✓ | ✓ | ✓ | MIP | ||
Torabi et al. [4] | ✓ | ✓ | ✓ | MOPSO | ||
Zhu and Zhang [5] | ✓ | ISFLA | ||||
He et al. [6] | ✓ | ✓ | ✓ | ✓ | HRB | |
Li and Yoon [7] | ✓ | ✓ | ✓ | ANNTS | ||
He et al. [8] | ✓ | ✓ | ✓ | HS | ||
Huang et al. [9] | ✓ | ✓ | ✓ | HMO | ||
This study | ✓ | ✓ | ✓ | ✓ | ✓ | MDE |
Component | Nozzle | Total Number of Components for the Nozzle | Quantity Ratio | ||
---|---|---|---|---|---|
Type | Quantity | Type | Size | ||
D | 15 | AN2 | Small | 50 | 20% |
B | 35 | ||||
A | 20 | AN3 | Small | 20 | 8% |
E | 80 | AN4 | Small | 80 | 32% |
C | 100 | AN5 | Small | 100 | 40% |
F | 10 | ANV1 | Large | 10 | 100% |
PCB | Number of Components | Component Types | Nozzle Types |
---|---|---|---|
PCB-1 | 322 | 17 | 5 |
PCB-2 | 396 | 14 | 4 |
PCB-3 | 532 | 14 | 4 |
PCB-4 | 586 | 16 | 3 |
PCB-5 | 614 | 17 | 2 |
PCB-6 | 638 | 18 | 4 |
PCB-7 | 682 | 19 | 5 |
PCB-8 | 696 | 17 | 5 |
PCB-9 | 720 | 15 | 3 |
PCB-10 | 796 | 17 | 2 |
Methods | MDE | DE | PSO | GA | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Similarity1 | Similarity2 | |||||||||
Gantry | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |
PCB-1 | 44 | 61 | 51 | 68 | 62 | 70 | 67 | 75 | 64 | 77 |
PCB-2 | 47 | 70 | 52 | 64 | 67 | 89 | 89 | 96 | 82 | 87 |
PCB-3 | 93 | 91 | 92 | 92 | 98 | 94 | 100 | 108 | 96 | 119 |
PCB-4 | 85 | 73 | 83 | 74 | 103 | 96 | 113 | 90 | 116 | 117 |
PCB-5 | 106 | 100 | 99 | 100 | 118 | 114 | 119 | 116 | 128 | 124 |
PCB-6 | 92 | 93 | 95 | 93 | 100 | 107 | 128 | 113 | 127 | 129 |
PCB-7 | 121 | 128 | 132 | 129 | 142 | 154 | 126 | 159 | 172 | 157 |
PCB-8 | 108 | 112 | 109 | 117 | 134 | 120 | 130 | 151 | 142 | 151 |
PCB-9 | 93 | 109 | 94 | 107 | 127 | 117 | 134 | 122 | 129 | 132 |
PCB-10 | 119 | 124 | 119 | 122 | 141 | 151 | 154 | 137 | 155 | 155 |
Average | 90.8 | 96.1 | 92.6 | 96.6 | 109.2 | 111.2 | 116 | 116.7 | 121.1 | 124.8 |
DE | PSO | GA | ||||
---|---|---|---|---|---|---|
Gantry | 1 | 2 | 1 | 2 | 1 | 2 |
MDE Similarity1 | −20.3% | −15.7% | −27.7% | −21.4% | −33.4% | −30.0% |
MDE Similarity2 | −18.0% | −15.1% | −25.2% | −20.8% | −25.3% | −29.2% |
PCB Methods | PCB-1 | PCB-2 | PCB-3 | PCB-4 | PCB-5 | PCB-6 | PCB-7 | PCB-8 | PCB-9 | PCB-10 | Average | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
MDE Similarity 1 | Gantry_1 | 5535.9 | 6386.0 | 14,393.6 | 13,189.3 | 7890.4 | 5687.5 | 14,087.7 | 5921.0 | 14,087.7 | 8882.6 | 9606.2 |
Gantry_2 | 22,098.5 | 24,283.0 | 35,681.5 | 38,810.7 | 45,165.2 | 53,235.6 | 52,695.1 | 49,152.5 | 52,695.1 | 51,267.8 | 42,508.5 | |
MDE Similarity 2 | Gantry_1 | 8996.7 | 6243.4 | 8045.6 | 4909.0 | 27,345.5 | 14,804.7 | 14,339.6 | 15,061.7 | 14,339.6 | 12,437.5 | 12,652.3 |
Gantry_2 | 28,887.4 | 24,629.2 | 36,614.3 | 38,195.4 | 45,436.8 | 43,432.9 | 52,207.5 | 58,298.6 | 52,207.5 | 52,018.6 | 43,192.8 | |
DE | Gantry_1 | 17,300.6 | 8164.9 | 17,093.5 | 18,870.2 | 16,074.5 | 20,976.4 | 29,878.2 | 16,623.0 | 29,878.2 | 22,145.1 | 19,700.5 |
Gantry_2 | 30,402.3 | 29,038.3 | 47,589.3 | 49,700.0 | 73,724.1 | 61,888.1 | 48,086.1 | 60,670.6 | 48,086.1 | 65,426.5 | 51,461.1 | |
PSO | Gantry_1 | 20,085.0 | 46,903.4 | 14,901.8 | 19,732.4 | 50,936.9 | 56,762.9 | 30,744.5 | 76,028.7 | 30,744.5 | 62,205.5 | 40,904.6 |
Gantry_2 | 26,791.4 | 65,493.1 | 68,364.6 | 44,386.8 | 56,528.2 | 51,164.0 | 52,767.6 | 75,556.7 | 52,767.6 | 61,737.6 | 55,555.8 | |
GA | Gantry_1 | 15,732.5 | 31,684.0 | 21,321.1 | 55,354.4 | 55,776.3 | 76,430.6 | 25,093.5 | 26,523.6 | 25,093.5 | 26,929.9 | 35,993.9 |
Gantry_2 | 34,702.8 | 27,899.8 | 66,586.1 | 22,457.9 | 52,666.3 | 37,960.3 | 48,536.2 | 72,913.3 | 48,536.2 | 63,998.6 | 47,625.8 |
Methods PCB | MDE | DE | PSO | GA | |
---|---|---|---|---|---|
Similarity1 | Similarity2 | ||||
PCB-1 | 194.1 | 193.5 | 211.4 | 197.5 | 212.8 |
PCB-2 | 277.3 | 282.8 | 301.9 | 324.8 | 297.2 |
PCB-3 | 184.6 | 179.3 | 194.7 | 227.9 | 233.2 |
PCB-4 | 233.8 | 222.3 | 242.0 | 245.7 | 250.0 |
PCB-5 | 287.8 | 294.3 | 312.1 | 321.4 | 313.6 |
PCB-6 | 274.0 | 284.0 | 288.3 | 314.4 | 313.7 |
PCB-7 | 318.5 | 304.2 | 373.2 | 343.3 | 352.6 |
PCB-8 | 245.5 | 267.4 | 284.6 | 284.0 | 282.1 |
PCB-9 | 350.5 | 349.4 | 387.1 | 409.6 | 361.8 |
PCB-10 | 296.5 | 305.0 | 329.0 | 340.6 | 308.6 |
Average | 266.26 | 268.22 | 292.43 | 300.92 | 292.56 |
DE | PSO | GA | |
---|---|---|---|
MDE Similarity1 | −9.8% | −13.0% | −9.8% |
MDE Similarity2 | −9.0% | −12.2% | −9.1% |
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Lin, C.-J.; Lin, C.-H. Using an Improved Differential Evolution for Scheduling Optimization of Dual-Gantry Multi-Head Surface-Mount Placement Machine. Mathematics 2021, 9, 2016. https://doi.org/10.3390/math9162016
Lin C-J, Lin C-H. Using an Improved Differential Evolution for Scheduling Optimization of Dual-Gantry Multi-Head Surface-Mount Placement Machine. Mathematics. 2021; 9(16):2016. https://doi.org/10.3390/math9162016
Chicago/Turabian StyleLin, Cheng-Jian, and Chun-Hui Lin. 2021. "Using an Improved Differential Evolution for Scheduling Optimization of Dual-Gantry Multi-Head Surface-Mount Placement Machine" Mathematics 9, no. 16: 2016. https://doi.org/10.3390/math9162016
APA StyleLin, C.-J., & Lin, C.-H. (2021). Using an Improved Differential Evolution for Scheduling Optimization of Dual-Gantry Multi-Head Surface-Mount Placement Machine. Mathematics, 9(16), 2016. https://doi.org/10.3390/math9162016