Cyber-Physical Scheduling System for Multiobjective Scheduling Optimization of a Suspension Chain Workshop Using the Improved Non-Dominated Sorting Genetic Algorithm II
Abstract
:1. Introduction
2. Research Background
2.1. Cyber-Physical System and Digital Twins
2.2. Multiobjective Scheduling Problem
2.3. Multiconstraint Scheduling Problem
2.4. About Simulation and Modeling
3. Model Establishment
3.1. Design of Cyber-Physical Scheduling Systems
3.2. Practical Application Context
- First, the mathematical model is constructed, which will be used for the design and improvement of the algorithm.
- Next, the discrete system simulation model is constructed to verify the algorithm’s results through simulation.
- Finally, the logical control model is constructed. These models, derived from the discrete system simulation model, will guide the operation of the suspension–chain–transportation system.
4. Algorithm Model Establishment
4.1. Symbol Definitions
4.2. Algorithm Framework Selection
4.3. Encoding
4.4. Constraints
- Within the same production line, no two operations on any workpiece should occur consecutively more than once.
- Across all production lines, there should be no excessive distance between any two consecutive operations on any workpiece.
4.5. Objective Function
- Maximize the product of the weight and the last output time of each order i, summed over all orders n:
- Minimize the number of tool changeovers across all production lines m, where is the total time spent on tool changes per production line:Here, represents the total tool change time for production line j.
4.6. Operator Design
4.6.1. Population Initialization
Algorithm 1 InsertGens |
Require: , , , Ensure: , ,
|
4.6.2. Crossover
4.6.3. Mutation
4.7. Fitting of Processing Time
4.8. Algorithm Convergence Results
5. Simulation Model Establishment
5.1. Simulation Fidelity
5.1.1. Randomly Repeated Experiments
5.1.2. Module Decoupling
5.1.3. Constraints and Assumptions
- The suspension chain is replaced with a roller conveyor line, and turntables are employed at corners instead. Since their performance and parameters are identical and Anylogic does not have a pre-packaged suspension chain model, substituting with an existing roller conveyor line ensures equivalent effectiveness while considerably simplifying the workload.
- The tray’s speed during operation is constant, and the acceleration of the tray on the conveyor belt is neglected. In production, trays move slowly; therefore, strict speed requirements are not necessary. Additionally, due to the significant acceleration of workpieces during movement, neglecting tray acceleration increases model stability.
5.2. The Logic Control Scheme
- Output sequence from loading ports 1–4 to I22.
- Output sequence from loading ports 5–8 to I27.
- Output sequence from two loading-port convergence nodes into mainline C1.
- Output sequence from four processing lines to P12.
- Output sequence from the initial processing and repeat processing workpieces into main processing line P1.
6. Joint Simulation
6.1. Simulation Parameters
6.2. Experimental Design
6.3. Simulation Result
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Name | Definition Range | Meaning |
---|---|---|
If workpiece be loaded | ||
Allow Carriers Loading | ||
- | If the total input sufficient | |
- | Activate Algorithm Logic |
Name | Definition Range | Data Type | Meaning |
---|---|---|---|
int | Current Input Lane with Carriages | ||
- | int | All Input Lanes with Carriages | |
- | int | First, Four Inputs with Carriages | |
- | int | Last Four Inputs with Carriages | |
int | Number of Changeovers per Station | ||
double | Output Time for Each Order | ||
double | Importance Index for Each Order |
Name | Definition Range | Data Type | Meaning |
---|---|---|---|
int | Input Section Capacity | ||
int | Output Section Capacity | ||
int | Cleaning and Masking Section Capacity | ||
int | Processing Section Capacity | ||
int | Multiple Processing Section Capacity | ||
int | Drying Section Capacity | ||
- | double | Safety Distance | |
- | List<double> | Interval of Workpiece Arrivals | |
- | double | Conveyor Speed | |
- | int | Number of Carriers | |
− | Cleaning Processing Time | ||
− | Time of (un)Loading Masking | ||
− | Time of Spray Coating | ||
double | Workpiece Loading Time | ||
double | Workpiece Unloading Time | ||
- | double | Changeover Time | |
- | int | Number of Orders | |
- | int | Number of Workpieces | |
int | Input Section Current Inventory | ||
int | Output Section Current Inventory | ||
int | Cleaning and Masking Section Current Inventory | ||
int | Processing Section Current Inventory | ||
int | Multiple Processing Section Current Inventory | ||
int | Drying Section Current Inventory |
Order | Color | Size | Type | Times | Num | Weight |
---|---|---|---|---|---|---|
1 | 3 | 8 | 1 | 1 | 6 | 0.60 |
2 | 1 | 10 | 1 | 2 | 3 | 0.65 |
3 | 1 | 5 | 2 | 2 | 9 | 2.90 |
4 | 2 | 6 | 2 | 2 | 11 | 0.68 |
5 | 3 | 4 | 3 | 2 | 14 | 0.53 |
6 | 1 | 3 | 3 | 1 | 11 | 0.07 |
7 | 1 | 3 | 4 | 2 | 6 | 1.70 |
8 | 2 | 1 | 4 | 1 | 3 | 0.22 |
9 | 3 | 1 | 5 | 1 | 6 | 1.80 |
10 | 1 | 3 | 5 | 2 | 12 | 0.01 |
11 | 3 | 1 | 6 | 2 | 3 | 0.47 |
12 | 3 | 3 | 6 | 2 | 9 | 0.48 |
13 | 1 | 1 | 7 | 2 | 11 | 1.55 |
14 | 1 | 3 | 7 | 1 | 3 | 0.48 |
15 | 3 | 1 | 8 | 2 | 14 | 1.24 |
16 | 3 | 1 | 8 | 2 | 4 | 0.43 |
Number of Experiments | Weighted Fitness |
---|---|
1 | −0.5000 |
2 | −0.4999 |
3 | −0.5000 |
4 | −0.4687 |
5 | −0.4999 |
6 | −0.5000 |
7 | −0.5000 |
8 | −0.2490 |
9 | −0.4892 |
10 | −0.4460 |
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Zhao, W.; Hu, J.; Lu, J.; Zhang, W. Cyber-Physical Scheduling System for Multiobjective Scheduling Optimization of a Suspension Chain Workshop Using the Improved Non-Dominated Sorting Genetic Algorithm II. Machines 2024, 12, 666. https://doi.org/10.3390/machines12090666
Zhao W, Hu J, Lu J, Zhang W. Cyber-Physical Scheduling System for Multiobjective Scheduling Optimization of a Suspension Chain Workshop Using the Improved Non-Dominated Sorting Genetic Algorithm II. Machines. 2024; 12(9):666. https://doi.org/10.3390/machines12090666
Chicago/Turabian StyleZhao, Wenbin, Junhan Hu, Jiansha Lu, and Wenzhu Zhang. 2024. "Cyber-Physical Scheduling System for Multiobjective Scheduling Optimization of a Suspension Chain Workshop Using the Improved Non-Dominated Sorting Genetic Algorithm II" Machines 12, no. 9: 666. https://doi.org/10.3390/machines12090666
APA StyleZhao, W., Hu, J., Lu, J., & Zhang, W. (2024). Cyber-Physical Scheduling System for Multiobjective Scheduling Optimization of a Suspension Chain Workshop Using the Improved Non-Dominated Sorting Genetic Algorithm II. Machines, 12(9), 666. https://doi.org/10.3390/machines12090666