A Parallel Algorithm for Scheduling a Two-Machine Robotic Cell in Bicycle Frame Welding Process
Abstract
:Featured Application
Abstract
1. Introduction
- Level 1
- The order in which jobs are processed in the system.
- Level 2
- Jobs to machines assignment.
- Move the frame elements from the storage field with kit containers and fix them in the positioner. The step is performed by a human operator, and—for safety reasons—with the robot disabled.
- Perform the welding job by the robotic arm. The time required to complete the job depends on the type and the size of the frame and the parameters of the positioner used. Human operator cannot enter the cell.
- Retrieve the finished frame and store it in a dedicated field. The step is performed by a human operator, and—for safety reasons—with the robot disabled.
- A new, parallel algorithm for CAP is proposed, suitable for an execution in a multi-processor environment (e.g., on a GPU).
- A formal analysis of the proposed algorithm is performed, showing time complexity on a -processor Exclusive Read Exclusive Write Parallel Random-Access Machine (EREW PRAM), where n is the number of jobs in a single production cycle.
- A Mixed Integer Linear Programming (MILP) model for CAP is proposed and its performance is discussed. The model is solved by a commercial software; with several standard improvement techniques tested, such as: Hot start, presolving, constraints reduction and providing bounds.
2. Related Work
2.1. Robotic Cells
2.2. Cyclic and Flexible Production
2.3. Additional Problem Constraints
3. Problem Definition
4. Mixed Integer Linear Formulation
5. Sequential Algorithm
5.1. Graph Model
5.2. Algorithm Description
- Build graph .
- Find highlighted path of the lowest weight .
- Transform into an assignment.
6. Parallel Algorithm
6.1. Algorithm Description
Algorithm 1: Parallel exact algorithm for CAP |
|
Algorithm 2: Building an assignment corresponding to a highlighted path |
|
6.2. Computational Complexity
7. Computational Experiments
7.1. Experimental Setup
- —sequential algorithm [12] run time;
- —parallel algorithm run time;
- —sequential MILP solver run time (for smaller instances only).
7.2. Experiments Results and Discussion
8. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number of Jobs n | Speedup CPU vs. GPU | Average Algorithm Run Time [s] | ||
---|---|---|---|---|
CPU [12] | GPU | MILP | ||
16 | 0.013 | 0.000006 | 0.0005 | 0.4775 |
32 | 0.074 | 0.000140 | 0.0019 | 36.0980 |
64 | 0.538 | 0.000880 | 0.0017 | 7597.6177 |
128 | 2.601 | 0.006282 | 0.0024 | – |
256 | 9.605 | 0.062134 | 0.0065 | – |
512 | 32.904 | 0.729642 | 0.0222 | – |
1024 | 75.606 | 7.453988 | 0.0986 | – |
2048 | 122.774 | 69.092194 | 0.5628 | – |
4096 | 216.115 | 643.553306 | 2.9778 | – |
8192 | 313.890 | 5589.780725 | 17.8080 | – |
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Gnatowski, A.; Niżyński, T. A Parallel Algorithm for Scheduling a Two-Machine Robotic Cell in Bicycle Frame Welding Process. Appl. Sci. 2021, 11, 8083. https://doi.org/10.3390/app11178083
Gnatowski A, Niżyński T. A Parallel Algorithm for Scheduling a Two-Machine Robotic Cell in Bicycle Frame Welding Process. Applied Sciences. 2021; 11(17):8083. https://doi.org/10.3390/app11178083
Chicago/Turabian StyleGnatowski, Andrzej, and Teodor Niżyński. 2021. "A Parallel Algorithm for Scheduling a Two-Machine Robotic Cell in Bicycle Frame Welding Process" Applied Sciences 11, no. 17: 8083. https://doi.org/10.3390/app11178083
APA StyleGnatowski, A., & Niżyński, T. (2021). A Parallel Algorithm for Scheduling a Two-Machine Robotic Cell in Bicycle Frame Welding Process. Applied Sciences, 11(17), 8083. https://doi.org/10.3390/app11178083