Solving Rescheduling Problems in Dynamic Permutation Flow Shop Environments with Multiple Objectives Using the Hybrid Dynamic Non-Dominated Sorting Genetic II Algorithm
Abstract
:1. Introduction
1.1. Flow Shop Problems
1.2. Rescheduling Systems
2. Problem Statement
- Factors related to the readiness of jobs and machines:
- ○
- rli is the time when job Ji is available for being processed after arriving to the shop floor (known as release time).
- ○
- rtj is the time when machine Mj is ready to process an incoming job (known as ready time).
- Jobs-related specification factors:
- ○
- pij indicates the processing time needed by the job Ji to be processed on the machine Mj.
- ○
- di represents the due date for job Ji, as requested by the client.
- ○
- wi indicates a weight for the job Ji, representing its urgency.
- Predictive-reactive-related factors:
- ○
- RT is the current rescheduling instant time.
- ○
- represents the starting time of job Ji on machine Mj in the predictive baseline schedule calculated initially.
- Disruption events-related factors:
- ○
- represents the starting time of a breakdown disruption for machine Mj.
- ○
- represents the end time of a breakdown disruption for machine Mj.
- xij are binary variables indicating the position of each Job Ji in the schedule:
- Si,j represents the starting time of job Ji on machine Mj in the calculated new optimal schedule.
- Ci indicates the completion time of job Ji, and it depends on the competition time on each machine Mj (Ci,j).
- yi,j,1, yi,j,2, and yi,j,3 are binary variables that represents three possible situations of machine breakdowns:
- ○
- is 1 (job already processed situation) in case operation of job Ji on machine Mj finishes before we have a breakdown in the machine; otherwise takes 0 value.
- ○
- is 1 (conflict situation) in case operation is not finished when the breakdown occurs; otherwise takes 0 value.
- ○
- is 1 (job starting time displacement situation) in case operation needs to be done after a machine breakdown; otherwise takes 0 value.
3. Proposed Solution
3.1. Rescheduling Architecture
3.2. Hybrid Dynamic NSGA-II Algorithm
4. Results
4.1. Parameter Calibration
4.2. Comparison of HDNSGA-II and RIPG Metaheuristics in Dynamic Multi-Objective Environments
5. Conclusions and Future Lines of Research
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Data Type | Range Established for Irace |
---|---|---|---|
Population size (N) | 54 | Integer | (50, 150) |
Crossover probability | 0.71 | Decimal | (0.5, 0.9) |
Mutation probability | 0.15 | Decimal | (0.05, 0.2) |
nneigh (consecutive positions where a job is reinserted in the local search phase) | 1 | Integer | (1, 12) |
Number of iterations after which an offspring population is obtained using the probabilistic EDA method (interval iterations) | 9 | Integer | (2, 10) |
Maximum consolidation ratio. Once passed, the population is reinitialized using the probabilistic model | 0.51 | Decimal | (0.4, 0.9) |
Maximum number of iterations to reach a consolidation rate greater than the maximum threshold | 55 | Integer | (30, 70) |
Maximum number of iterations improving the solution (the solution is improved in multi-objective when the size of the non-dominated solutions set is increased). Used in tabu search (k) | 2 | Integer | (1, 7) |
Number of iterations for which a movement is marked as tabu (tenure factor) | 3 | Integer | (1, 5) |
20 Jobs | Percentage | 50 Jobs | Percentage | ||||
---|---|---|---|---|---|---|---|
Metric | W− | W+ | W= | Metric | W− | W+ | W= |
Hipervolume | 90.67 | 0.00 | 9.33 | Hipervolume | 5.33 | 82.67 | 12.00 |
D1R | 92.00 | 0.00 | 8.00 | D1R | 8.00 | 66.67 | 25.33 |
RNDS | 57.33 | 5.33 | 37.33 | RNDS | 0.00 | 98.67 | 1.33 |
Epsilon | 80.00 | 0.00 | 20.00 | Epsilon | 9.33 | 69.33 | 21.33 |
100 Jobs | Percentage | 200 Jobs | Percentage | ||||
---|---|---|---|---|---|---|---|
Metric | W− | W+ | W= | Metric | W− | W+ | W= |
Hipervolume | 0 | 100 | 0 | Hipervolume | 0 | 100 | 0 |
D1R | 0 | 100 | 0 | D1R | 0 | 100 | 0 |
RNDS | 0 | 100 | 0 | RNDS | 0 | 100 | 0 |
Epsilon | 0 | 100 | 0 | Epsilon | 0 | 100 | 0 |
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Valledor, P.; Gomez, A.; Puente, J.; Fernandez, I. Solving Rescheduling Problems in Dynamic Permutation Flow Shop Environments with Multiple Objectives Using the Hybrid Dynamic Non-Dominated Sorting Genetic II Algorithm. Mathematics 2022, 10, 2395. https://doi.org/10.3390/math10142395
Valledor P, Gomez A, Puente J, Fernandez I. Solving Rescheduling Problems in Dynamic Permutation Flow Shop Environments with Multiple Objectives Using the Hybrid Dynamic Non-Dominated Sorting Genetic II Algorithm. Mathematics. 2022; 10(14):2395. https://doi.org/10.3390/math10142395
Chicago/Turabian StyleValledor, Pablo, Alberto Gomez, Javier Puente, and Isabel Fernandez. 2022. "Solving Rescheduling Problems in Dynamic Permutation Flow Shop Environments with Multiple Objectives Using the Hybrid Dynamic Non-Dominated Sorting Genetic II Algorithm" Mathematics 10, no. 14: 2395. https://doi.org/10.3390/math10142395
APA StyleValledor, P., Gomez, A., Puente, J., & Fernandez, I. (2022). Solving Rescheduling Problems in Dynamic Permutation Flow Shop Environments with Multiple Objectives Using the Hybrid Dynamic Non-Dominated Sorting Genetic II Algorithm. Mathematics, 10(14), 2395. https://doi.org/10.3390/math10142395