A Reinforcement Learning Approach to Solving
Hybrid Flexible Flowline Scheduling Problems
Bert Van Vreckem Dmitriy Borodin...
Authors
• Bert Van Vreckem, HoGent Business and Information
Management
bert.vanvreckem@hogent.be
• Dmitriy Borodin, OMPart...
Contents
1 Hybrid Flexible Flowline Scheduling Problems
2 A Machine Learning Approach
3 Learning Permutations with Precede...
Hybrid Flexible Flowline Scheduling Problems
Powerful model for complex real-life production scheduling
problems.
In α/β/γ...
Hybrid Flexible Flowline Scheduling Problems
Powerful model for complex real-life production scheduling
problems.
In α/β/γ...
Hybrid Flexible Flowline Scheduling Problems
Hybrid case: unrelated parallel machines
M11
M12
M13
M21
M22
M31
M32
M33
M34
...
Hybrid Flexible Flowline Scheduling Problems
Flexible case: stages may be skipped
M11
M12
M13
M21
M22
M41
M42
HFFSP MISTA2...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Machine eligibility
M11
M13
M21
M22
M31
M33
M42
HFFSP MIST...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Time lag between stages
Stage 1
Stage 2
Stage 3
Stage 4
HF...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Sequence dependent setup times
1 2 3 4 5 6 7 8 9 10 11 12
...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Sequence dependent setup times
1 2 3 4 5 6 7 8 9 10 11 12
...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Sequence dependent setup times
1 2 3 4 5 6 7 8 9 10 11 12
...
Hybrid Flexible Flowline Scheduling Problems
Other constraints: Precendence relations between jobs
1 2 3 4 5 6 7 8 9 10 11...
Hybrid Flexible Flowline Scheduling Problems
Precedence relations between jobs make the problem much
harder, in a way that...
Contents
1 Hybrid Flexible Flowline Scheduling Problems
2 A Machine Learning Approach
3 Learning Permutations with Precede...
A Machine Learning Approach
Scheduling Hybrid Flexible Flowline Scheduling Problems
Two stages:
• Job permutations
• Machi...
A Machine Learning Approach
Scheduling Hybrid Flexible Flowline Scheduling Problems
Two stages:
• Job permutations → Learn...
A Machine Learning Approach
Scheduling Hybrid Flexible Flowline Scheduling Problems
Two stages:
• Job permutations → Learn...
A Machine Learning Approach
Scheduling Hybrid Flexible Flowline Scheduling Problems
Two stages:
• Job permutations → Learn...
Reinforcement learning
At every discrete time step t:
• Agent percieves environment state s(t)
• Agent chooses action a(t)...
Learning Automata (LA)
Reinforcement Learning agents that choose action according to
probability distribution p(t) = (p1(t...
Learning Automata (LA)
Reinforcement Learning agents that choose action according to
probability distribution p(t) = (p1(t...
Learning Automata (LA)
Reinforcement Learning agents that choose action according to
probability distribution p(t) = (p1(t...
Learning Automaton update
1 2 3 4
0
0.2
0.4
0.6
0.8
1
i
pi
HFFSP MISTA2013: 29 August 2013 18/28
Learning Automaton update
1 2 3 4
0
0.2
0.4
0.6
0.8
1
i
pi
E.g. action 3 was chosen
HFFSP MISTA2013: 29 August 2013 18/28
Learning Automaton update
1 2 3 4
0
0.2
0.4
0.6
0.8
1
i
pi
E.g. action 3 was chosen
1 2 3 4
0
0.2
0.4
0.6
0.8
1
r(t) = 1
p...
Learning Automaton update
1 2 3 4
0
0.2
0.4
0.6
0.8
1
i
pi
E.g. action 3 was chosen
1 2 3 4
0
0.2
0.4
0.6
0.8
1
r(t) = 1
p...
Contents
1 Hybrid Flexible Flowline Scheduling Problems
2 A Machine Learning Approach
3 Learning Permutations with Precede...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
HFFSP MIS...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
(Wauters, 2012)
• A LA is assigned to every position of a permutation
• LAs pla...
Probabilistic Basic Simple Strategy (PBSS)
• PBSS: great results in several optimization problems that
involve learning pe...
Probabilistic Basic Simple Strategy (PBSS)
• PBSS: great results in several optimization problems that
involve learning pe...
Probabilistic Basic Simple Strategy (PBSS)
• PBSS: great results in several optimization problems that
involve learning pe...
Probabilistic Basic Simple Strategy (PBSS)
• PBSS: great results in several optimization problems that
involve learning pe...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Extending PBSS for precendence constraints
Updating probabilities:
• If the job permutation is invalid, perform an update ...
Contents
1 Hybrid Flexible Flowline Scheduling Problems
2 A Machine Learning Approach
3 Learning Permutations with Precede...
Experiments
• HFFSP Benchmark problems from (Ruiz et al., 2008)2
• problem sets with 5, 7, 9, 11, 13, 15 jobs, 96 instance...
Results
Instance set 5 7 9 11 13 15 overall
mean RD (%) 0.0697 2.0131 1.1568 1.6565 3.7294 7.9189 2.7484
best RD (%) -35.7...
Results
Instance set 5 7 9 11 13 15 overall
mean RD (%) 0.0697 2.0131 1.1568 1.6565 3.7294 7.9189 2.7484
best RD (%) -35.7...
Contents
1 Hybrid Flexible Flowline Scheduling Problems
2 A Machine Learning Approach
3 Learning Permutations with Precede...
Results and Discussion
Contributions:
• Extension of PBSS for learning permutations with precedence
constraints
• Simple m...
Results and Discussion
Contributions:
• Extension of PBSS for learning permutations with precedence
constraints
• Simple m...
Thank you!
Questions?
bert.vanvreckem@hogent.be
http://www.slideshare.net/bertvanvreckem/
HFFSP MISTA2013: 29 August 2013 ...
A Reinforcement Learning Approach for Hybrid Flexible Flowline Scheduling Problems
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A Reinforcement Learning Approach for Hybrid Flexible Flowline Scheduling Problems

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Paper presented at MISTA2013, Gent.

In this paper, we present a method based on Learning Automata to solve Hybrid Flexible Flowline Scheduling Problems (HFFSP) with additional constraints like sequence dependent setup times, precedence relations between jobs and machine eligibility. This category of production scheduling problems is noteworthy because it involves several types of constraints that occur in complex real-life production scheduling problems like those in process industry and batch production. In the proposed technique, Learning Automata play a dispersion game to determine the order of jobs to be processed in a way that makespan is minimized, and precedence constraint violations are avoided. Experiments on a set of benchmark problems indicate that this method can yield better results than the ones known until now.

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A Reinforcement Learning Approach for Hybrid Flexible Flowline Scheduling Problems

  1. 1. A Reinforcement Learning Approach to Solving Hybrid Flexible Flowline Scheduling Problems Bert Van Vreckem Dmitriy Borodin Wim De Bruyn Ann Now´e
  2. 2. Authors • Bert Van Vreckem, HoGent Business and Information Management bert.vanvreckem@hogent.be • Dmitriy Borodin, OMPartners dborodin@ompartners.com • Wim De Bruyn, HoGent Business and Information Management wim.debruyn@hogent.be • Ann Now´e, Artificial Intelligence Lab, Vrije Universiteit Brussel ann.nowe@vub.ac.be HFFSP MISTA2013: 29 August 2013 3/28
  3. 3. Contents 1 Hybrid Flexible Flowline Scheduling Problems 2 A Machine Learning Approach 3 Learning Permutations with Precedence Constraints 4 Experiments & results 5 Conclusion HFFSP MISTA2013: 29 August 2013 4/28
  4. 4. Hybrid Flexible Flowline Scheduling Problems Powerful model for complex real-life production scheduling problems. In α/β/γ notation1: HFFLm, ((RM(i) ) (m) i=1/Mj, rm, prec, Siljk, Ailjk, lag/Cmax 1 (Urlings, 2010) HFFSP MISTA2013: 29 August 2013 5/28
  5. 5. Hybrid Flexible Flowline Scheduling Problems Powerful model for complex real-life production scheduling problems. In α/β/γ notation1: HFFLm, ((RM(i) ) (m) i=1/Mj, rm, prec, Siljk, Ailjk, lag/Cmax Flowline Scheduling problems: jobs processed in consecutive stages. Stage 1 Stage 2 Stage 3 Stage 4 1 (Urlings, 2010) HFFSP MISTA2013: 29 August 2013 5/28
  6. 6. Hybrid Flexible Flowline Scheduling Problems Hybrid case: unrelated parallel machines M11 M12 M13 M21 M22 M31 M32 M33 M34 M41 M42 HFFSP MISTA2013: 29 August 2013 6/28
  7. 7. Hybrid Flexible Flowline Scheduling Problems Flexible case: stages may be skipped M11 M12 M13 M21 M22 M41 M42 HFFSP MISTA2013: 29 August 2013 7/28
  8. 8. Hybrid Flexible Flowline Scheduling Problems Other constraints: Machine eligibility M11 M13 M21 M22 M31 M33 M42 HFFSP MISTA2013: 29 August 2013 8/28
  9. 9. Hybrid Flexible Flowline Scheduling Problems Other constraints: Time lag between stages Stage 1 Stage 2 Stage 3 Stage 4 HFFSP MISTA2013: 29 August 2013 9/28
  10. 10. Hybrid Flexible Flowline Scheduling Problems Other constraints: Sequence dependent setup times 1 2 3 4 5 6 7 8 9 10 11 12 J1 J2M1 J1 J2M2 HFFSP MISTA2013: 29 August 2013 10/28
  11. 11. Hybrid Flexible Flowline Scheduling Problems Other constraints: Sequence dependent setup times 1 2 3 4 5 6 7 8 9 10 11 12 J1 J2M1 J1 J2M2 J2 J1M1 J2 J1M2 HFFSP MISTA2013: 29 August 2013 10/28
  12. 12. Hybrid Flexible Flowline Scheduling Problems Other constraints: Sequence dependent setup times 1 2 3 4 5 6 7 8 9 10 11 12 J1 J2M1 J1 J2M2 J2 J1M1 J2 J1M2 HFFSP MISTA2013: 29 August 2013 11/28
  13. 13. Hybrid Flexible Flowline Scheduling Problems Other constraints: Precendence relations between jobs 1 2 3 4 5 6 7 8 9 10 11 12 J1 J2M1 J1 J2M2 J2 J1M1 J2 J1M2 HFFSP MISTA2013: 29 August 2013 12/28
  14. 14. Hybrid Flexible Flowline Scheduling Problems Precedence relations between jobs make the problem much harder, in a way that MILP/CPLEX approach doesn’t work anymore for larger instances (Urlings, 2010) HFFSP MISTA2013: 29 August 2013 13/28
  15. 15. Contents 1 Hybrid Flexible Flowline Scheduling Problems 2 A Machine Learning Approach 3 Learning Permutations with Precedence Constraints 4 Experiments & results 5 Conclusion HFFSP MISTA2013: 29 August 2013 14/28
  16. 16. A Machine Learning Approach Scheduling Hybrid Flexible Flowline Scheduling Problems Two stages: • Job permutations • Machine assignment HFFSP MISTA2013: 29 August 2013 15/28
  17. 17. A Machine Learning Approach Scheduling Hybrid Flexible Flowline Scheduling Problems Two stages: • Job permutations → Learning Automata • Machine assignment HFFSP MISTA2013: 29 August 2013 15/28
  18. 18. A Machine Learning Approach Scheduling Hybrid Flexible Flowline Scheduling Problems Two stages: • Job permutations → Learning Automata • Machine assignment → Earliest Preparation Next Stage (EPNS) (Urlings, 2010) HFFSP MISTA2013: 29 August 2013 15/28
  19. 19. A Machine Learning Approach Scheduling Hybrid Flexible Flowline Scheduling Problems Two stages: • Job permutations → Learning Automata • Machine assignment → Earliest Preparation Next Stage (EPNS) (Urlings, 2010) HFFSP MISTA2013: 29 August 2013 15/28
  20. 20. Reinforcement learning At every discrete time step t: • Agent percieves environment state s(t) • Agent chooses action a(t) ∈ A = a1, . . . , an according to some policy • Environment places agent in new state s(t + 1) and gives reinforcement r(t) • Goal: learn policy that maximizes long term cumulative reward t r(t) Environment Agent s r a HFFSP MISTA2013: 29 August 2013 16/28
  21. 21. Learning Automata (LA) Reinforcement Learning agents that choose action according to probability distribution p(t) = (p1(t), . . . , pn(t)), with pi = Prob[a(t) = ai] and s.t. n i=1 pi = 1 pi(0) = 1 n (1) pi(t + 1) = pi(t) +αrewr(t)(1 − pi(t)) −αpen(1 − r(t))pi(t) (2) if ai is the action taken at instant t pj(t + 1) = pj(t) −αrewr(t)pj(t) +αpen(1 − r(t)) 1 n − 1 − pj(t) (3) if aj = ai HFFSP MISTA2013: 29 August 2013 17/28
  22. 22. Learning Automata (LA) Reinforcement Learning agents that choose action according to probability distribution p(t) = (p1(t), . . . , pn(t)), with pi = Prob[a(t) = ai] and s.t. n i=1 pi = 1 pi(0) = 1 n (1) pi(t + 1) = pi(t) +αrewr(t)(1 − pi(t)) −αpen(1 − r(t))pi(t) (2) if ai is the action taken at instant t pj(t + 1) = pj(t) −αrewr(t)pj(t) +αpen(1 − r(t)) 1 n − 1 − pj(t) (3) if aj = ai HFFSP MISTA2013: 29 August 2013 17/28
  23. 23. Learning Automata (LA) Reinforcement Learning agents that choose action according to probability distribution p(t) = (p1(t), . . . , pn(t)), with pi = Prob[a(t) = ai] and s.t. n i=1 pi = 1 pi(0) = 1 n (1) pi(t + 1) = pi(t) +αrewr(t)(1 − pi(t)) −αpen(1 − r(t))pi(t) (2) if ai is the action taken at instant t pj(t + 1) = pj(t) −αrewr(t)pj(t) +αpen(1 − r(t)) 1 n − 1 − pj(t) (3) if aj = ai HFFSP MISTA2013: 29 August 2013 17/28
  24. 24. Learning Automaton update 1 2 3 4 0 0.2 0.4 0.6 0.8 1 i pi HFFSP MISTA2013: 29 August 2013 18/28
  25. 25. Learning Automaton update 1 2 3 4 0 0.2 0.4 0.6 0.8 1 i pi E.g. action 3 was chosen HFFSP MISTA2013: 29 August 2013 18/28
  26. 26. Learning Automaton update 1 2 3 4 0 0.2 0.4 0.6 0.8 1 i pi E.g. action 3 was chosen 1 2 3 4 0 0.2 0.4 0.6 0.8 1 r(t) = 1 pi HFFSP MISTA2013: 29 August 2013 18/28
  27. 27. Learning Automaton update 1 2 3 4 0 0.2 0.4 0.6 0.8 1 i pi E.g. action 3 was chosen 1 2 3 4 0 0.2 0.4 0.6 0.8 1 r(t) = 1 pi 1 2 3 4 0 0.2 0.4 0.6 0.8 1 r(t) = 0 pi HFFSP MISTA2013: 29 August 2013 18/28
  28. 28. Contents 1 Hybrid Flexible Flowline Scheduling Problems 2 A Machine Learning Approach 3 Learning Permutations with Precedence Constraints 4 Experiments & results 5 Conclusion HFFSP MISTA2013: 29 August 2013 19/28
  29. 29. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation HFFSP MISTA2013: 29 August 2013 20/28
  30. 30. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation HFFSP MISTA2013: 29 August 2013 20/28
  31. 31. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation • Quality of solution is evaluated HFFSP MISTA2013: 29 August 2013 20/28
  32. 32. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation • Quality of solution is evaluated • Update probabilities according to LA update rule Linear Reward-Inaction (αpen = 0): HFFSP MISTA2013: 29 August 2013 20/28
  33. 33. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation • Quality of solution is evaluated • Update probabilities according to LA update rule Linear Reward-Inaction (αpen = 0): • Better result than best one so far: r(t) = 1 HFFSP MISTA2013: 29 August 2013 20/28
  34. 34. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation • Quality of solution is evaluated • Update probabilities according to LA update rule Linear Reward-Inaction (αpen = 0): • Better result than best one so far: r(t) = 1 • If not, r(t) = 0 HFFSP MISTA2013: 29 August 2013 20/28
  35. 35. Probabilistic Basic Simple Strategy (PBSS) (Wauters, 2012) • A LA is assigned to every position of a permutation • LAs play a dispersion game to choose unique action, resulting in a permutation • Quality of solution is evaluated • Update probabilities according to LA update rule Linear Reward-Inaction (αpen = 0): • Better result than best one so far: r(t) = 1 • If not, r(t) = 0 • Repeat until convergence HFFSP MISTA2013: 29 August 2013 20/28
  36. 36. Probabilistic Basic Simple Strategy (PBSS) • PBSS: great results in several optimization problems that involve learning permutations HFFSP MISTA2013: 29 August 2013 21/28
  37. 37. Probabilistic Basic Simple Strategy (PBSS) • PBSS: great results in several optimization problems that involve learning permutations • but doesn’t work well when precedence constraints are involved HFFSP MISTA2013: 29 August 2013 21/28
  38. 38. Probabilistic Basic Simple Strategy (PBSS) • PBSS: great results in several optimization problems that involve learning permutations • but doesn’t work well when precedence constraints are involved • PBSS only learns from positive experience (i.e. improving on previous solutions) HFFSP MISTA2013: 29 August 2013 21/28
  39. 39. Probabilistic Basic Simple Strategy (PBSS) • PBSS: great results in several optimization problems that involve learning permutations • but doesn’t work well when precedence constraints are involved • PBSS only learns from positive experience (i.e. improving on previous solutions) • Doesn’t learn to avoid invalid permutations HFFSP MISTA2013: 29 August 2013 21/28
  40. 40. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. HFFSP MISTA2013: 29 August 2013 22/28
  41. 41. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. • If the job permutation is valid, perform a LR−I update in all agents, depending on the resulting makespan ms and best makespan until now msbest: HFFSP MISTA2013: 29 August 2013 22/28
  42. 42. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. • If the job permutation is valid, perform a LR−I update in all agents, depending on the resulting makespan ms and best makespan until now msbest: • improved: r(t) = 1; HFFSP MISTA2013: 29 August 2013 22/28
  43. 43. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. • If the job permutation is valid, perform a LR−I update in all agents, depending on the resulting makespan ms and best makespan until now msbest: • improved: r(t) = 1; • equally good: r(t) = 1/2; HFFSP MISTA2013: 29 August 2013 22/28
  44. 44. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. • If the job permutation is valid, perform a LR−I update in all agents, depending on the resulting makespan ms and best makespan until now msbest: • improved: r(t) = 1; • equally good: r(t) = 1/2; • worse: r(t) = msbest 2ms ; HFFSP MISTA2013: 29 August 2013 22/28
  45. 45. Extending PBSS for precendence constraints Updating probabilities: • If the job permutation is invalid, perform an update with r(t) = 0 and αpen > 0 for all agents that are involved in the violation of precedence constraints. • If the job permutation is valid, perform a LR−I update in all agents, depending on the resulting makespan ms and best makespan until now msbest: • improved: r(t) = 1; • equally good: r(t) = 1/2; • worse: r(t) = msbest 2ms ; • no valid schedule found: r(t) = 0; HFFSP MISTA2013: 29 August 2013 22/28
  46. 46. Contents 1 Hybrid Flexible Flowline Scheduling Problems 2 A Machine Learning Approach 3 Learning Permutations with Precedence Constraints 4 Experiments & results 5 Conclusion HFFSP MISTA2013: 29 August 2013 23/28
  47. 47. Experiments • HFFSP Benchmark problems from (Ruiz et al., 2008)2 • problem sets with 5, 7, 9, 11, 13, 15 jobs, 96 instances in each set • + other constraints that make problems harder (precedence relations!) • αrew = 0.1; αpen = 0.5 (no tuning) • Run until converges, or at most 300 seconds 2 Available at http://soa.iti.es/problem-instances HFFSP MISTA2013: 29 August 2013 24/28
  48. 48. Results Instance set 5 7 9 11 13 15 overall mean RD (%) 0.0697 2.0131 1.1568 1.6565 3.7294 7.9189 2.7484 best RD (%) -35.70 -24.71 -26.92 -21.10 -43.34 -10.46 -43.34 # improved 11 12 18 12 9 6 68 # equal 62 40 19 18 8 7 154 # worse 23 44 59 66 79 82 354 HFFSP MISTA2013: 29 August 2013 25/28
  49. 49. Results Instance set 5 7 9 11 13 15 overall mean RD (%) 0.0697 2.0131 1.1568 1.6565 3.7294 7.9189 2.7484 best RD (%) -35.70 -24.71 -26.92 -21.10 -43.34 -10.46 -43.34 # improved 11 12 18 12 9 6 68 # equal 62 40 19 18 8 7 154 # worse 23 44 59 66 79 82 354 HFFSP MISTA2013: 29 August 2013 25/28
  50. 50. Contents 1 Hybrid Flexible Flowline Scheduling Problems 2 A Machine Learning Approach 3 Learning Permutations with Precedence Constraints 4 Experiments & results 5 Conclusion HFFSP MISTA2013: 29 August 2013 26/28
  51. 51. Results and Discussion Contributions: • Extension of PBSS for learning permutations with precedence constraints • Simple model + RL approach can yield good quality results for challenging HFFSP instances HFFSP MISTA2013: 29 August 2013 27/28
  52. 52. Results and Discussion Contributions: • Extension of PBSS for learning permutations with precedence constraints • Simple model + RL approach can yield good quality results for challenging HFFSP instances Discussion & future work: • Precedence relations do make the problem harder • Parameter tuning • Convergence • Larger instances (50, 100 jobs) • Explore possibilities for improvement in machine assignment HFFSP MISTA2013: 29 August 2013 27/28
  53. 53. Thank you! Questions? bert.vanvreckem@hogent.be http://www.slideshare.net/bertvanvreckem/ HFFSP MISTA2013: 29 August 2013 28/28

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