A distance-based ranking EDA for the permutation flowshop scheduling problem

1. Josu Ceberio A distance-based ranking EDA for the permutation flowshop scheduling problem

2. Previously… • EDAs for integer domains. • EDAs for real value domains. • Few efficient designs for permutation-based problems. POOR PERFORMANCE EHBSA and NHBSA (Tsutsui et al.)

3. Distance-based ranking models • The Mallows model is a distance-based exponential model. • Two parameters • Consensus ranking, • Spread parameter, • Probability distribution

4. Distance-based ranking models • Kendall’s tau distance • Decomposition of the distance • Factorization of the probability distribution 1 2 3 2 1 3 6 4 5 5 6 4 2 0 0 2 1

5. Distance-based ranking EDA • Generalized Mallows EDA is proposed. • A generalization of the Mallows model. • spread parameters. • Probability distribution

6. The problem • To check the performance we approach: • Permutation Flowshop Scheduling Problem. • Extensively studied. • The Mallows EDA demonstrated good performance.

7. Permutation Flowshop Scheduling Problem • Given a set of n jobs and m machines and processing times pij. • Find the sequence for scheduling jobs optimally. • Optimization criterion: Total Flow Time (TFT). Example j2 j5 j1 j4 j3 m1 Codification 1 3 2 5 4 m2 m3 m4 Objective function

8. Generalized Mallows EDAPreliminary experiments Spread parameters

9. Generalized Mallows EDAPreliminary experiments GM model convergence

10. Generalized Mallows EDAApproximating spread parameters Newton-Raphson • An upper bound for the spread parameters is fixed!!

11. Generalized Mallows EDAApproximating spread parameters

12. Generalized Mallows EDAPreliminary experiments Restart mechanism Standart evolutionary shape Improvement ! Restart mechanism shape

13. PFSPstate-of-the-art Asynchronus Genetic Algorithm (AGA) – Xu et al. 2009 Local Search (Swap) LR(n/m) GA VNS Crossover Local Search (Insert) VNS Shake

14. PFSP state-of-the-art Variable Neighborhood Search 4 (VNS4) – Costa et al. 2012 Local Search (Insert) LR(n/m) Local Search (Swap) Shake

15. PFSP state-of-the-art • Fundamentalist approaches rarely achieve optimum solutions. • Hybridization is the path to follow. • High presence of VNS algorithms.

16. First approach to the PFSP • GM-EDA does not succeed. • An hybrid approach is considered: Hybrid Generalized Mallows EDA (HGM-EDA)

17. Hybrid Generalized Mallows EDA Local Search (Swap) Generalized Mallows EDA Local Search (Insert) Orbit Shake VNS

18. Experimentation • Algorithms: AGA, VNS4, GM-EDA, VNS and HGM-EDA. • 20 repetitions • Taillard’s PFSP benchmarks: 100 instances • 20 x 05 • 20 x 10 • 20 x 20 • 50 x 05 • 50 x 10 • 50 x 20 • 100 x 05 • 100 x 10 • 100 x 20 • 200 x 10 • 200 x 20 • 500 x 20

19. Experimentation • Spread parameters upper bound. • Select the upper-theta that provides the best solutions for GM-EDA • Stopping criterion: maximum number of evaluations. • Evaluations performed by AGA in n x m x 0.4s.

20. Experimentation • Taillards benchmark

21. Experimentation • Taillards benchmark

22. Experimentation • Taillards benchmark

23. Experimentation • Taillards benchmark

24. Experimentation • Taillard’s benchmark - Summary

25. Experimentation • Taillard’s benchmark – Results analysis • HGM-EDA outperforms state-of-the-art results in some cases. • Which is the reason for the performance fall given in instances of 500x20? • Biased instances? • A tabu search algorithm was used for to choose the hardest instances. We generate a random benchmark

26. Experimentation • Random benchmark • New configurations between 200 and 500. • Total: 100 instances. • 250 x 10 • 250 x 20 • 300 x 10 • 300 x 20 • 350 x 10 • 350 x 20 • 400 x 10 • 400 x 20 • 450 x 10 • 450 x 20

27. Experimentation • Random benchmark - Summary

28. Experimentation • Random benchmark – Results analysis • Statistical Analysis confirms experimentation. • Friedman test + Shaffer’s static. • HGM-EDA and AGA are definitely the best algorithms. • VNS4 results do not match with those reported. • The performance falls onwards 400x20. What’s wrong with largest instances?

29. Analysis – Hybrid approachImprovement ratio EDA vs. VNS

30. Analysis – Generalized Mallows EDAAGA vs. GM-EDA

31. Analysis – Generalized Mallows EDAThetas convergence

32. Analysis – Generalized Mallows EDAThetas convergence

33. Analysis – Generalized Mallows EDAThetas convergence

34. Analysis – Generalized Mallows EDAThetas convergence

35. Analysis – Generalized Mallows EDAThetas convergence

36. Analysis – Generalized Mallows EDAThetas convergence Stops prematurely!!!

37. Analysis – HGM-EDA vs. AGAMore evaluations • One instance of 500x20

38. Analysis – Generalized Mallows EDALR vs. GM-EDA

39. Analysis – HGM-EDA vs. AGAMore evaluations • One instance of 500x20

40. Analysis – HGM-EDA vs. AGAMore evaluations • One instance of 500x20

41. Analysis – HGM-EDA vs. AGAMore evaluations • One instance of 500x20

42. Conclusions • Hybrid Generalized Mallows EDA is a efficient algorithm for solving the PFSP. • Succeed in 152/220 instances. • The participation of the GM-EDA is essential.

43. Future Work - PFSP • Test other parameters: evaluations, population size, theta bounds, selection size… • Include information of the instance. • Guided Initialization • Shake the solution of the LR(n/m) to build up the population?

44. Future Work – GM-EDA • Set different upper bounds to the spread parameters • Study other distances. • Is suitable Kendall’s-tau distance? • Other distances: Cayley, Ulam, Hamming • Study the problem. • Other problems: • TSP • QAP • LOP (work in progress)

45. Eskerrikasko Josu Ceberio Eskerrikasko Josu Ceberio

46. Distance-based ranking EDA • Mallows EDA • Learning and Sampling