1. Josu Ceberio

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 12345623165420021

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 p ij.  Find the sequence for scheduling jobs optimally.  Optimization criterion: Total Flow Time (TFT). Codification 1 3 2 5 4 m1m1 m2m2 m3m3 m4m4 j1j1 j3j3 j2j2 j5j5 j4j4 Example Objective function

8. Generalized Mallows EDA Preliminary experiments Spread parameters

9. Generalized Mallows EDA Preliminary experiments GM model convergence

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

11. Generalized Mallows EDA Approximating spread parameters

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

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

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

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

18. Experimentation  Algorithms: AGA, VNS 4, 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 20 x 520 x 1020 x 20 AGA 139322000332911 VNS 4 139322000332911 GM-EDA 139342000920003 VNS 139322000332911 HGM-EDA 139322000332911

21. Experimentation  Taillards benchmark 50 x 550 x 1050 x 20 AGA 6630185916121294 VNS 4 6675786479121739 GM-EDA 6630986948122830 VNS 6630985980121386 HGM-EDA 6630785958121317

22. Experimentation  Taillards benchmark 100 x 5100 x 10100 x 20 AGA 240102 288988374974 VNS 4 242974292425378402 GM-EDA 241346292472379691 VNS 240162289438375410 HGM-EDA 240122 288902374664

23. Experimentation  Taillards benchmark 200 x 10200 x 20500 x 20 AGA 10395071243928 6754943 VNS 4 104852012521656770472 GM-EDA 104614612525457225665 VNS 104184612464746863483 HGM-EDA 10363031237959 6861070

24. Experimentation  Taillard’s benchmark - Summary 20x0520x1020x2050x0550x1050x20100x05100x10100x20200x10200x20500x20 AGA ✔✔✔✔✔✔✔✔ VNS 4 ✔✔✔ GM-EDA VNS ✔✔✔ HGM-EDA ✔✔✔✔✔✔✔

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 250x10250x20300x10300x20350x1 0 350x20400x10400x20450x10450x20 AGA ✔✔✔ VNS 4 GM-EDA VNS HGM-EDA ✔✔✔✔✔✔✔

28. Experimentation  Random benchmark – Results analysis Statistical Analysis confirms experimentation. ○ Friedman test + Shaffer’s static. HGM-EDA and AGA are definitely the best algorithms. VNS 4 results do not match with those reported. The performance falls onwards 400x20. What’s wrong with largest instances?

29. Analysis – Hybrid approach Improvement ratio EDA vs. VNS

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

31. Analysis – Generalized Mallows EDA Thetas convergence

36. Stops prematurely!!!

37. Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDA x1 67106506841042 x2 67086566816514 x3 67081626769335 x4 6708123 6778298 x5 6708029 6779509 x6 6708029 6775003 x7 6706879 x8 6706879  One instance of 500x20

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

39. Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDA x1 67106506841042 x2 67086566816514 x3 67081626769335 x4 6708123 6778298 x5 6708029 6779509 x6 6708029 6775003 x7 6706879 x8 6706879  One instance of 500x20

40. Analysis – HGM-EDA vs. AGA More evaluations Max eval.AGAHGM-EDAGuided HGM-EDA x1 671065068410426743775 x2 670865668165146721295 x3 670816267693356732300 x4 6708123 67782986707129 x5 6708029 67795096716032 x6 6708029 67750036712273 x7 6706879 x8 6706879  One instance of 500x20

41. Analysis – HGM-EDA vs. AGA More 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. Eskerrik asko Josu Ceberio Eskerrik asko Josu Ceberio

46. Distance-based ranking EDA  Mallows EDA Learning and Sampling 0...n - 2 1... n - 1