Frédéric Saubion LERIA

1. Learning and Intelligent OptimizatioN Conference AutonomousSearch Frédéric Saubion LERIA

2. Learning and Intelligent OptimizatioN Conference Based on joint works on thistopicwith : G. Di Tollo A. Fiahlo Y. Hamadi F. Lardeux J. Maturana E. Monfroy M. Schoenauer M. Sebag

3. Outline Introduction Main Ideas Taxonomy of AS Focus on examples Conclusion and challenges

4. SolvingConstraintOptimization and SatifactionProblems Generic modeling tools for engineers (Decision) Variables Domains Constraints Introduction Mathematical Model Solver

5. SatifactionProblems • Mapcoloringproblem Introduction

6. SatifactionProblems • Mapcoloringproblem Introduction

7. SatifactionProblems • Mapcoloringproblem Introduction

8. OptimizationProblems Introduction Travelling SalesmanProblem : find a round trip across cities with minimal cost

9. OptimizationProblems Introduction Travelling SalesmanProblem : find a round trip across cities with minimal cost

10. OptimizationProblems Introduction Travelling SalesmanProblem : find a round trip across cities with minimal cost

11. Problems are more and more complex • Searchlandscapes are difficult to explore • Many variables • Complexconstraints Introduction

12. Problems are more and more complex • Searchlandscapes are difficult to explore • Exploration vs. Exploitation Balance Introduction

13. Devising more and more complex Solvingalgorithms Boolean Variable {0,1} • An illustrative example : solving SAT • SAT CNF instance Introduction Assignment (1 0 0) Litterals Clauses

14. Devising more and more complex Solvingalgorithms Introduction How to explore the binary search space (assignments) to find a solution ?

15. Devising more and more complex Solvingalgorithms Introduction Use Local Search

16. Devising more and more complex Solvingalgorithms Basic Local Search Introduction 0 1 0 1 1 Choose a random initial assignment

17. Devising more and more complex Solvingalgorithms Basic Local Search Introduction Compute the number of true and false clauses

18. Devising more and more complex Solvingalgorithms Basic Local Search Introduction 0 1 1 1 1 Move to a neighbor 0 1 0 1 1 Try to improve by changing a value (flip)

19. Devising more and more complex Solvingalgorithms Basic Local Search Introduction Until finding a solution

20. Devising more and more complex Solvingalgorithms Introduction Short overview of the story : a first greedy version GSAT • Bart Selman, Hector J. Levesque, David G. Mitchell: A New Method for Solving Hard SatisfiabilityProblems.AAAI 1992: 440-446 A first boat for binary seas

21. Devising more and more complex Solvingalgorithms Introduction 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 Problem : Many possible moves (many variables)

22. Devising more and more complex Solvingalgorithms Restrict neighborhood Introduction Select a false clause C

23. Devising more and more complex Solvingalgorithms Get stuck in local optima Introduction

24. Devising more and more complex Solvingalgorithms Add pertubations Introduction Select a false clause C With a random probability p Perform a random flip for C With (1-p) Select the variable with best IMP Perform best move If solution then stop Else go on Parameter !

25. Devising more and more complex Solvingalgorithms Use restarts Introduction Parameter ! False Clauses Iterations

26. Devising more and more complex Solvingalgorithms Introduction • WalkSAT : adding a noise and random restart • Henry A. Kautz, Bart Selman: Noise Strategies for Improving Local Search..AAAI 1994

27. Devising more and more complex Solvingalgorithms How to break ties ? Introduction +3 +3 0 1 0 1 1 0 0 +3

28. Devising more and more complex Solvingalgorithms Add more sophisticated heuristics Introduction Compute the age of the variable If the best variable is not the most recent then flip Else With a random probability p’ Perform a random flip the second best With (1-p’) Flip the best Parameter !

29. Devising more and more complex Solvingalgorithms • Novelty : using more strategies to perform improvements (age of the variable) • D.A. McAllester, B. Selman and H. Kautz. Evidence for invariant in local search.In Proceedings of AAAI-97, AAAI Press 1997, pages 321-326. Introduction

30. Devising more and more complex Solvingalgorithms Introduction • And improvements go on … • Novelty +,Novelty ++, …, TNM, Sattime…

31. Devising more and more complex Solvingalgorithms • Captain Jack : many indicators and thus selection strategies • Dave A. D. Tompkins, Adrian Balint, Holger H. Hoos: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. SAT 2011: 302-316 Introduction

32. Devising more and more complex Solvingalgorithms • Adding more parameters and heuristics Introduction More flexible algorithms Fit to different instances Set parameters/heuristics values Understand the behavior

33. The AlgorithmSelectionProblem Main ideas • John Rice. The algorithm selection problem. Technical Report CSD-TR • 152, Computer science department, Purdue University, 1975.

34. The AlgorithmSelectionProblem Main ideas • John Rice. The algorithm selection problem. Technical Report CSD-TR • 152, Computer science department, Purdue University, 1975.

35. Related Questions Tuning the parameters Using several algorithms for solving a class of problems Main ideas

36. Related Questions Tuning the parameters Adjusting the parameters of one algorithm Main ideas

37. Main Objectives Tuning the parameters Need for more autonomous solving tools Main ideas Increasing number of works in this trend : LION, Special sessions in EA conferences (GECCO,…) …

38. Ideas for More AutonomousSolvers Tuning the parameters • How to use an algorithm that includes • Many parameters • Many possible heuristics or components Ideas

39. Ideas for More AutonomousSolvers Tuning the parameters • How to use an algorithm that include • Many parameters • Many possible heuristics or components • How to automate all these choices ? Ideas

40. Off-lineAutomatedTuning Tuning the parameters Run your solver on some problems Experiment automatically parameters values Ideas

41. Off-lineAutomatedTuning Tuning the parameters Run your solver on new problems with these parameters values Ideas

42. Off-lineAutomatedTuning Tuning the parameters Question : Generality of the parameters ? Ideas

43. On-line Parameter Control Tuning the parameters Try to react during the resolution by changing the parameter Ideas

44. On-line Parameter Control Tuning the parameters Example : try to increase some parameter when possible Ideas

45. On-line Parameter Control Tuning the parameters Question : How to react efficiently ? Ideas

46. Hyper Heuristics Tuning the parameters Combine basic solving heuristics Ideas

47. Hyper Heuristics Tuning the parameters Get new solvers Ideas

48. Hyper Heuristics Tuning the parameters Question : How to learn the suitable solver ? Ideas

49. Portfolios BasedSolvers Tuning the parameters Use different types of solvers Ideas

50. Portfolios BasedSolvers Tuning the parameters Learn how to select the right solver for a given problem Ideas