This presentation provides a review of the early work of hyper-heuristics, current work that is being undertaken followed by a discussion of open research challenges. This is a Powerpoint Slideshow version. A PDF version is also available.

1. Hyper-heuristics: Past Present and Future Graham Kendall gxk@cs.nott.ac.uk

4. Fisher H. and Thompson G.L. (1963) Probabilistic Learning Combinations of Local Job-shop Scheduling Rules. In Muth J.F. and Thompson G.L. (eds) Industrial Scheduling, Prentice Hall Inc., New Jersey, 225-251 Based on (I assume) Fisher H. and Thompson G.L. (1961) Probabilistic Learning Combinations of Local Job-shop Scheduling Rules. In Factory Scheduling Conference, Carnegie Institute of Technology

7. SIO: Shortest Imminent Operation (“First on, First Off”)

8. LRT: Longest Remaining Time

10. SIO: 67 time units

11. LRT: 61 time units

12. Optimal: 55 time units

13. SIO should be used initially (get the machines to start work) and LRT later (work on the longest jobs)

14. Why not combine the two heuristics?

16. An unbiased random combination of scheduling rules is better than any of them taken separately

17. “Learning is possible, but there is a question as to whether learning is desirable given the effectiveness of the random combination”

18. “It is not clear what is being learnt as the original conjecture was not strongly supported”

21. The chunk is atomic from a GA perspective.

22. The chunks abc means to put the first untackled task of the ath uncompleted job into the earliest place it will fit in the developing schedule, then put the bth uncompleted job into ….

23. A schedule builder decodes the chromosome.

25. Experimented with different GA parameters

28. Used in the context of an automated theorem prover

30. Remarks Pi = (Ai x Ti) + (Bi x Si) where Pi the priority index for job i at its current stage Ai a 1 x m coefficient vector for job i Ti a m x 1 vector which contains the remaining operation times for job i in process order Bi the due date priority coefficient for job i Sithe due date slack for job i m the maximum number of processing stages for jobs 1 to i

31. Remarks Pi = (Ai x Ti) + (Bi x Si) where Pi the priority index for job i at its current stage Ai a 1 x m coefficient vector for job i Ti a m x 1 vector which contains the remaining operation times for job i in process order Bi the due date priority coefficient for job i Sithe due date slack for job i m the maximum number of processing stages for jobs 1 to i A = (1,0,0,0,0,…,0), B = 0 Shortest Imminent Operation Time A = (0,0,0,0,0,…,0), B = 1 Due Date Sequencing

32. Remarks Pi = (Ai x Ti) + (Bi x Si) where Pi the priority index for job i at its current stage Ai a 1 x m coefficient vector for job i Ti a m x 1 vector which contains the remaining operation times for job i in process order Bi the due date priority coefficient for job I Sithe due date slack for job i m the maximum number of processing stages for jobs 1 to i A search is performed over Ai and Bi in order to cause changes in the processing sequences.

33. Norenkov I. P. and Goodman E D. (1997) Solving Scheduling Problems via Evolutionary Methods for Rule Sequence Optimization. In proceedings of the 2nd World Conference on Soft Computing (WSC2)

35. The allele at the ith position is the heuristic to be applied at the ith step of the scheduling process.

37. Storer R.H., Wu S.D. and Vaccari R. (1992) New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling. Management Science, 38(10), 1495-1509

39. H2 Hn Heuristics to Choose Heuristics Hyper-heuristic Data flow Domain Barrier Data flow Set of low level heuristics H1 …… Evaluation Function

41. f1 = How well has each heuristic performed

42. f2 = How well have pairs of heuristics performed

44. Recent heuristics are made tabu

47. Consider constructive heuristics as orderings

48. Adapt the ordering by a heuristic modifier according to the penalty imposed by certain features

50. Heuristics could be one off (disposal) heuristics or could be applicable to many problem instancesData flow Domain Barrier Data flow Set of low level heuristics H1 …… Evaluation Function

51. Generating heuristics Burke E. K., Hyde M. and Kendall G. Evolving Bin Packing Heuristics With Genetic Programming. In Proceedings of the 9th International Conference on Problem Parallel Solving from Nature (PPSN 2006), pp 860-869, LNCS 4193, Reykjavik, Iceland, 9-13 Sepetmber 2006

53. First-fit heuristic evolved from Genetic Programming without human input on benchmark instancesFor each piece, p, not yet packed For each bin, i output = evaluate(p, fullness of i, capacity of i) if (output > 0) place piece p in bin i break fi End For End For

58. Why are some hyper-heuristics better than others – and on what class of problems?

60. Two major elements to an ant algorithm.

61. Pheromone values

63. Visibility Heuristic Synergy Ant Algorithm based hyper-heuristics

65. Will the scientific community accept that this is a fair way to compare results?Different Evaluations

67. User feedback?

68. Within a given value of best known solution?

69. We get bored running the algorithm?

70. The cost of accepting the solution is acceptable?

71. Two evaluation mechanisms?Not Good Enough!

73. Meet a critical deadline?

74. Run as long as we can?

75. Can be embedded in a realtime system?Soon Enough!

77. Can be embedded in “off-the-shelf” software?

78. Development costs are significantly lower writing a bespoke system?

79. Can be run on a standard PC, rather than requiring specialised hardware?Cheap Enough!

85. Similarities with genetic algorithms etc., but there is a wide scope of possible research in this area.Arthur Samuel 1901 – 1990 An AI Pioneer

87. There has been success with exact methods and meta-heuristics

89. Introduce/delete heuristics as the search progresses?

90. Prohibit some areas of the search space?

92. Tools such as GA-LIB help the community to utilise the tools and to carry out research

95. Can we move between different search spaces during the search?Stephen Hawking 1942 -

97. Can we offer guarantees of solution quality and/or robustness?Stephen Hawking 1942 -

98. Questions/Discussion