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 PDF Slideshow. A Powerpoint Slideshow version is also available.
1. Hyper-heuristics: Past Present and Future
The University of Nottingham
Graham Kendall
gxk@cs.nott.ac.uk
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
2. Contents
The University of Nottingham
Past
• A selection of early work
Present
• Current State of the Art
Albert Einstein
Future 1879 - 1955
• Potential Research Directions for the Future
“We can't solve problems by using the
same kind of thinking we used when
we created them.”
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
3. Contents
The University of Nottingham
Past
• A selection of early work
Present
• Current State of the Art
Albert Einstein
Future 1879 - 1955
• Potential Research Directions for the Future
“We can't solve problems by using the
same kind of thinking we used when
we created them.”
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
4. The University of Nottingham
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
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
5. Good
Facility Order Matrix
The University of Nottingham
Number
1 3(1) 1(3) 2(6) 4(7) 6(3) 5(6)
2 2(8) 3(5) 5(10) 6(10) 1(10) 4(4)
3 3(5) 4(4) 6(8) 1(9) 2(1) 5(7)
4 2(5) 1(5) 3(5) 4(3) 5(8) 6(9)
5 3(9) 2(3) 5(5) 6(4) 1(3) 4(1)
6 2(3) 4(3) 6(9) 1(10) 5(4) 3(1)
6 x 6*6 Test Problem (times in brackets)
“The number of feasible active schedules is, by a conservative estimate, well over
a million, so their complete enumeration is out of the question.”
• Also 10 (jobs) x 10 (operations) and 20 (jobs)
x 5 (operations) problems
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
6. Good
Facility Order Matrix
The University of Nottingham
Number
1 3(1) 1(3) 2(6) 4(7) 6(3) 5(6)
2 2(8) 3(5) 5(10) 6(10) 1(10) 4(4)
3 3(5) 4(4) 6(8) 1(9) 2(1) 5(7)
4 2(5) 1(5) 3(5) 4(3) 5(8) 6(9)
5 3(9) 2(3) 5(5) 6(4) 1(3) 4(1)
6 2(3) 4(3) 6(9) 1(10) 5(4) 3(1)
6 x 6*6 Test Problem (times in brackets)
Job 3, 1, 2, 5, 4, 6
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
7. Good
Facility Order Matrix
The University of Nottingham
Number
1 3(1) 1(3) 2(6) 4(7) 6(3) 5(6)
2 2(8) 3(5) 5(10) 6(10) 1(10) 4(4)
3 3(5) 4(4) 6(8) 1(9) 2(1) 5(7)
4 2(5) 1(5) 3(5) 4(3) 5(8) 6(9)
5 3(9) 2(3) 5(5) 6(4) 1(3) 4(1)
6 2(3) 4(3) 6(9) 1(10) 5(4) 3(1)
6 x 6*6 Test Problem (times in brackets)
• Two Rules
• SIO: Shortest Imminent Operation (“First on,
First Off”)
• LRT: Longest Remaining Time
• Only require knowledge of “your”
machine
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
8. • Monte Carlo: 58 time Units
The University of Nottingham
• SIO: 67 time units
• LRT: 61 time units
• Optimal: 55 time units
• SIO should be used initially (get the
machines to start work) and LRT later
(work on the longest jobs)
• Why not combine the two heuristics?
• Four learning models, rewarding good
heuristic selection
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
9. Remarks
The University of Nottingham
• Not sure about reproducibility (e.g.
reward/punishment functions)
• An unbiased random combination of
scheduling rules is better than any of them
taken separately
• “Learning is possible, but there is a question as
to whether learning is desirable given the
effectiveness of the random combination”
• “It is not clear what is being learnt as the
original conjecture was not strongly
supported”
• “It is likely that combinations of 5-10 rules
would out-perform humans”
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
10. The University of Nottingham
Fang H-L., Ross P. and Corne D. (1993) A Promising genetic
Algorithm Approach to Job-Shop Scheduling, Reschecduling, and
Open-Shop Scheduling Problems. In Forrest S. (ed) Fifth International
Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo,
375-383
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
11. Representation
The University of Nottingham
• For a j x m problem, a string represents j x m
chunks.
• The chunk is atomic from a GA perspective.
• 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
….
• A schedule builder decodes the chromosome.
• Fairly standard GA e.g. population size of 500,
rank based selection, elitism, 300 generations,
crossover rate 0.6, adaptive mutation rate
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
12. Other Remarks
The University of Nottingham
• Considered Job-Shop Scheduling and Open-
Shop Scheduling
• Experimented with different GA parameters
• Results compared favourably with best known
or optimal
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
13. The University of Nottingham
Denzinger J. and Fuchs M. (1997) High Performance ATP Systems by
Combining Several AI Methods. In proceedings of the Fifteenth
International Joint Conference on Artificial Intelligence (IJCAI 97),
102-107
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
14. Remarks
The University of Nottingham
• The first paper to use the term Hyper-heuristic
• Used in the context of an automated theorem
prover
• A hyper-heuristic stores all the information
necessary to reproduce a certain part of the
proof and is used instead of a single heuristic
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
15. The University of Nottingham
O’Grady P.J. and Harrison (1985) A General Search Sequencing Rule
for Job Shop Sequencing. International Journal of Production
Research, 23(5), 961-973
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
16. Remarks
The University of Nottingham
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
Si the due date slack for job i
m the maximum number of processing stages
for jobs 1 to i
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
17. Remarks
Pi = (Ai x Ti) + (Bi x Si)
The University of Nottingham
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
Si the 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
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
18. Remarks
Pi = (Ai x Ti) + (Bi x Si)
The University of Nottingham
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
Si the 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.
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
19. The University of Nottingham
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)
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
20. Remarks
The University of Nottingham
• Similar in idea to Fang, Ross and Corne (1994)
• The allele at the ith position is the heuristic to
be applied at the ith step of the scheduling
process.
• Comparison with using eight single heuristics
and the Heuristic Combination Method (HCM)
was found to be superior.
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
21. Other (Selected) Papers
The University of Nottingham
• Crowston W.B., Glover F., Thompson G.L. and
Trawick J.D. (1963) Probabilistic and Parameter
Learning Combinations of Local Job Shop
Scheduling Rules. ONR Research Memorandum,
GSIA, Carnegie Mellon University
• 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
• Battiti R. (1996) Reactive Search: Toward Self
Tuning Heuristics. In Rayward-Smith R.J., Osman
I.H., Reeves C.R. and Smith G.D. (eds) Modern
Heuristics Search methods, John Wiley, 61-83
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
22. Contents
The University of Nottingham
Past
• A selection of early work
Present (Heuristics to Choose Heuristics)
• Current State of the Art
Albert Einstein
Future 1879 - 1955
• Potential Research Directions for the Future
“We can't solve problems by using the
same kind of thinking we used when
we created them.”
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
23. Heuristics to Choose Heuristics
The University of Nottingham
Hyper-heuristic
Data flow
Domain Barrier
Data flow
Set of low level heuristics
H1 H2 Hn
……
Evaluation Function
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
24. Choice Function
The University of Nottingham
• f1 + f2 + f3
• f1 = How well has each
heuristic performed
• f2 = How well have pairs of
heuristics performed
• f3 = Time since last called
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
25. Tabu Search
The University of Nottingham
• Low level heuristics compete
with each other
• Recent heuristics are made tabu
• Rank low level heuristics based
on their estimated performance
potential
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
26. Case Based Heuristic Selection
The University of Nottingham
• Find heuristics that worked well
in previous similar problem
solving situations
• Features discovered in similarity
measure – key research issue
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
27. Adaptive Ordering Strategies
The University of Nottingham
• Based on Squeaky Wheel
Optimisation
• Consider constructive heuristics
as orderings
• Adapt the ordering by a heuristic
modifier according to the penalty
imposed by certain features
• Generative
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
28. Contents
The University of Nottingham
Past
• A selection of early work
Present (Generating Heuristics)
• Current State of the Art
Future
• Potential Research Directions for the Future
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
29. Generating heuristics
The University of Nottingham
Hyper-heuristic
• Rather than supply a set of low
level heuristics, generate the Data flow
heuristics automatically
Domain Barrier
• Heuristics could be one off Data flow
(disposal) heuristics or could be
applicable to many problem
instances Set of low level heuristics
H1 H2 Hn
……
Evaluation Function
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
30. Generating heuristics
The University of Nottingham
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
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
31. Generating heuristics
The University of Nottingham
• Evolves a control program that
decides whether to put a given
piece into a given bin
• First-fit heuristic evolved from
Genetic Programming without
human input on benchmark
instances
For 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
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
32. Contents
The University of Nottingham
Past
• A selection of early work
Present
• Current State of the Art
Albert Einstein
Future 1879 - 1955
• Potential Research Directions for the Future
“We can't solve problems by using the
same kind of thinking we used when
we created them.”
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
33. Results on Standard Datasets
The University of Nottingham
•Many early papers investigated JSSP.
There is an opportunity to investigate if
the current state of the art is able to beat
these and set new benchmarks
•Why not apply hyper-heuristics to more
current benchmarks (TSP, VRP, QAP
etc.).
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
34. Benchmark datasets
The University of Nottingham
•We need to add to resources such as
OR-LIB so that we are able to compare
hyper-heuristic approaches.
•We need to have access to benchmarks
that are understandable, perceived as fair
and which are not open to many
interpretations.
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
35. Comparison against benchmarks
The University of Nottingham
•Using the “good enough, soon enough,
cheap enough” mantra we don’t claim to
be competitive with bespoke solutions,
but we are interested if we can beat best
known solutions.
•Why are some hyper-heuristics better
than others – and on what class of
problems?
•Robustness vs quality and how do we
measure that?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
36. Ant Algorithm based Hyper-heuristics
The University of Nottingham
•Ant algorithms draw their inspiration
from the way ants forage for food.
•Two major elements to an ant
algorithm.
•Pheromone values
•Heuristic values
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
37. Ant Algorithm based hyper-heuristics
The University of Nottingham
Trail Visibility
Intensity
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
38. Ant Algorithm based hyper-heuristics
The University of Nottingham
Heuristic Visibility
Synergy
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
39. “Good enough, soon enough, cheap
enough”
The University of Nottingham
•What does this actually mean?
•Will the scientific community accept
that this is a fair way to compare results?
Different Evaluations
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
40. “Good enough, soon enough, cheap
enough”
The University of Nottingham
•How do we know if a solution is “good
enough”?
•User feedback?
•Within a given value of best known
solution?
•We get bored running the Not Good Enough!
algorithm?
•The cost of accepting the solution is
acceptable?
•Two evaluation mechanisms?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
41. “Good enough, soon enough, cheap
enough”
The University of Nottingham
•How do we know if a solution is “soon
enough”?
•Meet a critical deadline?
•Run as long as we can?
•Can be embedded in a realtime
system? Soon Enough!
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
42. “Good enough, soon enough, cheap
enough”
The University of Nottingham
•How do we know if a solution is
“cheap enough”?
•Can be embedded in “off-the-shelf”
software?
•Development costs are significantly
lower writing a bespoke system?
Cheap Enough!
•Can be run on a standard PC, rather
than requiring specialised hardware?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
43. Comparing Hyper-heuristics
The University of Nottingham
•How can we compare different hyper-
heuristics so that reviewers have a way
of fairly judging new contributions
•What do we mean by “One hyper-
heuristic is better than another”?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
44. Anti-heuristics
The University of Nottingham
•There is/has been a significant amount
of research investigating how we can
“choose which heuristic to select at each
decision point”
•There could also be some benefit in
investigating hyper-heuristics that are
obviously bad and seeing if the hyper-
heuristic is able to learn/adapt not to use
them
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
45. Minimal Heuristics
The University of Nottingham
•Many of the hyper-heuristic papers
effectively say “choose a set of low level
heuristics…”
•But, can we define a minimal set of
heuristics that operate well across
different problems (e.g. add, delete and
swap)?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
46. Evolve heuristics
The University of Nottingham
•We can ignore “choose a set of low level
heuristics…” if we can generate our own
set of human competitive heuristics
•We have utilised genetic programming
and adaptive constructive heuristics but
there remains lots of scope for further
investigation.
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
47. Co-evolution
The University of Nottingham
•Heuristics compete for survival
•Similarities with genetic algorithms etc.,
but there is a wide scope of possible
research in this area.
Arthur Samuel
1901 – 1990
An AI Pioneer
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
48. Hybridisations
The University of Nottingham
•Is there anything to be gained from
hybridising various methodologies?
•There has been success with exact
methods and meta-heuristics
•What about hybridising hyper-heuristics
with meta-heuristics, exact approaches,
user interaction etc?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
49. User interaction
The University of Nottingham
•How can users interact with hyper-
heuristics?
•Introduce/delete heuristics as the
search progresses?
•Prohibit some areas of the search
space?
•Provide a time/quality trade off?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
50. Framework
The University of Nottingham
•There is a large learning curve and high
buy-in to develop a hyper-heuristic
•Tools such as GA-LIB help the
community to utilise the tools and to
carry out research
•But, what should this framework enable
you to do? Choose heuristics, generate
heuristics?
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
51. A unifying theory
The University of Nottingham
•What is the formal relationship between
heuristics, meta-heuristics and hyper-
heuristics (and even exact methods)?
Stephen Hawking
1942 -
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
52. A unifying theory
The University of Nottingham
•Can we analyse the landscape of the
different search methodologies?
•Can we move between different search Stephen Hawking
spaces during the search?
1942 -
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
53. A unifying theory
The University of Nottingham
•Can we offer convergence guarantees?
•Can we offer guarantees of solution
quality and/or robustness?
Stephen Hawking
1942 -
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)
54. Questions/Discussion
The University of Nottingham
Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)