Hyperheuritics: Past, Present and Future

Graham Kendall, Hyper-heuristics: Past, Present and Future (uploaded to Slideshare.com : 25th April 2010)

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Hyper-heuristics: Past Present and Future

Graham Kendall

[email protected]


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Albert Einstein

1879 - 1955

ContentsPast

• A selection of early work

Present

• Current State of the Art

Future

• Potential Research Directions for the Future“We can't solve problems by using the

same kind of thinking we used when

we created them.”


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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


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Good

NumberFacility Order Matrix

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


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Good


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)


Job 3, 1, 2, 5, 4, 6


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• Two Rules• SIO: Shortest Imminent Operation (“First on,

First Off”)

• LRT: Longest Remaining Time

• Only require knowledge of “your”

machine

Good


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)



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• Monte Carlo: 58 time Units

• 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


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• 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”

Remarks


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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


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Representation

• 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


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Other Remarks

• Considered Job-Shop Scheduling and Open-

Shop Scheduling

• Experimented with different GA parameters

• Results compared favourably with best known

or optimal


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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


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Remarks

• 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


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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


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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

Si the due date slack for job i

m the maximum number of processing stages

for jobs 1 to i


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Remarks

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


where



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


m the maximum number of processing stages for jobs 1 to i


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Remarks

A search is performed over Ai and Bi in order to

cause changes in the processing sequences.


where



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


m the maximum number of processing stages for jobs 1 to i


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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)


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Remarks

• 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.


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Other (Selected) Papers

• 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


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Albert Einstein

1879 - 1955

ContentsPast


Present (Heuristics to Choose Heuristics)


Future



we created them.”


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Domain Barrier

……

Set of low level heuristics

Evaluation Function

Hyper-heuristic

Data flow

Data flow

H1 H2 Hn

Heuristics to Choose Heuristics


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Choice Function

• f1 + f2 + f3

• f1 = How well has each heuristic performed

• f2 = How well have pairs of heuristics performed

• f3 = Time since last called


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• Low level heuristics compete with each other

• Recent heuristics are made tabu

• Rank low level heuristics based on their estimated performance potential

Tabu Search


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• Find heuristics that worked well in previous similar problem solving situations

• Features discovered in similarity measure – key research issue

Case Based Heuristic Selection


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• 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

Adaptive Ordering Strategies


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ContentsPast


Present (Generating Heuristics)


Future

• Potential Research Directions for the Future


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• Rather than supply a set of low level heuristics, generate the heuristics automatically

• Heuristics could be one off(disposal) heuristics or could be applicable to many problem instances

Generating heuristics

Domain Barrier

……

Set of low level heuristics

Evaluation Function

Hyper-heuristic

Data flow

Data flow

H1 H2 Hn


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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


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• 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


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Albert Einstein

1879 - 1955

ContentsPast


Present


Future



we created them.”


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Results on Standard Datasets

•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.).


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Benchmark datasets

•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.


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Comparison against benchmarks

•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?


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Ant Algorithm based Hyper-heuristics

•Ant algorithms draw their inspiration

from the way ants forage for food.

•Two major elements to an ant

algorithm.

•Pheromone values

•Heuristic values


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Ant Algorithm based hyper-heuristics

Trail

Intensity

Visibility


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Ant Algorithm based hyper-heuristics

Heuristic

Synergy

Visibility


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Different Evaluations

“Good enough, soon enough, cheap

enough”

•What does this actually mean?

•Will the scientific community accept

that this is a fair way to compare results?


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Not Good Enough!


enough”

•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

algorithm?

•The cost of accepting the solution is

acceptable?

•Two evaluation mechanisms?


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Soon Enough!


enough”

•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?


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Cheap Enough!


enough”

•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?

•Can be run on a standard PC, rather

than requiring specialised hardware?


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Comparing Hyper-heuristics

•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”?


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Anti-heuristics

•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


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Minimal Heuristics

•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)?


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Evolve heuristics

•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.


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Co-evolution

•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


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Hybridisations

•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?


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User interaction

•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?


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Framework

•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?


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Stephen Hawking

1942 -

A unifying theory

•What is the formal relationship between

heuristics, meta-heuristics and hyper-

heuristics (and even exact methods)?


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Stephen Hawking

1942 -

A unifying theory

•Can we analyse the landscape of the

different search methodologies?

•Can we move between different search

spaces during the search?


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Stephen Hawking

1942 -

A unifying theory

•Can we offer convergence guarantees?

•Can we offer guarantees of solution

quality and/or robustness?


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Questions/Discussion

Hyperheuritics: Past, Present and Future

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