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Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Graham Kendall

The University of Nottingham

gxk@cs.nott.ac.uk http://www.cs.nott.ac.uk/~gxk

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Contents

• What is a hyper-heuristic?
• What motivates hyper-heuristic

research?

• Hyper-heuristic Methods
• Observations and Future Potential
• Questions/Discussions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

What is a hyper-heuristic?

• Simple Idea: Heuristics to choose

heuristics

• Operates on a search space of heuristics

rather than directly on a search space of solutions

• Meta-heuristics have been used with some

success as hyper-heuristics, as have other approaches such as case based reasoning

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

What is the difference between a hyper- heuristic and a meta-heuristic?

• All the term hyper-heuristic says is: “Operate on

a search space of heuristics”.

• We have a high level search method (the hyper-

heuristic) - which may (or may not) be a meta- heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

What is the difference between a hyper-heuristic and a meta- heuristic?

• A hyper-heuristic searches through a space
• f heuristics (which, potentially, could be

meta-heuristics)

• Most meta-heuristic implementations
• perate directly on a search space of

potential solutions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Different Search Spaces

Hyper-heuristic Heuristics Potential Solutions

Operates upon Operates upon

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Contents

• What is a hyper-heuristic?
• What motivates hyper-heuristic

research?

• Hyper-heuristic Methods
• Observations and Future Potential
• Questions/Discussions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Motivations behind hyper-heuristic research

• What is our strategic research vision?
• What game to play?

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

The “Best Quality Solution” Game

• We have a problem (e.g. exam

timetabling)

• We have a set of benchmark problems
• We develop new methodologies (ever

more sophisticated)

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

The “Best Quality Solution” Game

• Apply methodologies to benchmarks
• Compare with other “players”
• The goal is to “get better quality

solutions” than the other players

• Good Game

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

The “Best Quality Solution” Game

e.g. Exam Timetabling Benchmark Instances

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Consequences of “Best Quality Solution” Game

• Handcrafted bespoke decision support

methodologies

• Made to Measure – NOT off the peg
• Rolls-Royce systems
• We compare Rolls-Royces with Bentleys

with Mercedes with Ferraris…….. And it works

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

A New Game?

• What about Ford Model Ts’?
• Do we have the technology to mass produce

decision support systems?

• Develop decision support systems that are
• ff the peg?
• Can we develop the ability to automatically

work well on different problems?

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

A new game to play: Many Walls?

• Raising the level of generality
• Still want to get as high up the wall as

possible ……… BUT………

• We want to be able to operate on as

many different walls as possible

• The goal is to increase the number of

walls you can operate on – while still getting acceptably high up each wall

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Raising the Level of Generality

One Method

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Evaluating Different Methods

• It IS a new game
• Cannot sensibly compare a Model T

to a Rolls Royce – different functions for different clientele

• Raising the level of generality is the

goal

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Evaluating Different Methods

• Still want solution quality to be as high as

possible though

• Good Enough – Soon Enough – Cheap

Enough

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

A Grand Challenge

• Automating the heuristic design process
• Deeper understanding of how high we

can raise the level of generality: What are the limits?

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

A Grand Challenge

The General Solver Doesn’t exist…. Problem Specific Solvers More General These situations exist Significant scope for future research

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Hyper-heuristics

• Motivated by raising the level of generality
• Role to play in BOTH games

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Contents

• What is a hyper-heuristic?
• What motivates hyper-heuristic

research?

• Hyper-heuristic Methods
• Observations and Future Potential
• Questions/Discussions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Intellectual Roots

• Hyper-heuristic research has many of its

roots in the mid-nineties

• But can be traced back to the 60’s

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Intellectual Roots

• Fisher H. and Thompson G.L. Probabilistic Learning

Combinations of Local Job-shop Scheduling Rules. In Factory Scheduling Conference, Carnegie Institute of Technology, May 10-12, 1961

• Fisher H. and Thompson G.L. Probabilistic Learning

Combinations of Local Job-shop Scheduling Rules. Ch 15,:225- 251, Prentice Hall, New Jersey, 1963

• Crowston W.B., Glover F., Thompson G.L. and Trawick J.D.

Probabilistic and Parameter Learning Combinations of Local Job Shop Scheduling Rules. ONR Research Memorandum, GSIA, Carnegie Mellon University, Pittsburgh, (117), 1963

The learning mechanism used probabilistic weightings

• f low level heuristics which represented scheduling

rules

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Intellectual Roots

• H-L Fang, P.M.Ross and D.Corne. A Promising Hybrid

GA/Heuristic Approach for Open-Shop Scheduling Problems'', in Proceedings of ECAI 94: 11th European Conference on Artificial Intelligence, A. Cohn (ed), pp 590- 594, John Wiley and Sons Ltd, 1994 The chromosome was a set of heuristics that was chosen to schedule a job on a machine. As opposed to the “normal” method of having the chromosome as representing a set of jobs to be scheduled in a given order.

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Intellectual Roots

• Hart E, Ross P. and Nelson J.A.D. Solving a Real World

Problem using an Evolving Heuristically Driven Schedule

• Builder. Evolutionary Computing 6(1):61-80, 1998
• Hart E, Ross P. and Nelson J.A.D. Scheduling Chicken

Catching: An Investigation into the Success of a Genetic Algorithm on a Real World Scheduling Problem. Annals of Operations Research 92:363-380, 1999 Problem is decomposed into two sub-problems, each being solved with a GA. The chromosomes represent heuristics.

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Domain Barrier

……

Set of low level heuristics Evaluation Function Hyper-heuristic Data flow Data flow H1 H2 Hn

A Hyper-heuristic Framework

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Choice Function

f1 + f2 + f3 How well has each heuristic done + How well have pairs of heuristics done + Time since last called Applied to sales summit scheduling, CS&IT presentations, nurse rostering

Domain Barrier Set of low level heuristics Evaluation Function Data flow Data flow Hn H2 H1

……

Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Sales Summit Scheduling Low level heuristics are based on three types of neighbourhood moves:

• Add / Remove one delegate to / from the current solution
• Add / remove a meeting to / from the current solution

(random, 1st improving, best improving, etc)

• Remove excess of meetings from an overloaded delegate

Choice function Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

CS&IT Presentation Scheduling

• Produced solutions that were better than manually

produced solutions

• Solutions used in CS&IT

Nurse Rostering

• Competitive with other results in the literature
• Same algorithm worked across a range of problems

Choice function Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Simple moving strategies as low level heuristics
• Low level heuristics compete with each other
• Recent heuristics in tabu
• Rank low level heuristics based on their estimated

performance potential

• Easily applicable on both nurse rostering and

course timetabling: Competitive results on both problems with the same settings

Tabu Search Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Find heuristics that worked well in previous

similar problem solving situations

• Features discovered in similarity measure –

key research issue

• Across both exam and course timetabling

problems

Case Based Heuristic Selection

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Low level heuristics are constructive

heuristics

• Knowledge discovery on features

determining how similar two problem situations are

• Comparison between heuristic selection by

CBR and systematic mechanisms

Case Based Heuristic Selection

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

solution No CBR System Heuristic Selector Construct Solution Case Base Yes Stop? problem

Case Based Heuristic Selection

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Low level heuristics are graph colouring based

heuristics

• Sequences of graph heuristics searched by

different searching algorithms under a unified framework

• Search space of heuristics presents different

characteristics

Graph Based Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Heuristic Search Space Solution Search Space A B C a b c d

• Comparable results on both course and exam

benchmark using the same algorithm

• Hybridisations with local search (search in two

spaces)

Graph Based Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Based on Squeaky Wheel Optimisation (Joslin and

Clemens- 1999)

• Consider constructive heuristics as orderings
• Adapt the ordering by a heuristic modifier

according to the penalty imposed by certain features

• Generate new orderings (heuristics) which are

(automatically) tailored to the particular problem instance in hand

Adaptive Ordering Strategies

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Construct good sequences
• f heuristic moves
• “Ants” move from heuristic

to heuristic

Pheromone represents how well heuristics work together? Visibility represents the time taken by the next heuristic?

Ant Based Hyper-heuristic

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Genetic Programming Hyper-heuristic

• Genetic programming to automatically evolve good

heuristics on packing bins in bin packing problems

• Evolve new heuristics based on functions rather

than choose from pre-defined ones

• First-fit heuristic evolved from Genetic

Programming without human input on benchmark instances

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Genetic Algorithms
• Simulated Annealing
• Great Deluge Algorithm
• Fuzzy Reasoning
• Multi-objective Hyper-heuristics
• Learning Classifier Systems
• Variable Neighbourhood Search

Some other Hyper-heuristic Methods

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Two Introductory Publications

Overview of Recent Literature: E.K.Burke, G. Kendall, J.Newall, E.Hart, P.Ross & S.Schulenburg, Hyper-Heuristics: An Emerging Direction in Modern Search Technology, Handbook of Metaheuristics (eds. F.Glover & G.Kochenberger), pp 457 – 474, Kluwer, 2003. Tutorial: P.Ross, Hyper-heuristics, Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques (eds. E.K.Burke & G.Kendall), pp 529-556, Springer 2005.

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Some Recent Publications

• Burke E.K., Kendall G. and Soubeiga E. A Tabu-Search Hyper-Heuristic

for Timetabling and Rostering. Journal of Heuristics, 9(6), 451-470, 2003

• P. Ross, J.G. Marin Blasques, S. Schulenburg, E. Hart. Learning a

Procedure that Can Solve Hard Bin-Packing Problems: A New GA-Based Approach to Hyper-heuristics, Proc. Genetic and Evolutionary Computation (GECCO 2003), Springer LNCS Vol 2724, 1295-1306

• L. Han, G. Kendall. Investigation of a Tabu Assisted Hyper-Heuristic

Genetic Algorithm. In Proceedings of Congress on Evolutionary Computation (CEC2003), Canberra, Australia, 2230-2237 (Vol. 3), 2003

• E.K.Burke and J.P. Newall, Solving Examination Timetabling Problems

through Adaptation of Heuristic Orderings, Annals of Operations Research 129, 107-134, 2004

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• P.Ross, S.Schulenburg, J.G.Marín-Blázquez and E.Hart. Hyper-

heuristics:Learning to combine simple heuristics in bin-packing problems, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2002), New York, July 9-13 2002, pp 942-948.

• H.Terashima-Marín, P.M.Ross, and M.Valenzuela-Rendón. Evolution of

constraint satisfaction strategies in examination timetabling, Proceedings

• f the Genetic and Evolutionary Computation Conference (GECCO

1999), pp 635-642. Morgan Kaufmann, 1999.

• Kendall G. and Mohd Hussin N., An Investigation of a Tabu Search

Based Hyper-heuristic for Examination Timetabling , Multi-disciplinary Scheduling: Theory and Applications (eds G.Kendall, E.K.Burke, S.Petrovic and M.Gendreau, Springer 2005, pp 309-328.

Some Recent Publications

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• E.K. Burke, J.D. Landa Silva, E. Soubeiga. Multi-objective Hyper-

heuristic Approaches for Space Allocation and Timetabling. In: Ibaraki T., Nonobe K., Yagiura M. (eds.), Meta-heuristics: Progress as Real Problem Solvers, Springer, 2005

• E.K. Burke, S. Petrovic, R. Qu. Hybrid Graph Heuristics within a Hyper-

heuristic Approach to Exam Timetabling Problems, The Next Wave in Computing, Optimization, and Decision Technologies (eds. B.L. Golden,

• S. Raghavan & E.A. Wasil). 79-91, Springer 2005
• Bai, R., Kendall, G., An Investigation of Automated Planograms Using a

Simulated Annealing Based Hyper-heuristic, In: Ibaraki T., Nonobe K., Yagiura M. (eds.), Meta-heuristics: Progress as Real Problem Solvers, Selected Papers from the 5th Metaheuristics International Conference (MIC 2003), Springer, pp. 87-108, 2005.

Some Recent Publications

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• K. Dowsland, E. Soubeiga, E.K Burke. A Simulated Annealing Hyper-

heuristic for Determining Shipper Sizes. Accepted for publication in the European Journal of Operational Research in 2007.

• H. Asmuni, E.K. Burke, J. Garibaldi. Fuzzy Multiple Ordering Criteria for

Examination Timetabling, Practice and Theory of Automated Timetabling V (eds. E.K. Burke & M. Trick), Springer LNCS volume 3616, 2005, pp 334-353.

• Burke, E.K., Kendall, G., Landa Silva, J.D., O'Brien, R. and Soubeiga, E.,

An Ant Algorithm Hyperheuristic for the Project Presentation Scheduling Problem, Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, Scotland, pp. 2263-2270, September 2-5, 2005.

• E.K. Burke, S. Petrovic and R. Qu. Case Based Heuristic Selection for

Timetabling Problems, Journal of Scheduling, vol 9, no. 2, 115-132, 2006

Some Recent Publications

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Ozcan E., Bilgin N. and Korkmaz E.E.: Hill Climbers and Mutational

Heuristics in Hyperheuristics. In: Proc. of the 9th International Conference on Parallel Problem Solving from Nature, Springer LNCS Vol 4193, 2006

• Han L. and Kendall G. Guided Operators for a Hyper-Heuristic Genetic

Algorithm, Proceedings of AI-2003: Advances in Artificial Intelligence. The 16th Australian Conference on Artificial Intelligence, Perth, Australia 3-5 Dec 2003, Springer Lecture Notes in Artificial Intelligence Vol 2903, pp 807-820

• E.K. Burke, A. Meisels, B.McCollum, S. Petrovic, R. Qu. A Graph-

Based Hyper Heuristic for Timetabling Problems. European Journal of Operational Research, 176, 177-192, 2007

Some Recent Publications

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Kendall G. and Mohd Hussin N., A Tabu Search Hyper-heuristic

Approach to the Examination Timetabling Problem at the MARA University of Technology, Practice and Theory of Automated Timetabling V, Springer Lecture notes in Computer Science Vol 3616, 2005, pp 270- 293.

• E.K. Burke, M.R. Hyde and G. Kendall. Evolving Bin Packing Heuristics

with Genetic Programming, Proceedings of the 9th International Conference on Parallel Problem Solving from Nature (PPSN 2006), Springer LNCS Vol 4193, Reykjavik, Iceland. Sep 2006, pp 860-869

• Rattadilok, P., Gaw, A. and Kwan, R.S.K, Distributed Choice Function

Hyper-heuristics for Timetabling and Scheduling, Practice and Theory of Automated Timetabling V, Springer Lecture notes in Computer Science Vol 3616, 2005, pp 51-67

Some Recent Publications

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Contents

• What is a hyper-heuristic?
• What motivates hyper-heuristic

research?

• Hyper-heuristic Methods
• Observations and Future Potential
• Questions/Discussions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Observations of Current Research

• Variety of high level methodologies
• Meta-heuristics (TS, SA, GAs, GP, VNS,

Ants, etc)

• Case based reasoning, fuzzy system
• Choice functions, Heuristic modifier
• Multi-objective

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Observations of Current Research

• Low level heuristics
• Constructive vs. Improvement as low level

heuristic

• Hybridisations on both constructive,

improvement, etc

• Combination of heuristic selection &

acceptance criteria

• Automatically evolve new heuristics

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Shown to be simple and effective
• Mostly tested on benchmark and real

world problems

• Significant scope for exploring generality

issues and automation of the heuristic design process

• Driven by real world issues

Observations of Current Research

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Future Directions

• Automating the Heuristic Design Process –

Grand Scientific Challenge

• Systems applicable to a wider range of

problems – systems to build systems

• In-depth understanding of heuristic space
• Hybridisations with other techniques

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

• Further exploration of the evolution of

heuristics to underpin the development of more general methodologies

• Deepen our understanding of the

limitations of raising the level of generality

• Develop evaluation methods to measure

levels of generality – multi-objective?

Future Directions

Hyper-heuristics: Raising the Level of Generality of Search Methodologies

Questions/Discussions?