HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Hybridization of Genetic Algorithms andConstraint Propagation for the BACP

ICLP 2005, Sitges (Barcelona), Spain

Tony Lambert, Carlos Castro, Eric Monfroy, María CristinaRiff, and Frédéric Saubion

LINA, Université de Nantes, France

LERIA, Université d’Angers, France

Universidad Santa María, Valparaíso, Chile

October 3, 2005

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Hybridization for CSP

• complete methods (such as propagation + split)• complete exploration of the search space• detects if no solution• generally slow for hard combinatorial problems• global optimum

• incomplete methods (such as genetic algorithms)• focus on some “promising” parts of the search space• does not answer to unsat. problems• no guaranteed global optimum• “fast” to find a “good” solution

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Hybridization : getting the best of both methods

• But, generally :• Ad-hoc systems• Master-slaves approaches

• Idea :• Fine grain control• More strategies

• Technique :• Decomposing solvers into basic functions• Adapting chaotic iterations for hybrid solving

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Our Purpose : Hybrid Model

• Integration of genetic algorithms• Use of an existing theoretical model for CSP solving• Definition of the solving process

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Abstract Model K.R. Apt [CP99]

CSP

Applicationof functions

Constraint Reduction functions

Fixed point

Partial Ordering

Abstraction

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

The theoretical model for CSP solving

Partial ordering :

Ω1

Ω2

Ω3

Ω4

Ω5

Set of CSP

domain reduction function orApplication of a reduction :

splitting function

Terminates with a fixed point : set of solutions or inconsistent CSP

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

GA process as moves on partial ordering

Moves on a partial ordering

1p

2p

3p

4p

p5

State of GA

state to anotherFunction to pass from one GA

Terminates with a fixed point : maximum number of iteration

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Integration of generations for GA into the CSP

• A generation :• Depends on a CSP• Corresponds to a GA state

• A structure contains :• A set of domains• A set of constraints• A (list of) population for GA.

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

CP + AG : Optimisation for balanced curriculum

MaxMin

ab

c

d

e j

f

g

hi

k

abc

de

jf

g

hik

Constraints

a before b c

hifkd

j " " b " " f " "

" " " " " "

j c e

Periods

Courses

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

BACP 8

0

20

40

60

80

100

16171819202122232425

range

evaluation

propagationgenetic algorithm

split

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HYBRIDIZATION MODEL SOME RESULTS CONCLUSION

Conclusion

• A generic model for hybridizing complete (CP) andincomplete (GA) methods

• Implementation of modules working on the same structure• Complementarity of methods• Design of strategies

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