Hybridization of Genetic Algorithms and Constraint Propagation for the BACP

1. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
Hybridization of Genetic Algorithms and
Constraint Propagation for the BACP
ICLP 2005, Sitges (Barcelona), Spain
Tony Lambert, Carlos Castro, Eric Monfroy, María Cristina
Riff, 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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2. 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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3. 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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4. 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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5. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
Abstract Model K.R. Apt [CP99]
Abstraction
Reduction functions
Constraint
Application
of functions
CSP
Fixed point
Partial Ordering
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6. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
The theoretical model for CSP solving
Partial ordering :
Ω1
Application of a reduction :
Ω2
domain reduction function or
splitting function
Ω3
Set of CSP
Ω4
Ω5
Terminates with a fixed point : set of solutions or inconsistent CSP
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7. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
GA process as moves on partial ordering
Moves on a partial ordering
p
1
Function to pass from one GA
state to another
p
2
State of GA
p
3
p
4
p
5
Terminates with a fixed point : maximum number of iteration
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8. 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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9. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
CP + AG : Optimisation for balanced curriculum
Constraints
Courses
a before b
g
a
e d cquot; quot;j
b
c hquot; quot;b
i h
f j k iquot; quot;f
fquot; quot;j
kquot; quot;c
dquot; quot;e
Max
Min k
i e j
h
c f
b
d g a
Periods
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10. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
BACP 8
100
propagation
genetic algorithm
split
80
60
range
40
20
0
25 24 23 22 21 20 19 18 17 16
evaluation
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11. HYBRIDIZATION MODEL SOME RESULTS CONCLUSION
Conclusion
• A generic model for hybridizing complete (CP) and
incomplete (GA) methods
• Implementation of modules working on the same structure
• Complementarity of methods
• Design of strategies
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