semet cec05
TRANSCRIPT
An Efficient Memetic, Permutation-based Evolutionary Algorithm for Real-World Train Timetabling
Y. Semet, M. SchoenauerINRIAOrsay, France
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Roadmap
A scheduling problemMany constraintsA permutation/ES approach
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Zooming on one node…
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Space/Time Diagrams
A global overview of the railway network Visual representation of the phenotypeHelps to graphically visualize constraints
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Constraints
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
The Swap MutationSwapping 2 close by elements (d<R), T timesT realization of a binomial law Calibrated decrease (cf. sim. ann.)
[ 1 4 3 2 5 6 7 8 ]
[ 1 2 3 4 5 6 7 8 ]
R
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Scheduler
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 1
i
Space
Time
j
Train c’ is already scheduled
α
Train c is being scheduled
αSafety spacing threshold
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 1
i
Space
Time
j
Train c’ is already scheduled
α
Train c is being scheduled
αSafety spacing threshold
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 2
i
Space
Time
j
Train c’ is already scheduled
Train c is being scheduled
α α
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 2
i
Space
Time
j
Train c is being scheduled
α α
Kick !
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 2
i
Space
Time
j
Train c is being scheduled
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Solving conflicts: case 2
i
Space
Time
j
Train c is now scheduled
Train c’ is being re-scheduled
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Procédure de kick…
Idée : retirer de la grille le train qui gêne le train en cours puis le remettre dans la grille après avoir terminé le train en coursImpose la conversion de la permutation en pilePermutation déstructurée
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
« Kick » : Illustration
2 4 5 3 6 8 7 1
2 4 5 3 6 8 7 1
2 4 3 6 5 8 7 1
1
7
8
6
3
5
4
2
1
7
8
6
1
7
8
5
6
1
7
8
5
1
7
8
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Conséquences
Des cycles peuvent apparaître : tous les trains ne peuvent alors entrer dans la grilleSeuil sur le nombre de « kicks » = 7Grille incomplètes fortement pénaliséesSuccès (grille complète) dans 2/3 des cas pour un échantillonnage aléatoire (population initiale)Succès systématique après un peu d’optimisation
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Global picture
Sélection
+
μ parentsKeep μ best individuals
λ offspring
= [3 4 5 1 2 6 8 7]
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Hybridization
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
A large and complex instance
541 trains…
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Results after 1 hour
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Final results after 4 hours
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Other directions
Various metaheuristicsRadius-based approaches
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Where we are now…
Memetic Train Timetabling, Semet & Schoenauer - CEC'05 - September, 4th. 2005
Conclusion
{semet,marc}@lri.fr