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