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LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław, Poland.

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Page 1: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGO

AAIA’2012 \ WCO’201209 – 12 september, 2012

S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE)

Wrocław, Poland.

Page 2: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

2

Introduction

The Dial a Ride Problem

NP-HARD (with time constraints)

Randomized greedy insertion techniques

Constraint propagation

S. Deleplanque, A. Quilliot

Static/Dynamic

Wrocław, Poland, 9 - 12 September, 2012

Page 3: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

3

Outline

Introduction State of the art / model Constraint propagation & insertion techniques Experiments

Conclusion

Wrocław, Poland, 9 - 12 September, 2012

S. Deleplanque, A. Quilliot

Page 4: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

4

The DARP(TW)

//20Angers 11-13 Avril 2012

DARPTW’s input A homogeneous vehicle fleet VH, A common capacity CAP of a vehicle in VH, A transit network G=(V,E) which contains some

node Depot, A demand set D :

DARPTW’s output VH’s routes taking in charge D in such a way the

performance is the highest possible.

D=(D i=(oi , d i ,Δ i , F (o i) , F (d i) ,Q i) ,i∈ I )

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Page 5: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

5

The DARP(TW)

//20Angers 11-13 Avril 2012

Time constraints Load constraints

D=(D i=(oi , d i ,Δ i , F (o i) , F (d i) ,Q i) ,i∈ I )

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

“A common capacity CAP of a vehicle in VH”

Easy

Hard

Page 6: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

6

Performance criterions

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

In the reviews… Travel distance, QoS:

• Passenger waiting time,• Ride time;

(Robustness, reliability).

Page 7: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

7

Short state of the art – 1/2

//20Angers 11-13 Avril 2012

Dynamic Programming• An exact algorithm for the single vehicle many-to-many

dial-a-ride problem with time windows - H. Psaraftis - Transportation Science - 1983 ;

• Comparison of three algorithms for solving the convergent demand responsive transportation problem – R. Chevrier et al. – ITSC - 2006 ;

Column generation • Time constrained routing and scheduling - J. Desrosiers

et al., - Book – 1995.

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Page 8: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

8

Short state of the art – 2/2

//20Angers 11-13 Avril 2012

Genetic algorithm• Intractability of the dial-a-ride problem and a

multiobjective solution using simulated annealing - J. Baugh et al. - Engineering Optimization - 1998 ;

Tabu search• A tabu search heuristic algorithm for the static multi-

vehicle dial-a-ride problem - J.-F. Cordeau et al., - Transportation Research – 2003 ;

Insertion techniques (IT)• A heuristic algorithm for the multi-vehicle advance

request dial-a-ride problem - J. Jaw et al. - Transportation Research – 1986.

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Telebus Berlin

Page 9: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

9

Insertion Techniques : Motives

//20Angers 11-13 Avril 2012

+ CPU time, + programming time, + adaptability, + eases the integration in a dynamic context.

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Page 10: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

10

A tour Γ : a list

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

e.g. with 2 demands inserted

Page 11: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

11

Performance – tour Γ cost

//20Angers 11-13 Avril 2012

Global Duration

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Riding Time

Waiting Time

Page 12: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

12

Propagation time constraintsInference rules

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Rule R1

Rule R2

Page 13: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

13

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Rule R3

Rule R4

Rule R5

Propagation time constraintsInference rules

Page 14: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

14

Propagation time constraintsprocedure Propagate

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Procedure Propagate(G: Tour, L: List of nodes, FS: Time windows set related to the node set of G): (Res: Boolean, FR: Time windows set related to node set of G);

Not Stop; While L Nil and Not Stop do z <- First(L); L <- Tail(L);

For i = 1..5 do Compute all the pairs (x, y) which make possible an application of the rule Ri and which are such that x = z or y = z;

For any such pair (x, y) do Apply the rule Ri; If NFact is not in L then Insert NFact in L;If Fail then Stop;

Propagate <- (Not Stop, FS);

Page 15: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

15

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Initialize all the sets; // Including FreeWhile J Nil do

Pick up some demand i0 in J; Remove i0 from J;If FREE(i0) = Nil then Reject ← Reject {i0};Else Derive from FREE(i0) (k0, x0, y0, v0);T(k0) ← INSERT(T(k0), x0, y0, i0); // Insertion of oi0 and di0

d ← EVAL2(T(k0)).d; Insert i0 into I1; // Compute the new performance

For any x in T(k0) do t(x) ← d(x); For any i J do

Update Free(i) with the procedure Test-Insert(T(k0), x, y, i) which includes the constraint propagation;

Perf ← PerfA, B, C(T, t);INSERTION ← (T, t, Perf, Reject);

Procedure Insertion

Page 16: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

16

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Experiments

Instances of :

and

We compare our results with (AG)

(RV)

Page 17: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

17

Experiments – Objective function

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

The (AG)‘s objective function uses 5 criterions: (coefficients)• Travel distance (8)• Excess ride time (3)• Passenger waiting (1)• Total duration (1)• Early arrival (|D|)

Page 18: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

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18

Experiments

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Page 19: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

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Future Works

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

DARP with vehicle 2-preemption

DARP with load preemption

Page 20: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGOwww.themegallery.com

20

Future works

//20Angers 11-13 Avril 2012

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Rule R6

Rule R7

DARP with vehicle 2-preemption 2 new inference rules R6 and R7:

Page 21: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGO//20www.themegallery.com

Angers 11-13 Avril 2012

21

And… Dynamic context (robustness), Reliability constraint.

S. Deleplanque, A. Quilliot

Wrocław, Poland, 9 - 12 September, 2012

Future works

Page 22: LOGO AAIA’2012 \ WCO’2012 09 – 12 september, 2012 S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE) Wrocław,

LOGO

AAIA’2012 \ WCO’201209 – 12 september, 2012

Wrocław, Poland.

S. Deleplanque, A. Quilliot (speaker)