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

LOGO 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, September, 2012

LOGO 3 Outline  Introduction  State of the art / model  Constraint propagation & insertion techniques  Experiments  Conclusion Wrocław, Poland, September, 2012 S. Deleplanque, A. Quilliot

LOGO 4 The DARP(TW) //20 Angers 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. S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012

LOGO 5 The DARP(TW) //20 Angers Avril 2012  Time constraints  Load constraints S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 “A common capacity CAP of a vehicle in VH ” Easy Hard

LOGO 6 Performance criterions //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012  In the reviews…  Travel distance,  QoS: Passenger waiting time, Ride time;  (Robustness, reliability).

LOGO 7 Short state of the art – 1/2 //20 Angers 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 ; Comparison of three algorithms for solving the convergent demand responsive transportation problem – R. Chevrier et al. – ITSC ;  Column generation Time constrained routing and scheduling - J. Desrosiers et al., - Book – S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012

LOGO 8 Short state of the art – 2/2 //20 Angers Avril 2012  Genetic algorithm Intractability of the dial-a-ride problem and a multiobjective solution using simulated annealing - J. Baugh et al. - Engineering Optimization ;  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 – S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Telebus Berlin

LOGO 9 Insertion Techniques : Motives //20 Angers Avril 2012  + CPU time,  + programming time,  + adaptability,  + eases the integration in a dynamic context. S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012

LOGO 10 A tour Γ : a list //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 e.g. with 2 demands inserted

LOGO 11 Performance – tour Γ cost //20 Angers Avril 2012 Global Duration S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Riding Time Waiting Time

LOGO 12 Propagation time constraints Inference rules //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Rule R1 Rule R2

LOGO 13 //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Rule R3 Rule R4 Rule R5 Propagation time constraints Inference rules

LOGO 14 Propagation time constraints procedure Propagate //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, 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 R i and which are such that x = z or y = z; For any such pair (x, y) do Apply the rule R i ; If NFact is not in L then Insert NFact in L; If Fail then Stop; Propagate <- (Not Stop, FS);

LOGO 15 //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Initialize all the sets; // Including Free While J  Nil do Pick up some demand i 0 in J; Remove i 0 from J; If FREE(i 0 ) = Nil then Reject ← Reject  {i 0 }; Else Derive from FREE(i 0 ) (k 0, x 0, y 0, v 0 ); T(k 0 ) ← INSERT(T(k 0 ), x 0, y 0, i 0 ); // Insertion of oi 0 and di 0 d ← EVAL2(T(k 0 )).d; Insert i 0 into I 1 ; // Compute the new performance For any x in T(k 0 ) do t(x) ← d(x); For any i  J do Update Free(i) with the procedure Test-Insert(T(k 0 ), x, y, i) which includes the constraint propagation; Perf ← Perf A, B, C (T, t); INSERTION ← (T, t, Perf, Reject); Procedure Insertion

LOGO 16 //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Experiments Instances of : and We compare our results with(AG) (RV)

LOGO 17 Experiments – Objective function //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, 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|)

LOGO 18 Experiments //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012

LOGO 19 Future Works //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 DARP with vehicle 2-preemption DARP with load preemption

LOGO 20 Future works //20 Angers Avril 2012 S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Rule R6 Rule R7 DARP with vehicle 2-preemption 2 new inference rules R6 and R7:

LOGO //20 Angers Avril  And…  Dynamic context (robustness),  Reliability constraint. S. Deleplanque, A. Quilliot Wrocław, Poland, September, 2012 Future works

LOGO AAIA’2012 \ WCO’ – 12 september, 2012 Wrocław, Poland. S. Deleplanque, A. Quilliot (speaker)