logo aaia’2012 \ wco’2012 09 – 12 september, 2012 s. deleplanque, a. quilliot. limos, cnrs,...
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AAIA’2012 \ WCO’201209 – 12 september, 2012
S. Deleplanque, A. Quilliot. LIMOS, CNRS, BLAISE PASCAL UNIVERSITY, Clermont-Ferrand (FRANCE)
Wrocław, Poland.
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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
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Outline
Introduction State of the art / model Constraint propagation & insertion techniques Experiments
Conclusion
Wrocław, Poland, 9 - 12 September, 2012
S. Deleplanque, A. Quilliot
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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
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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
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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).
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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
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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
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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
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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
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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
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Propagation time constraintsInference rules
//20Angers 11-13 Avril 2012
S. Deleplanque, A. Quilliot
Wrocław, Poland, 9 - 12 September, 2012
Rule R1
Rule R2
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//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
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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);
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//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
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//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)
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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|)
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Experiments
//20Angers 11-13 Avril 2012
S. Deleplanque, A. Quilliot
Wrocław, Poland, 9 - 12 September, 2012
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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
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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:
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Angers 11-13 Avril 2012
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And… Dynamic context (robustness), Reliability constraint.
S. Deleplanque, A. Quilliot
Wrocław, Poland, 9 - 12 September, 2012
Future works
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AAIA’2012 \ WCO’201209 – 12 september, 2012
Wrocław, Poland.
S. Deleplanque, A. Quilliot (speaker)