pso algorithms for generalized multi-depot vrp with pickup & delivery requests pandhapon...
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PSO algorithms for Generalized Multi-depot VRP
with pickup & delivery requests
Pandhapon Sombuntham 108026
BackgroundProposed ApproachesExperimentSummaryQ&A
Contents
Transportation of Material
Right Time
Route Planning
Right Place
Right Quantity
?
Background
Location A
Location B
Depot
otb-games.comTo A To B
VRP(Vehicle Routing Problem)
ShipmentDone
ShipmentDone To Depot
VRPSPD(Vehicle Routing Problem with
simultaneous pickup & delivery)
ShipmentDone
To B
No direct shipment between Locations
(except depot)
Background
Depot
otb-games.com
Location A
Location B
To B
PDP(Pickup & Delivery Problem)
FinishedShipment
Empty truck
Vehicle Station
• Direct shipment• 3 Roles of Locations
• Pickup Location• Delivery Location• Vehicle Station
• One role for a location
To B
clipartof.com
Delivery Location
Pickup Location
Background
Location A
Location B
1To A
2To B
Location C
7To A
• Allow… Direct shipment… Can pickup more than 1 item from a location to deliver to more than one destinations.… Location can play multiple roles
6To D
3To B
4To C
5To C
8To B
GVRP – MDPDPGeneralized Vehicle Routing
problemfor multi-depot with pickup and
delivery requests
Location D
Any location can play multiple
roles
Deliver
Background
Depot (Supply Node)
Customer( Demand Node)
VRP(Vehicle Routing Problem)
PDP(Pickup & Delivery Problem)
1
1
22
3
3
4
4
GVRP – MDPDPGeneralized Vehicle Routing problem
for multi-depot with pickup and delivery requests
PickupDeliver
Deliver Deliver
Vehicle StationPickup Location
Deliver Location
Location with VehicleLocation w/o Vehicle
Allow Multiple roles
for each location
Many pickups at a location
Limousine service at Airport in Big city
Example
mitchellslimousines.net
Airport
To C
clipartof.com
To B
clipartof.com
To A
clipartof.com
A
B
C
Airport
StationMany
pickups at airport
Airport is both pickup and delivery
location
Pooling Vehicle
SME
Location A
Location B
1To A
2To B
Location C
7To A
6To D
3To B
4To C
5To C
8To B
GVRP – MDPDPGeneralized Vehicle Routing
problemfor multi-depot with pickup and
delivery requests
Location D
• SME• Sharing Fleet of vehiclesAmong alliances
Any location can play multiple
roles
+Many Pickups
at locations
Daily operation
100s itemsConsider
?
100000000
120000000
140000000
160000000
180000000
200000000
220000000
44000000 54000000 64000000 74000000 84000000 94000000
Y -C
oord
inat
e
X -Coordinate
VRP
P
P
P
P
Vehicle capacity
Heterogeneous vehicle
On-Time delivery
Maximum Route time
Direct shipments
Many pickups items at any locations
Multiple-role locations
PDP
P
P
P
P
P
GVRP-MDPDR
PPPPPPP
ExperiencePoor
Utilization
Proposed Approach
Decoding
Based on Particle Swarm Optimization (PSO) framework for solving the vehicle routing problems ,i.e. CVRP VRPSPD ,and VRPTW (Ai & Kachitvichyanukul, 2009a,2009b,2009c)
PSO with multiple social learning terms of Pongchairerks & Kachitvichyanukul [10],[11]
PSO
Encoding
rigasturists.lvistockphoto.com
http://talkfeeleez.files.wordpress.com/
Initialize particles with random position and zero velocity
Evaluate fitness value
Update pbest and gbest
Meet stopping criterion?
Update velocity and position
Start
EndYES
NO
Thesis Framework
GVRP-MDPDRGVRP-MDPDR GLNPSOGLNPSO
ApplicationApplication
Encoding(Solution
representation)
Encoding(Solution
representation)DecodingDecoding
SD1 SD2 SD3
Preliminary Test Effect on TimeAppropriate
Swarm size & steps
Comparison algorithms
Test Instances
PDPTW (Li & Lim,2001) Special cases of GVRP-MDPDR
Newly Generated Instances 20-100 locations with 30-100 items involved
Half-random-half-clusteredRandomly distributedClustered
Test on PDPTW
Case
Best known solution
Best of 5 Replications
Average
NV Distance NV Distance NV Distance
lc101 10 828.94 10 828.94 10.00 828.94lc102 10 828.94 10 828.94 10.00 828.94
lc103 9 1035.35 9 1063.63 9.40 977.47
lc104 9 860.01 9 863.36 9.00 884.14lc105 10 828.94 10 828.94 10.00 828.94lc106 10 828.94 10 828.94 10.20 890.53lc107 10 828.94 10 828.94 10.00 828.94lc108 10 826.44 10 826.44 10.20 839.41lc109 9 1000.60 10 827.82 10.00 828.04lc201 3 591.56 3 591.56 3.00 591.56lc202 3 591.56 3 591.56 3.00 591.56lc203 3 585.56 3 591.17 3.00 591.17lc204 3 590.60 3 590.60 3.00 616.26
Application on Real case
100000000
120000000
140000000
160000000
180000000
200000000
220000000
44000000 54000000 64000000 74000000 84000000 94000000
Y -C
oord
inat
e
X -Coordinate
Vehicle capacity
Heterogeneous vehicle
On-Time delivery
Maximum Route time
Direct shipments
Many pickups items at any locations
Multiple-role locations
128 itemsConsider
PPPPPPP
Vehicle ID 27Items 18No. of Visit 12Route Time 534
SequenceLocation
VisitPickup Items Deliver Items
1 652 62 62,633 55 55,57,584 54 555 59 61 626 61 57,61,637 53 52,538 46 46 539 50 46
10 45 5211 62 5812 65
Application with Multi-Objective PSO (MOPSO)
GVRP-MDPDRGVRP-MDPDR GLNPSOGLNPSO
ApplicationApplication
Encoding(Solution
representation)
Encoding(Solution
representation)DecodingDecoding
MOPSOMOPSO
w1 x Cost1x NV + w2 x Cost2 x Total distance = Total Cost
Multi-Objective PSO
Two objective functions Number of Vehicle used Total distances
MOPSO Trade-off solutions Pareto front optimality (Nguyen et al., 2010)
Multi-Objective PSO
2900
2950
3000
3050
3100
3150
3200
3250
3300
3350
12 13 14 15 16 17 18
Tota
l Dis
tanc
e
Number of Vehicles Used
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Erc1
Provide
Alternatives for the decision
maker to analyze
the tradeoff.
More Generalized case of VRP Add practical consideration
Extend PSO Framework Experiments Application with Real-word
Decision Supports tools
Summary
Vehicle capacity
Heterogeneous vehicle
On-Time delivery
Maximum Route time
Direct shipments
Many pickups items at any locations
Multiple-role locations
PPPPPPP
Further study Develop encoding and decoding Procedure
• Randomness & Logical methods
Analyze more about properties of the problem More Practical consideration MOPSO
• More objectives to considered
Adaptive PSO
Recommendation
Q&A
Best Wishes
For your attentions