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