Hybrid Genetic

Algorithm for Solving

Multi Constraint Vehicle

Routing Problem

Carry Prameswari23611001

Introduction

Previous Work

Hybrid Genetic Algorithm

Multi-Constraint VRP

Analysis

Conclusion and Future Work

Outline

Introduction

Find the minimum

total traveling distance

with CONSTRAINTS

that must be fulfilled

Introduction:Vehicle Routing Problem

Introduction:Vehicle Routing Problem

Airline businessShuttle Travel

LogisticSupply chain

Package delivery

NetworkingCommunication

VRP in our daily life

Previous Work

Previous Works

• Capacitated• Simultaneous

Pickup and Delivery

VRP

• Max. 12 Destination Point

Case Study• Genetic

Algorithm• Prins Splitting

Procedure

Method

BP

BA

C

DE

A:B:

C:

D:

E:

Previous WorksVRP with

Simultaneous Pick-up & Delivery Constraint

BP

BA

C

DE

A:B:

C:

D:

E:

Previous Works VRP with SPD and Vehicle spec.

constraint

Previous Works Genetic Algorithm

BP

BA

C

DE

BA C D E

1 2 3 4 5

Genetic AlgorithmInitializatio

n

Evaluation & Selection

Crossover

Mutatio

n

EvaluationSelection:

Roulette Wheel Procedure

10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 101 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1

Novel Order Cross Over Inversion Mutation

1 2 3 4 5 6 7 8 9 101 2 3 8 9 104 5 6 7

1 2 3 4 5 6 7 8 9 10

Swapping Mutation

1 2 3 4 5 6 7 8 9 1084

Current Research

C VRP SPD

GA + Prins Slitting

Procedure

Local Search

Multi-Trips

Time Window

Previous Work

Add. Solving Method

Additional Constraints

SCOPE : Basic constraint CVRP-SPD.VRP TW only consider about travelling and service time .

Hybrid Genetic Algorithm

Hybrid Genetic Algorithm

GA

Local

Search

Hybrid Genetic Algorith

m

Position-Oriented Genes Exchange

Static Move Descriptor (SMD):a. 1-0 Exchange Moveb. 1-1 Exchange Movec. 2-opt Move

Hybrid Genetic Algorithm

Local Search: Position-Oriented Genes Exchange

1 2 3 4 5 2 1 3 4 52 1 3 4 53 2 1 4 54 2 3 1 55 2 3 4 1

1 2 3 4 51 3 2 4 51 4 3 2 51 5 3 4 2

1 2 3 4 5

Hybrid Genetic Algorithm

Local Search: 1-0 Exchange Move

1 2 3 4 5

1 3 1 3 2 4 5

2 5 1 2 5 3 4

New Chromosomes From 1-0 Exchange Move LS procedure

2 1 3 4 5

3 2 1 4 5

4 2 3 1 5

5 2 3 4 1

1 3 2 4 5

1 4 3 2 5

1 5 3 4 2

1 2 4 3 5

1 2 5 4 3

1 2 3 5 4

Local Search: 1-1 Exchange Move

Hybrid Genetic Algorithm

1 2 3 4 5

1 2 3 4 5

1 3 3 2 1 4 5

2 5 1 5 3 4 2

New Chromosomes From 1-1 Exchange Move LS procedure

1 3 2 4 5

1 4 2 3 5

1 5 2 3 4

1 2 4 3 5

1 2 5 3 4

1 2 3 5 4

1 2 3 4 5

1 2 3 4 5

1 3 3 4 5 1 2

2 4 1 4 5 2 3

Local Search: 2 - opt Exchange Move

Hybrid Genetic Algorithm

New Chromosomes From 2-opt Exchange LS procedure

2 3 4 5 1

3 4 5 1 2

4 5 1 2 3

5 1 2 3 4

1 3 4 5 2

1 4 5 2 3

1 5 2 3 4

1 2 4 5 3

1 2 5 3 4

1 2 3 5 4

Multi-Constraint VRP

Multi-Constraint VRP

BP

A

B

C

A:

B:C:

Vehicle Capacity : 5 paxSolution:

1st trip: Base – A – B – C – Base

2nd trip: Base – B – Base

Multi-Trips

Multi-Constraint VRP

Multi-TripsSteps taken to

tackle this

constraint

Point A B CDeliv 2 7 1

Pickup 6 4 2

Point A1 A2 B1 B2 CDeliv 2 0 5 2 1

Pickup 5 1 4 0 2

Solution:

1st trip: Base – A – B – C – Base

2nd trip: Base – A – B – Base

Exist demand that excess vehicle capacity?

Go to GA process

Go directly to the GA process

N

Y

Associate point coordinates to the basic

Reconstruct pick-up and delivery

demand

Associate pick-up and delivery

demand matrix

Reconstruct coordinate points

matrix according to the new demand

matrix

Multi-Constraint VRP

Multi-TripsCase Execution

Destination Point 1 2 3 4 5 6 7 8 9 10 B

Delivery Demand 5 3 16 4 2 2 20 1 2 4 -

Pickup Demand 4 1 18 3 1 1 18 2 4 3 -

Coordinate X 6 8 9 10 7 4 1 0 0 2 5

Coordinate Y 9 10 8 7 6 8 9 8 7 7 5

Vehicle Capacity15 pax

Trip Sequence Delivery Pick-up1st trip: base – 1 – 2 – 3 – 4 – 5 – base

2nd trip: base – 3 – base3rd trip: base – 7 – base4th trip: base – 6 – 7 – 8 – 9 – 10– base

Point 1 : 5Point 2 : 3Point 3 : 1Point 4 : 4Point 5 : 2Point 3 : 15Point 7 : 15Point 6 : 2Point 7 : 5Point 8 : 1Point 9 : 2Point 10 : 4

Point 1 : 4Point 2 : 1Point 3 : 3Point 4 : 3Point 5 : 1Point 3 : 15Point 7 : 15Point 6 : 1Point 7 : 3Point 8 : 2Point 9 : 4Point 10 : 3

Multi-Constraint VRP

Time Window

time interval, given an earliest arrival time and latest arrival time.

considering service time and total traveling time.

determine the optimal route for both customer’s delivery and pick-up demand to destination point which have specified time

Key point

Multi-Constraint VRP

Time WindowChange the matrix of distance into travel time matrix

Fitness function adjustmentTime calculation the main object of the calculation

Final display adjustment:present the departure and arrival time at each point of the optimal route obtained

Steps taken to

tackle this

constraint

Destination Point 1 2 3 4 B

Coordinate X 40 45 60 65 50

Coordinate Y 70 90 80 60 50

Service time (minutes)

10 10 10 10 10

Earliest Arrival (EA) 7.00 7.00 7.30 6.00 ~

Latest Departure (LD)

8.30 8.30 9.00 7.30 ~

Multi-Constraint VRPTime Window

Case Execution

Total Dist : 128.68

Total Dist 128.68

Multi-Constraint VRP

Time WindowCase Execution

Destination Point

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B

Delivery Demand

30 20 10 20 0 10 30 10 10 10 20 20 20 10 10 -

Pickup Demand

30 10 10 10 10 10 10 20 40 10 30 40 30 10 20 -

Coordinate X

68 66 65 65 63 60 60 67 65 62 62 60 60 58 55 40

Coordinate Y

60 55 55 60 58 55 60 85 85 82 80 80 85 75 80 50

Service time (minutes)

20 40 40 20 30 30 30 20 10 30 10 10 20 10 30 -

Analysis

Analysis

Local Search Placement Analysis

Local Search Comparison

Analysis

Local Search Performance

Analysis

Analysis

Analysis

Analysis

Case Study

Destination Point

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B

Delivery Demand

30 20 10 20 0 10 30 10 10 10 20 20 20 10 10 -

Pickup Demand

30 10 10 10 10 10 10 20 40 10 30 40 30 10 20 -

Coordinate X 68 66 65 65 63 60 60 67 65 65 62 60 60 58 55 40

Coordinate Y 60 55 55 60 58 55 60 85 85 82 80 80 85 75 80 50

Parameters:

Vehicle capacity (Q)= 150Max. distance (D) = 4000Number of vehicle (H)= 2Penalty Function (PF) = 1000000Population Size = 40Max Generation = 100Crossover Probability = 0.85Muatation Probability = 0.05

Optimal Fitness Value : 189.651

Selected chromosome

Calculate distance using Prins Splitting

Procedure

Performed Local Search

For 1 to number of Genes:

Find better chromosome? SaveY

N

Local Search as a Fitness Function

End

Generate initial population

Evaluate each chromosome

(Procedure on the next flowchart)

Population converged or

Max. Generation reached?

Selection

Reproduction(Procedure on the next

flowchart)

Select two parent chromosomes

Mutation (probability)?

Crossover (probability)?

Child = Parent 1

Child = Parent 1

Perform Crossover

YN

YN

Calculate distance using Prins Splitting

Procedure

Performed Local Search

Find better chromosome?

Child = New chromosome

Y

Child = Parent 1

Local Search as a Mutation Procedure

Analysis

Local Search Placement Analysis

No.Placement of Local Search

Mean

Fitness Value

No. of VehicleComputational Time (second)

1As a Fitness

Function201.21 2.2 714.88

2As a Mutation

Procedure190.83 2.3 43.14

Analysis

No. Type of Local Search

Mean

Fitness Value No. of VehicleComputational

Time (second)

1 PLS 190.83 2.3 43.13

A 1-1 exchange move 190.99 2.34 28.93

B 1-0 exchange move 190.66 2.37 28.55

C 2-2 opt exchange move 192.23 2.42 13.67

2 A+B 202.24 2.25 65.34

3 A+C 192.56 2.38 22.73

4 B+C 197.21 2.5 30.79

5 A+B+C 200.73 2.26 63.47

Local Search Comparison Analysis

Analysis

Local Search Performance Analysis

15 point 20 point 25 point 30 point 35 point

Q=120;   Q=140;   Q=230;   Q=200;   Q=250;  

D=1000;   D=1000;   D=1000;   D=1000;   D=1000;  

H=10;   H=10;   H=10;   H=10;   H=10;  

PF=1000000; PF=1000000;   PF=1000000; PF=1000000; PF=1000000;

PopSize = 80;   PopSize = 100;   PopSize = 150;   PopSize = 200;   PopSize = 100;  

MaxG = 300;   MaxG = 300;   MaxG = 500;   MaxG = 550;   MaxG = 600;  

Pcrsovr = 0.9;   Pcrsovr = 0.9;   Pcrsovr = 0.9;   Pcrsovr = 0.9;   Pcrsovr = 0.9;  

Pmut = 0.1;   Pmut = 0.1;   Pmut = 0.1;   Pmut = 0.1;   Pmut = 0.1;  

Optimal Route:Base-11-14-15-13-12-Base

Base-7-10-6-3-2-BaseBase-1-5-8-9-4-Base

Fitness Value:71.8003

Number of Vehicle used:3

Computational Time:97.799 sec

Optimal Route:Base-17-20-19-15-14-Base

Base-1-5-8-9-6-BaseBase-2-3-10-7-4-12-BaseBase-18-16-13-11-Base

Fitness Value:95.4184

Number of Vehicle used:4

Computational Time:397.873217 sec

AnalysisLocal Search Performance Analysis

Optimal Route:Base-16-17-20-19-15-14-13-7-Base

Base-2-5-3-6-10-9-8-4-1-BaseBase-21-22-24-25-23-28-12-11-Base

Fitness Value:95.1245

Number of Vehicle used:3

Computational Time:1670.22 sec

Optimal Route:Base-6-8-9-10-7-4-Base

Base-13-11-2-23-24-5-3-1-12-BaseBase-16-18-17-19-20-14-15-Base

Base-30-22-25-26-29-28-27-21-BaseFitness Value:

133.29Number of Vehicle used:

4Computational Time:

5204.85 sec

AnalysisLocal Search Performance Analysis

Optimal Route:Base-7-6-9-3-21-23-2-5-8-10-Base

Base-4-1-12-16-17-BaseBase-18-20-19-15-14-13-11-Base

Base-33-32-31-34-35-30-28-29-22-26-BaseFitness Value:

149.3730Number of Vehicle used:

5Computational Time:

4089.0482

AnalysisLocal Search Performance Analysis

No.

Number of Point

Destination on Test

Case

Mean Mean of Fitness

Value−Optimal

Fitness Value (∆)Fitness Value No. of VehicleComputational

Time (second)

1 15 71.9201 3.2 99.0231 0.1198

2 20 97.8146 4.3 402.9787 2.3962

3 25 101.4521 3.5 1967.54 6.3276

4 30 165.956 4.4 5823.72 32.666

5 35 210.6423 5.5 4892.143 61.2703

Conclusion & Future Works

Conclusions

Hybrid Genetic Algorithm that combines Local Search and GA

has been successfully developed to solve multi constraint vehicle

routing problems

From 4 type of LS method, 1-0 exchange move is the most preferable method to be combined with GA

VRP with time window and multi-trips constraint could be solved

without causing major change in basic Hybrid GA solver

Future Works

Conclusions and Future Works

There are still a lot of constraints in VRP problem to be included, for instance:Multi vehicle, multi depot, split delivery

Comparison between GA with other heuristic method.

Thank You