L7 Problem Solving n Search p6 Ga Ex

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241-320 Design Architecture and Engineeringfor Intelligent System

SuntornSuntorn WitosurapotWitosurapot

Contact Address:Phone: 074 287369 or

Email: [email protected]

November 2009

Lecture 7:Problem Solving and Search – part 6

Informed Search (Genetic Algorithms - Examples)

241-320 Design Architecture & Engineering for Intelligent System

Problem Solving and Search – part 3 3

Recall: The Evolutionary Cycle of GA

selection

population evaluation

modification

discard

deleted members

parents

modifiedoffspring

evaluated offspring

initiate &evaluate



Example: Traveling Salesman Problem

Find the shortest distance journey of a givenset of cities so that– each city is visited only once– the total distance traveled is minimized

Assume we know the distancebetween each city



Problem

This is known to be a hard problem to solve because the number of possible routes is N! where N = the number of cities

There is no simple algorithm that gives the best answer quickly 3,628,800.0010

362,880.009

40,320.008

5,040.007

720.006

120.005

24.004

6.003

2.002

1.001

n!n



Problem

Design a chromosome encoding, a mutation operation and a crossover function for the Travelling Salesman Problem (TSP)

Assume number of cities N = 8 After all operations the produced chromosomes

should always represent valid possible journeys (visit each city once only)

There is no single answer to this, many different schemes have been used previously

2



Representation

Representation is an ordered list of citynumbers known as an order-based GA.

1) London 3) Dunedin 5) Beijing 7) Tokyo2) Venice 4) Singapore 6) Phoenix 8) Victoria

CityList1 (3 5 7 2 1 6 4 8)CityList2 (2 5 7 6 8 1 3 4)



Mutating Permutations

Changing just one entry in the permutationwould give an inadmissible solution

Alternative:– Pick two allele values at random– Move the second to follow the first, shifting the

rest along to accommodate– Note that this preserves most of the order and the

adjacency information

1 2 3 4 5 6 7 8 9 1 2 3 45 6 7 8 9



Crossover operators for permutations “Normal” crossover operators will often lead to

inadmissible solutions, i.e.– Child goes to some cities twice, and – never goes to some cities

Many specialised operators have been devised whichfocus on combining order or adjacency informationfrom the two parents

1 2 3 4 5

5 4 3 2 1

1 2 3 2 1

5 4 3 4 5



Order 1 Crossover

Idea is to preserve relative order that elements occur Informal procedure:

1. Choose an arbitrary part from the first parent2. Copy this part to the first child3. Copy the numbers that are not in the first part, to

the first child:• starting right from cut point of the copied part,• using the order of the second parent• and wrapping around at the end

4. Analogous for the second child, with parent rolesreversed



(3 5 7 2 1 6 4 8)Example: Order 1 Crossover (2 5 7 6 8 1 3 4)

Parent1

Parent2

( _ _ 7 2 1 6 _ _ )Child1

3. Copy the numbers thatare not in the first part,to the first child:

• starting right fromcut point of

the copied part ofthe second

parent,• using the order of

the secondparent and

• wrapping aroundat the end

( 3 4 2 5 7 6 8 1 )

( 3 4 2 5 7 6 8 1 )

( 3 4 5 8)

1. Choose an arbitrary part from the 1st parent2. Copy this part to the first child

( 5 8 7 2 1 6 3 4 )Child11



Crossover

Parent1 (3 5 7 2 1 6 4 8)Parent2 (2 5 7 6 8 1 3 4)

Child1 (5 8 7 2 1 6 3 4)Child2

Crossover combines inversion & recombination:

Q: Can you find the Order1 crossover of Child2 ?

A: (5 2 7 6 8 1 4 3 )

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Mutation

Mutation involves reordering of the list:

* *Before: (5 8 7 2 1 6 3 4)

After: (5 8 6 2 1 7 3 4)



TSP Example: 30 Cities

0

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120

0 10 20 30 40 50 60 70 80 90 100

x

y



Solution i (Distance = 941)TSP30 (Performance = 941)

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0 10 20 30 40 50 60 70 80 90 100

x

y



Solution j (Distance = 800)TSP30 (Performance = 800)

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120

0 10 20 30 40 50 60 70 80 90 100

x

y



Solution k (Distance = 652)TSP30 (Performance = 652)

0

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100

120

0 10 20 30 40 50 60 70 80 90 100

x

y



Best Solution (Distance = 420)TSP30 Solution (Performance = 420)

0

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0 10 20 30 40 50 60 70 80 90 100

x

y

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Overview of PerformanceTSP30 - Overview o f Pe rform ance

0

200

400

600

800

1000

1200

1400

1600

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Ge n e ratio ns (1000)

Dis

tanc

e

Best

Wors t

A verage



Demo: TSP using Genetic Algorithms Web site: http://www.lalena.com/AI/Tsp/



Demo: TSP using GA (cont.)

Extract file to a directory Notice the file (Cities.xml)

for the city list



Demo: TSP using GA: Control Parameters

Population Size: the initial number of random toursthat are created when the algorithm starts.– A large population takes longer to find a result.– A smaller population increases the chance that every

tour in the population will eventually look the same. Group Size / Neighborhood: the number of tours

are chosen from the population in each generation,.– The best 2 tours are the parents. The worst 2 tours

get replaced by the children.– For group size, a high number will increase the

likelyhood that the really good tours will be selected asparents, but it will also cause many tours to never beused as parents.

– A large group size will cause the algorithm to runfaster, but it might not find the best solution.



Demo: TSP using GA: Control Parameters (cont.)

Mutation % - The percentage that each child after crossover will undergo mutation

# Nearby Cities - As part of a greedy initial population, the GA will prefer to link cities that are close to each other to make the initial tours.

Maximum Generations - How many crossoversare run before the algorithm is terminated.



Demo: TSP using GA: Algorithms

The GA algorithm of this program does not work on the Order 1 Crossover such as we have learned

It use the alternate links between cities in both directions for each tour

AB

C

D

E

F

5



Suggested Web Site A recommended tutorials on GA can be found at

http://www.obitko.com/tutorials/genetic-algorithms/example-function-minimum.php



Suggested Web Site (cont.)Single step feature allows you to see & learn the GA easily



Change crossover & mutation probabilityMoreover, the effects of crossover and mutation probability for a GA performance can be also seen



A "Hello World!" Genetic Algorithm Example http://www.generation5.org/content/2003/gahelloworld.asp?Action=

List&Topic=Genetic%20Algorithms See a simple program (~ 138 lines of C++ Code)

Basically, all this does it go through each member of the population and compare it with the target string. It adds up the differences between the characters and uses the cumulative sum as the fitness value (therefore, the lower the value, the better).



Reading

The thai paper named“จีนเนติกอัลกอริทึม” thatcan be downloaded from the LMS website (L6_reading_GA.zip)

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L7 Problem Solving n Search p6 Ga Ex

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