Genetic Algorithms and Ant Colony Optimisation (lecture slides)

D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield

Genetic Algorithms and

Ant Colony Optimisation

- An Introduction -

Prof. Dr. Dagmar Monett Díaz Computer Science Dept.

Faculty of Cooperative Studies

Berlin School of Economics and Law

[email protected]

Europe Week, 3rd – 7th March 2014

D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 2

Can you guess what it is?








By Roger Alsing

At http://rogeralsing.com/2008/12/07/genetic-programming-evolution-of-mona-lisa/

After 904 314 iterations, the evolution of only 50 semi-

transparent polygons is almost perfect to Mona Lisa!!

Evolution of Mona Lisa

http://rogeralsing.com/2008/12/07/genetic-programming-evolution-of-mona-lisa/












Agenda


Agenda

Where does the major content come from?

What are metaheuristics?

What is to be optimised?

Examples of metaheuristics

What do GA and ACO have in common?

Genetic Algorithms

Ant Colony Systems

Metaheuristics: current trends

Further reading, sources of inspiration, and more…


©


Genetic Algorithms in

Search, Optimization, and

Machine Learning

David E. Goldberg

432 pp.

Addison-Wesley, 1989

ISBN-13: 978-0201157673

What I also use in my lectures at the HWR…

13


Genetic Algorithms

+ Data Structures

= Evolution Programs

Zbigniew Michalewicz

3rd, revised and extended Edition

Springer-Verlag, 1999

ISBN-13: 978-3540606765

What I also use in my lectures at the HWR…

14


Ant Colony Optimization

Marco Dorigo and Thomas Stützle

MIT Press, Cambridge, MA, 2004

ISBN-13: 978-3540606765

15

Further reading


Further reading

M. Dorigo, M. Birattari and T. Stützle (2006): “Ant Colony

Optimization: Artificial Ants as a Computational Intelligence

Technique”.

Available at

http://iridia.ulb.ac.be/IridiaTrSeries/rev/IridiaTr2006-

023r001.pdf

M. Dorigo and K. Socha (2007): “An Introduction to Ant

Colony Optimization”.

Available at

http://iridia.ulb.ac.be/IridiaTrSeries/rev/IridiaTr2006-

010r003.pdf

16

http://iridia.ulb.ac.be/IridiaTrSeries/rev/IridiaTr2006-023r001.pdf







What are metaheuristics?


A metaheuristic is…

„[…] a master strategy that guides and modifies

other heuristics (like local search procedures) to

produce solutions beyond those that are normally

generated in a quest for local optimality.“

18

According to Laguna (2002)


What is to be optimised?


Bowled function

20

Z = X.^2 + Y.^2


Mexican hat

21

Z = sin(sqrt(X.^2+Y.^2)) ./ sqrt(X.^2+Y.^2)


The peaks surface

22

[X,Y,Z] = peaks(30);

surfc(X,Y,Z)

colormap hsv Image © http://www.mathworks.de/de/help/matlab/ref/surfc.html

http://www.mathworks.de/de/help/matlab/ref/surfc.html


TSP example nr. 1

23

By Dantzig, Fulkerson, and

Johnson (1954)

Solved instance:

42 cities in USA

Image © http://www.tsp.gatech.edu

http://www.tsp.gatech.edu/


TSP example nr. 2

24

By Groetschel and Holland

(1987)

Solved instance:

666 interesting

places in the world




TSP example nr. 3

25

By Applegate, Bixby,

Chvatal, and Cook

(2001)

Solved instance:

15,112 German cities




By Applegate, Bixby,

Chvatal, Cook, and

Helsgaun (2004)

Solved instance:

24,978 cities in

Sweden


TSP ex. nr. 4



By Nagata (2009)

Solved instance:

100,000 cities

(Mona Lisa TSP)


TSP ex. nr. 5



TSP ex. nr. 6

28

By Helsgaun

(2009)

Solved instance:

1,904,711 cities

(World TSP)




Other domains

29

Quadratic assignment problems

Scheduling problems

Vehicle routing

Routing in communication networks

Graph colouring

Design problems in engineering

And many, many more!


Examples of metaheuristics


Metaheuristics

31

Traditional approaches:


Metaheuristics

32


EC (Evolutionary Computation)

• GA (Genetic Algorithms), ES (Evolution

Strategies), GP (Genetic Programming), etc.


Metaheuristics

33





SA (Simulated Annealing), TS (Tabu Search),

ANN (Artificial Neural Networks), EDA (Estimation

of Distribution Algorithms), ACO (Ant Colony

Optimization), etc.


Metaheuristics

34





SA (Simulated Annealing), TS (Tabu Search),

ANN (Artificial Neural Networks), EDA (Estimation

of Distribution Algorithms), ACO (Ant Colony

Optimization), etc.

Hybrid metaheuristics recent approaches!


What do GA and ACO have in

common?


GA and ACO

36


GA and ACO

37

Nature-inspired algorithms

GA (Holland, 1975): simulates the process of

natural selection (i.e. Darwin’s theory of evolution)

ACO (Dorigo, 1991): simulates behaviour of ant

colonies


GA and ACO

38





colonies

Population-based algorithms


GA and ACO

39





colonies


Stochastic search methods (probabilities are used)


GA and ACO

40





colonies



Near-optimal solutions are to be found (global

convergence is not guaranteed)


GA and ACO

41





colonies



Near-optimal solutions are to be found (global

convergence is not guaranteed)

Parameter tuning plays an important role


Genetic Algorithms

– Pseudo code –


GA pseudo code

43

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );

P = survive P( t ), P'( t )

statistics P( t );

}

end GA;


GA pseudo code

44

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Initialize a usually random

population of individuals


GA pseudo code

45

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Evaluate the fitness of all

individuals


GA pseudo code

46

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Compute statistics, keep

the best individual so far,

etc.


GA pseudo code

47

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Test for termination criteria


GA pseudo code

48

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Select a sub-population for

offspring production


GA pseudo code

49

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Stochastically perturb

genes of selected

parents (apply mutation

operators) and recombine

them (apply crossover

operators)


GA pseudo code

50

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Evaluate the new fitness

of all individuals


GA pseudo code

51

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );

P = survive P( t ), P'( t );

statistics P( t );

}

end GA;

Select the survivors for

next generations. Should

you apply elitism?


GA pseudo code

52

begin GA;

t = 0;

random P( t );

evaluate P( t );

statistics P( t );

while not done {

t = t+1;

P' = select P( t );

recombine P'( t );

evaluate P'( t );


statistics P( t );

}

end GA;

Compute new statistics


What are the basic components

in a GA?

What should be defined?

Image © renjith krishnan at http://www.freedigitalphotos.net/


Genetic Algorithms

– Basic components –


Basic components

55


Basic components

56

A genetic representation of solutions to the

problem,


Basic components

57


problem,

a way to create an initial population of solutions,


Basic components

58


problem,


an evaluation function (i.e., the environment),

rating solutions in terms of their ‘fitness’


Basic components

59


problem,




‘genetic’ operators that alter the genetic

composition of children during reproduction, and


Basic components

60


problem,




‘genetic’ operators that alter the genetic

composition of children during reproduction, and

values for the parameters (population size,

probabilities of applying genetic operators, etc.)


Genetic Algorithms

– Genetic operators –


Example of crossover operator

62

Single point crossover (Also “Simple crossover”)

Parents:

Offspring:

Crossover point: kth position

. . . . . .

1 k k+1 q

P1=(x1, …, xq)

P2=(y1, …, yq)

O1=(x1, …, xk, yk+1, …, yq)

O2=(y1, …, yk, xk+1, …, xq)


Example of mutation operator

63

Boundary mutation

When using floating point representation: assign the new

allele the value of one of the boundaries:

if r < 0.5 then

NewAllele := LowerBound;

else NewAllele := UpperBound;

with r generated at random in [0, 1]

LowerBound UpperBound

NewAllele = or

OldAllele


Genetic Algorithms

– Other issues –


Other issues

65

Representation of individuals

Selection mechanisms

Parallel implementations

Adaptive Genetic Algorithms

Other evolutionary algorithms

Application domains




ACO

67

Strategies of real ants (e.g. to find food) are used

to solve optimisation problems

The behaviour of the system (swarm) emerges as

a result of the indirect communication of individuals

through the environment (‘stigmergy’)

Ants lay and follow pheromone trails

Deposited pheromone on a path depends on the

quality of that solution. It evaporates with time.

Ants collectively search the solution space



– Pseudo code –


ACO pseudo code (i)

69

© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf

http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf


ACO pseudo code (i)

70




ACO pseudo code (i)

71


Ant lifecycle



ACO pseudo code (i)

72


The pheromone trail intensity

automatically decreases over time



ACO pseudo code (i)

73


E.g., activation of a local

optimisation procedure



ACO pseudo code (ii)

74

© Dorigo & Di Caro at

http://informatics.indiana.edu/jbollen/

I501F13/readings/dorigo99ant.pdf






75




Where to go next?

E.g., go to nearest

node or follow

more intense

pheromone trail?






76




Update pheromone

trail locally






77




Update pheromone

trail after constructing

a complete solution






78




Free allocated

resources





Metaheuristics: current trends


Current trends

Combination of aspects from different

metaheuristics, Artificial Intelligence, Operations

Research techniques, etc.

Parallel algorithms to distribute the

computational effort.

Optimization of parameters (i.e. configuration

process) is a relevant issue

Application to other domains


Configuration of algorithms

(or “fine-tuning” of algorithms)

Not all metaheuristic algorithms are auto-adaptive (in particular the hybrid approaches)

Usually, control parameters are set by hand or in the spirit of brute-force mechanisms; time-consuming task

Few published research works; not yet an established research area

Distributed, remote or parallel execution of configuration algorithms: not existing (?)

Shortcomings:

Special topic in most recent conferences and workshops; current open question!!


Homework:

“Search for implementations of GA

and ACO that simulate their

functioning and evaluate them!”



Assessment



Questions

84

Mention and comment three similarities

between Genetic Algorithms and Ant Colony

Optimisation!

Mention and comment three differences!

PLEASE ANSWER AT:

https://docs.google.com/forms/d/1Mog_vgm1hFV4CLnM1XjYUYVmPlepH6iu9OTeivKONQA/viewform

https://docs.google.com/forms/d/1Mog_vgm1hFV4CLnM1XjYUYVmPlepH6iu9OTeivKONQA/viewform


References


Others…

86


Further reading and sites…

Metaheuristics Network, at

http://www.metaheuristics.net/

Ant Colony Optimization, official Web site of the

ant colony metaheuristic, at http://www.aco-

metaheuristic.org/

87

http://www.metaheuristics.net/

http://www.aco-metaheuristic.org/




Can you guess what it is?


516 – 7


1 013 – 9


2 520 – 15


3 519 – 16


5 012 – 21


7 015 – 21


10 016 – 24


15 017 – 25


20 039 – 27


35 008 – 38


51 479 – 52


160 768 – 86


356 051 – 103


1 008 736 – 140


?


Timmy


Slides of the talk per request:

[email protected]

Prof. Dr. Dagmar Monett Díaz

monettdiaz

@dmonett

http://monettdiaz.com

Education

Genetic Algorithms and Ant Colony Optimisation (lecture slides)