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
dagmar@monettdiaz.com
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

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

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

TSP example nr. 1
23
By Dantzig, Fulkerson, and
Johnson (1954)
Solved instance:
42 cities in USA
Image © 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

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

ACO
pseudo code (ii)
75
Where to go next?
E.g., go to nearest
node or follow
more intense
pheromone trail?

ACO
pseudo code (ii)
76
Update pheromone
trail locally

ACO
pseudo code (ii)
77
Update pheromone
trail after constructing
a complete solution

ACO
pseudo code (ii)
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

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

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:
dagmar@monettdiaz.com
Prof. Dr. Dagmar Monett Díaz
monettdiaz
@dmonett
http://monettdiaz.com

Genetic Algorithms and Ant Colony Optimisation (lecture slides)

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (20)

Similar a Genetic Algorithms and Ant Colony Optimisation (lecture slides)

Similar a Genetic Algorithms and Ant Colony Optimisation (lecture slides) (6)

Más de Dagmar Monett

Más de Dagmar Monett (20)

Último

Último (20)

Genetic Algorithms and Ant Colony Optimisation (lecture slides)