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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?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 10
Agenda
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 11
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…
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 12
©
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Ant Colony Optimization
Marco Dorigo and Thomas Stützle
MIT Press, Cambridge, MA, 2004
ISBN-13: 978-3540606765
15
Further reading
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 17
What are metaheuristics?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 19
What is to be optimised?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Bowled function
20
Z = X.^2 + Y.^2
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Mexican hat
21
Z = sin(sqrt(X.^2+Y.^2)) ./ sqrt(X.^2+Y.^2)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
TSP example nr. 1
23
By Dantzig, Fulkerson, and
Johnson (1954)
Solved instance:
42 cities in USA
Image © http://www.tsp.gatech.edu
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
TSP example nr. 2
24
By Groetschel and Holland
(1987)
Solved instance:
666 interesting
places in the world
Image © http://www.tsp.gatech.edu
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
TSP example nr. 3
25
By Applegate, Bixby,
Chvatal, and Cook
(2001)
Solved instance:
15,112 German cities
Image © http://www.tsp.gatech.edu
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 26
By Applegate, Bixby,
Chvatal, Cook, and
Helsgaun (2004)
Solved instance:
24,978 cities in
Sweden
Image © http://www.tsp.gatech.edu
TSP ex.
nr. 4
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 27
By Nagata (2009)
Solved instance:
100,000 cities
(Mona Lisa TSP)
Image © http://www.tsp.gatech.edu
TSP ex.
nr. 5
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
TSP ex.
nr. 6
28
By Helsgaun
(2009)
Solved instance:
1,904,711 cities
(World TSP)
Image © http://www.tsp.gatech.edu
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Other domains
29
 Quadratic assignment problems
 Scheduling problems
 Vehicle routing
 Routing in communication networks
 Graph colouring
 Design problems in engineering
 And many, many more!
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 30
Examples of metaheuristics
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Metaheuristics
31
 Traditional approaches:
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Metaheuristics
32
 Traditional approaches:
 EC (Evolutionary Computation)
• GA (Genetic Algorithms), ES (Evolution
Strategies), GP (Genetic Programming), etc.
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Metaheuristics
33
 Traditional approaches:
 EC (Evolutionary Computation)
• GA (Genetic Algorithms), ES (Evolution
Strategies), GP (Genetic Programming), etc.
 SA (Simulated Annealing), TS (Tabu Search),
ANN (Artificial Neural Networks), EDA (Estimation
of Distribution Algorithms), ACO (Ant Colony
Optimization), etc.
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Metaheuristics
34
 Traditional approaches:
 EC (Evolutionary Computation)
• GA (Genetic Algorithms), ES (Evolution
Strategies), GP (Genetic Programming), etc.
 SA (Simulated Annealing), TS (Tabu Search),
ANN (Artificial Neural Networks), EDA (Estimation
of Distribution Algorithms), ACO (Ant Colony
Optimization), etc.
 Hybrid metaheuristics  recent approaches!
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 35
What do GA and ACO have in
common?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
GA and ACO
36
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
GA and ACO
38
 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
 Population-based algorithms
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
GA and ACO
39
 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
 Population-based algorithms
 Stochastic search methods (probabilities are used)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
GA and ACO
40
 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
 Population-based algorithms
 Stochastic search methods (probabilities are used)
 Near-optimal solutions are to be found (global
convergence is not guaranteed)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
GA and ACO
41
 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
 Population-based algorithms
 Stochastic search methods (probabilities are used)
 Near-optimal solutions are to be found (global
convergence is not guaranteed)
 Parameter tuning plays an important role
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 42
Genetic Algorithms
– Pseudo code –
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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;
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Initialize a usually random
population of individuals
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Evaluate the fitness of all
individuals
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Compute statistics, keep
the best individual so far,
etc.
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Test for termination criteria
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Select a sub-population for
offspring production
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Stochastically perturb
genes of selected
parents (apply mutation
operators) and recombine
them (apply crossover
operators)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Evaluate the new fitness
of all individuals
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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 );
P = survive P( t ), P'( t )
statistics P( t );
}
end GA;
Compute new statistics
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 53
What are the basic components
in a GA?
What should be defined?
Image © renjith krishnan at http://www.freedigitalphotos.net/
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 54
Genetic Algorithms
– Basic components –
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
55
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
56
 A genetic representation of solutions to the
problem,
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
57
 A genetic representation of solutions to the
problem,
 a way to create an initial population of solutions,
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
58
 A genetic representation of solutions to the
problem,
 a way to create an initial population of solutions,
 an evaluation function (i.e., the environment),
rating solutions in terms of their ‘fitness’
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
59
 A genetic representation of solutions to the
problem,
 a way to create an initial population of solutions,
 an evaluation function (i.e., the environment),
rating solutions in terms of their ‘fitness’
 ‘genetic’ operators that alter the genetic
composition of children during reproduction, and
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Basic components
60
 A genetic representation of solutions to the
problem,
 a way to create an initial population of solutions,
 an evaluation function (i.e., the environment),
rating solutions in terms of their ‘fitness’
 ‘genetic’ operators that alter the genetic
composition of children during reproduction, and
 values for the parameters (population size,
probabilities of applying genetic operators, etc.)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 61
Genetic Algorithms
– Genetic operators –
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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)
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 64
Genetic Algorithms
– Other issues –
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Other issues
65
 Representation of individuals
 Selection mechanisms
 Parallel implementations
 Adaptive Genetic Algorithms
 Other evolutionary algorithms
 Application domains
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 66
Ant Colony Optimization
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 68
Ant Colony Optimization
– Pseudo code –
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO pseudo code (i)
69
© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO pseudo code (i)
70
© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO pseudo code (i)
71
© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
Ant lifecycle
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO pseudo code (i)
72
© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
The pheromone trail intensity
automatically decreases over time
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO pseudo code (i)
73
© Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
E.g., activation of a local
optimisation procedure
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO
pseudo code (ii)
74
© Dorigo & Di Caro at
http://informatics.indiana.edu/jbollen/
I501F13/readings/dorigo99ant.pdf
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO
pseudo code (ii)
75
© Dorigo & Di Caro at
http://informatics.indiana.edu/jbollen/
I501F13/readings/dorigo99ant.pdf
Where to go next?
E.g., go to nearest
node or follow
more intense
pheromone trail?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO
pseudo code (ii)
76
© Dorigo & Di Caro at
http://informatics.indiana.edu/jbollen/
I501F13/readings/dorigo99ant.pdf
Update pheromone
trail locally
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO
pseudo code (ii)
77
© Dorigo & Di Caro at
http://informatics.indiana.edu/jbollen/
I501F13/readings/dorigo99ant.pdf
Update pheromone
trail after constructing
a complete solution
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
ACO
pseudo code (ii)
78
© Dorigo & Di Caro at
http://informatics.indiana.edu/jbollen/
I501F13/readings/dorigo99ant.pdf
Free allocated
resources
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 79
Metaheuristics: current trends
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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!!
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 82
Homework:
“Search for implementations of GA
and ACO that simulate their
functioning and evaluate them!”
Image © renjith krishnan at http://www.freedigitalphotos.net/
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 83
Assessment
Image © renjith krishnan at http://www.freedigitalphotos.net/
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 85
References
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Others…
86
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
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
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 88
Can you guess what it is?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
516 – 7
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
1 013 – 9
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
2 520 – 15
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
3 519 – 16
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
5 012 – 21
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
7 015 – 21
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
10 016 – 24
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
15 017 – 25
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
20 039 – 27
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
35 008 – 38
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
51 479 – 52
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
160 768 – 86
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
356 051 – 103
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
1 008 736 – 140
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 103
?
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
Timmy
D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 105
Slides of the talk per request:
dagmar@monettdiaz.com
Prof. Dr. Dagmar Monett Díaz
monettdiaz
@dmonett
http://monettdiaz.com

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Genetic Algorithms and Ant Colony Optimisation (lecture slides)

  • 1. 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
  • 2. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 2 Can you guess what it is?
  • 3. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 4. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 5. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 6. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 7. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 8. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  • 9. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 10. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 10 Agenda
  • 11. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 11 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…
  • 12. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 12 ©
  • 13. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 14. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 15. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Ant Colony Optimization Marco Dorigo and Thomas Stützle MIT Press, Cambridge, MA, 2004 ISBN-13: 978-3540606765 15 Further reading
  • 16. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 17. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 17 What are metaheuristics?
  • 18. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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)
  • 19. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 19 What is to be optimised?
  • 20. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Bowled function 20 Z = X.^2 + Y.^2
  • 21. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Mexican hat 21 Z = sin(sqrt(X.^2+Y.^2)) ./ sqrt(X.^2+Y.^2)
  • 22. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 23. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 1 23 By Dantzig, Fulkerson, and Johnson (1954) Solved instance: 42 cities in USA Image © http://www.tsp.gatech.edu
  • 24. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 2 24 By Groetschel and Holland (1987) Solved instance: 666 interesting places in the world Image © http://www.tsp.gatech.edu
  • 25. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 3 25 By Applegate, Bixby, Chvatal, and Cook (2001) Solved instance: 15,112 German cities Image © http://www.tsp.gatech.edu
  • 26. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 26 By Applegate, Bixby, Chvatal, Cook, and Helsgaun (2004) Solved instance: 24,978 cities in Sweden Image © http://www.tsp.gatech.edu TSP ex. nr. 4
  • 27. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 27 By Nagata (2009) Solved instance: 100,000 cities (Mona Lisa TSP) Image © http://www.tsp.gatech.edu TSP ex. nr. 5
  • 28. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP ex. nr. 6 28 By Helsgaun (2009) Solved instance: 1,904,711 cities (World TSP) Image © http://www.tsp.gatech.edu
  • 29. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Other domains 29  Quadratic assignment problems  Scheduling problems  Vehicle routing  Routing in communication networks  Graph colouring  Design problems in engineering  And many, many more!
  • 30. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 30 Examples of metaheuristics
  • 31. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 31  Traditional approaches:
  • 32. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 32  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.
  • 33. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 33  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.  SA (Simulated Annealing), TS (Tabu Search), ANN (Artificial Neural Networks), EDA (Estimation of Distribution Algorithms), ACO (Ant Colony Optimization), etc.
  • 34. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 34  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.  SA (Simulated Annealing), TS (Tabu Search), ANN (Artificial Neural Networks), EDA (Estimation of Distribution Algorithms), ACO (Ant Colony Optimization), etc.  Hybrid metaheuristics  recent approaches!
  • 35. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 35 What do GA and ACO have in common?
  • 36. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 36
  • 37. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 38. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 38  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  Population-based algorithms
  • 39. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 39  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  Population-based algorithms  Stochastic search methods (probabilities are used)
  • 40. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 40  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  Population-based algorithms  Stochastic search methods (probabilities are used)  Near-optimal solutions are to be found (global convergence is not guaranteed)
  • 41. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 41  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  Population-based algorithms  Stochastic search methods (probabilities are used)  Near-optimal solutions are to be found (global convergence is not guaranteed)  Parameter tuning plays an important role
  • 42. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 42 Genetic Algorithms – Pseudo code –
  • 43. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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;
  • 44. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Initialize a usually random population of individuals
  • 45. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Evaluate the fitness of all individuals
  • 46. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Compute statistics, keep the best individual so far, etc.
  • 47. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Test for termination criteria
  • 48. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Select a sub-population for offspring production
  • 49. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Stochastically perturb genes of selected parents (apply mutation operators) and recombine them (apply crossover operators)
  • 50. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Evaluate the new fitness of all individuals
  • 51. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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?
  • 52. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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 ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Compute new statistics
  • 53. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 53 What are the basic components in a GA? What should be defined? Image © renjith krishnan at http://www.freedigitalphotos.net/
  • 54. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 54 Genetic Algorithms – Basic components –
  • 55. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 55
  • 56. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 56  A genetic representation of solutions to the problem,
  • 57. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 57  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,
  • 58. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 58  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’
  • 59. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 59  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’  ‘genetic’ operators that alter the genetic composition of children during reproduction, and
  • 60. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 60  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’  ‘genetic’ operators that alter the genetic composition of children during reproduction, and  values for the parameters (population size, probabilities of applying genetic operators, etc.)
  • 61. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 61 Genetic Algorithms – Genetic operators –
  • 62. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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)
  • 63. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 64. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 64 Genetic Algorithms – Other issues –
  • 65. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Other issues 65  Representation of individuals  Selection mechanisms  Parallel implementations  Adaptive Genetic Algorithms  Other evolutionary algorithms  Application domains
  • 66. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 66 Ant Colony Optimization
  • 67. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 68. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 68 Ant Colony Optimization – Pseudo code –
  • 69. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 69 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
  • 70. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 70 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
  • 71. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 71 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf Ant lifecycle
  • 72. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 72 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf The pheromone trail intensity automatically decreases over time
  • 73. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 73 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf E.g., activation of a local optimisation procedure
  • 74. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 74 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf
  • 75. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 75 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Where to go next? E.g., go to nearest node or follow more intense pheromone trail?
  • 76. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 76 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Update pheromone trail locally
  • 77. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 77 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Update pheromone trail after constructing a complete solution
  • 78. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 78 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Free allocated resources
  • 79. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 79 Metaheuristics: current trends
  • 80. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 81. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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!!
  • 82. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 82 Homework: “Search for implementations of GA and ACO that simulate their functioning and evaluate them!” Image © renjith krishnan at http://www.freedigitalphotos.net/
  • 83. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 83 Assessment Image © renjith krishnan at http://www.freedigitalphotos.net/
  • 84. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 85. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 85 References
  • 86. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Others… 86
  • 87. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 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
  • 88. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 88 Can you guess what it is?
  • 89. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 516 – 7
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  • 103. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 103 ?
  • 104. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Timmy
  • 105. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 105 Slides of the talk per request: dagmar@monettdiaz.com Prof. Dr. Dagmar Monett Díaz monettdiaz @dmonett http://monettdiaz.com