Genetic Algorithms:
A Tutorial
“Genetic Algorithms are
good at taking large,
potentially huge search
spaces and navigating
them, looking for optimal
combinations of things,
solutions you might not
otherwise find in a
lifetime.”
- Salvatore Mangano
Computer Design, May 1995
Wendy Williams
Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
A Simple Example
The Traveling Salesman Problem:
Find a tour of a given set of cities so that

each city is visited only once
 the total distance traveled is minimized
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Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
Classes of Search Techniques
Search techniques
C alculus-based techniques
D irect m ethods
F inonacci
G uided random search techniques
Indirect m ethods
N ew ton
Evolutionary algorithm s
Evolutionary strategies
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Metaheuristic Algorithms
D ynam ic program m ing
G enetic algorithm s
Parallel
C entralized
Sim ulated annealing
Enum erative techniques
D istributed
3
Sequential
Steady-state
G enerational
Genetic Algorithms: A Tutorial
Components of a GA
A problem to solve, and ...
 Encoding technique
(gene, chromosome)
 Initialization procedure
(creation)
 Evaluation function
(environment)
 Selection of parents
(reproduction)
 Genetic operators
(mutation, recombination)
 Parameter settings
(practice and art)
Wendy Williams
Metaheuristic Algorithms
4
Genetic Algorithms: A Tutorial
Simple Genetic Algorithm
{
initialize population;
evaluate population;
while TerminationCriteriaNotSatisfied
{
select parents for reproduction;
perform recombination and mutation;
evaluate population;
}
}
Wendy Williams
Metaheuristic Algorithms
5
Genetic Algorithms: A Tutorial
The GA Cycle of Reproduction
reproduction
children
modification
modified
children
parents
population
evaluation
evaluated children
deleted
members
discard
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Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
Population
population
Chromosomes could be:






Bit strings
Real numbers
Permutations of element
Lists of rules
Program elements
... any data structure ...
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Metaheuristic Algorithms
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(0101 ... 1100)
(43.2 -33.1 ... 0.0 89.2)
(E11 E3 E7 ... E1 E15)
(R1 R2 R3 ... R22 R23)
(genetic programming)
Genetic Algorithms: A Tutorial
Reproduction
children
reproduction
parents
population
Parents are selected at random with
selection chances biased in relation to
chromosome evaluations.
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Metaheuristic Algorithms
8
Genetic Algorithms: A Tutorial
Chromosome Modification
children
modification
modified children


Modifications are stochastically triggered
Operator types are:
 Mutation
 Crossover (recombination)
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Metaheuristic Algorithms
9
Genetic Algorithms: A Tutorial
Mutation: Local Modification


Before:
(1 0 1 1 0 1 1 0)
After:
(0 1 1 0 0 1 1 0)
Before:
(1.38 -69.4 326.44 0.1)
After:
(1.38 -67.5 326.44 0.1)
Causes movement in the search space
(local or global)
Restores lost information to the population
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Metaheuristic Algorithms
10
Genetic Algorithms: A Tutorial
Crossover: Recombination
*
P1
P2
(0 1 1 0 1 0 0 0)
(1 1 0 1 1 0 1 0)
(0 1 0 0 1 0 0 0)
(1 1 1 1 1 0 1 0)
C1
C2
Crossover is a critical feature of genetic
algorithms:
 It greatly accelerates search early in
evolution of a population
 It leads to effective combination of
schemata (subsolutions on different
chromosomes)
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Metaheuristic Algorithms
11
Genetic Algorithms: A Tutorial
Evaluation
modified
children
evaluated
children
evaluation


The evaluator decodes a chromosome and
assigns it a fitness measure
The evaluator is the only link between a
classical GA and the problem it is solving
Wendy Williams
Metaheuristic Algorithms
12
Genetic Algorithms: A Tutorial
Deletion
population
discarded members
discard


Generational GA:
entire populations replaced with each
iteration
Steady-state GA:
a few members replaced each generation
Wendy Williams
Metaheuristic Algorithms
13
Genetic Algorithms: A Tutorial
A Simple Example
The Traveling Salesman Problem:
Find a tour of a given set of cities so that

each city is visited only once
 the total distance traveled is minimized
Wendy Williams
Metaheuristic Algorithms
14
Genetic Algorithms: A Tutorial
Representation
Representation is an ordered list of city
numbers known as an order-based GA.
1) London
2) Venice
3) Dunedin
4) Singapore
CityList1
(3 5 7 2 1 6 4 8)
CityList2
(2 5 7 6 8 1 3 4)
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Metaheuristic Algorithms
5) Beijing 7) Tokyo
6) Phoenix 8) Victoria
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Genetic Algorithms: A Tutorial
Crossover
Crossover combines inversion and
recombination:
*
*
Parent1
(3 5 7 2 1 6 4 8)
Parent2
(2 5 7 6 8 1 3 4)
Child
(5 8 7 2 1 6 3 4)
This operator is called the Order1 crossover.
Wendy Williams
Metaheuristic Algorithms
16
Genetic Algorithms: A Tutorial
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)
Wendy Williams
Metaheuristic Algorithms
17
Genetic Algorithms: A Tutorial
TSP Example: 30 Cities
100
90
80
70
y
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
x
Wendy Williams
Metaheuristic Algorithms
18
Genetic Algorithms: A Tutorial
Solution i (Distance = 941)
TS P 30 (P er for m ance = 941)
100
90
80
70
y
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
x
Wendy Williams
Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
Solution j(Distance = 800)
TS P 30 (P er for mance = 800)
100
90
80
70
y
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
x
Wendy Williams
Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
Solution k(Distance = 652)
TS P 30 (P er for m ance = 652)
100
90
80
70
y
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
x
Wendy Williams
Metaheuristic Algorithms
21
Genetic Algorithms: A Tutorial
Best Solution (Distance = 420)
TS P 30 S olution (P er for mance = 420)
100
90
80
70
y
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
x
Wendy Williams
Metaheuristic Algorithms
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Genetic Algorithms: A Tutorial
Overview of Performance
T S P 30 - O ver view o f P er fo r m an ce
1600
1400
Dista nc e
1200
1000
800
600
400
200
0
B es t
1
3
5
7
9
11
13
15
17
19
G e n e ra ti o n s (1 0 0 0 )
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Metaheuristic Algorithms
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23
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27
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W o rs t
A ve ra g e
Genetic Algorithms: A Tutorial
Some GA Application Types
Domain
Application Types
Control
gas pipeline, pole balancing, missile evasion, pursuit
Design
semiconductor layout, aircraft design, keyboard
configuration, communication networks
Scheduling
manufacturing, facility scheduling, resource allocation
Robotics
trajectory planning
Machine Learning
designing neural networks, improving classification
algorithms, classifier systems
Signal Processing
filter design
Game Playing
poker, checkers, prisoner’s dilemma
Combinatorial
Optimization
set covering, travelling salesman, routing, bin packing,
graph colouring and partitioning
Wendy Williams
Metaheuristic Algorithms
24
Genetic Algorithms: A Tutorial
% Genetic Algorithm Operators
randomOrder = randperm(popSize);
for p = 4:4:popSize
rtes = pop(randomOrder(p-3:p),:);
dists = totalDist(randomOrder(p-3:p));
[ignore,idx] = min(dists); %#ok
bestOf4Route = rtes(idx,:);
routeInsertionPoints = sort(ceil(n*rand(1,2)));
I = routeInsertionPoints(1);
J = routeInsertionPoints(2);
for k = 1:4 % Mutate the Best to get Three New Routes
tmpPop(k,:) = bestOf4Route;
switch k
case 2 % Flip
tmpPop(k,I:J) = tmpPop(k,J:-1:I);
case 3 % Swap
tmpPop(k,[I J]) = tmpPop(k,[J I]);
case 4 % Slide
tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
otherwise % Do Nothing
end
end
newPop(p-3:p,:) = tmpPop;
end
pop = newPop;
end
if showResult
% Plots the GA Results
figure('Name','TSPO_GA | Results','Numbertitle','off');
subplot(2,2,1);
pclr = ~get(0,'DefaultAxesColor');
if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);
else plot(xy(:,1),xy(:,2),'.','Color',pclr); end
title('City Locations');
subplot(2,2,2);
imagesc(dmat(optRoute,optRoute));
title('Distance Matrix');
subplot(2,2,3);
if dims > 2, plot3(xy(optRoute,1),xy(optRoute,2),xy(optRoute,3),'r.-');
else plot(xy(optRoute,1),xy(optRoute,2),'r.-'); end
title(sprintf('Total Distance = %1.4f',minDist));
subplot(2,2,4);
plot(distHistory,'b','LineWidth',2);
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Williams
title('Best
Solution
History');
set(gca,'XLim',[0
numIter+1],'YLim',[0
1.1*max([1 distHistory])]);
Metaheuristic
Algorithms
end
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Genetic Algorithms: A Tutorial