2015 Artificial Intelligence Techniques at Engineering Seminar - Chapter 2 - Part 2: Genetic Algorithms

Artificial Intelligence Techniques
applied to Engineering
Part 2. Genetic Fuzzy Systems
Enrique Onieva Caracuel
@EnriqueOnieva
1.Fuzzy Logic
2.Genetic Algorithms
3.Genetic Fuzzy Systems
4.Applications to Intelligent
Transportation Systems: My Experience

Técnicas de Inteligencia Artificial aplicadas a la Ingeniería
@EnriqueOnieva 2014/2015 2
Optimization
Is the process of looking for the best solution over
a set of feasible solutions
Applications:
 Routes calculation
 Process planning
 Resource assignment
 Pattern classification
Can be formulated as:
 𝒎𝒊𝒏{𝒇(𝒙)│𝒙∈𝑿, 𝑿⊆𝑺 }

Example
Traveling Salesman Problem (TSP)
 A set of nodes
 To visit all the notes
 One time in each node
 Each arc (i-j) has a distance or cost associated
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Example
 A set of nodes
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29! Feasible routes
(8,8418·1030
)

Example
 A set of nodes
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(8,8418·1030
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Representation
 It has to be defined how genetic characteristics of the
individuals in the population are represented
 Very important in the GA definition
 It affects to the definition of genetic operators
(selection, crossover, mutation)
 Types:
 Bit string
 Floating point
 integer
 LISP, Expressions, …
1

Representation
Requirements:
 To allow to represent any solution
 Not allowing to represent infeasible solutions
 Adjusted to the problem
Small changes in the individual must represent small changes
in the solution
 Easy to decode
2

Representation
1. Binary coding:
 Selection problems
Back packing problems
2. Real coding:
 Real optimization problems:
Find solution to:
𝑥1 + 10 · 𝑥2 + (𝑥3 · 𝑥4) + 𝑠𝑒𝑛(𝑥5 + 𝑥6) + cos⁡(
𝑥7
𝑥8
) = 0
Distribution of 4 Gaussian
membership function in a fuzzy
system
3
0 2 4 6 8
0
0.5
1

Representation
3. Integer coding:
 Grouping problems
Clustering
4. Permutation coding:
 Sequencing problems:
Traveling salesman problem
Task to realize in a industrial chain
4

Evaluation
 Evaluation (fitness):
 Measures the quality of each individual
 Allows to distinguish among good and bad individuals
 Problem dependent
 Fast execution (if possible)
 Key: it decides the individuals to be selected
 In general:
 Is the most time consuming process in a real application
 Can be a routine, a simulation or any external process
 Approximate function can be used to reduce the execution
time
1

Genetic Algorithm 2

Genetic Algorithm
Generational Model Steady-State Model

Initialization
Uniform over the search space:
 Can generate ANY individual
Binary string: [0,1] with equal probability
Real coding: uniform value in the interval
Integer coding: all the values have the same probability
Permutation coding: random permutation
Choose the initial population according with an
heuristic

Selection
Best individuals have higher chances of being
selected
Bad individuals must have any chance of being
selected
Selective Pressure: degree in which reproduction
is directed to best individuals

Selection Operators
Roulette: probability of being selected is
proportional to the fitness
 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 =⁡
𝐹𝑖𝑡𝑛𝑒𝑠𝑠 𝑖
𝐹𝑖𝑡𝑛𝑒𝑠𝑠
Linear order: probability of
being selected is proportional to the order of the
individual
Tournament: K individuals are selected randomly,
the best of them is picked
Individual Fitness Probability
1 26 0,302
2 17 0,197
3 6 0,069
4 16 0,186
5 21 0,244

Crossover
 Offspring has to inherit some characteristics from
each parent
 It has to be designed according with the
representation
 Must produce feasible individuals

Crossover Operators
One Point Crossover
N-Points Crossover
Uniform Crossover
1
Parents
Offspring
Offspring
Offspring

Crossover Operators
Real Coding
 𝑋 = 𝑥1, 𝑥2, 𝑥3, … 𝑥 𝑛 𝑌 = {𝑦1, 𝑦2, 𝑦3, … 𝑦𝑛}
 Arithmetic crossover
𝐴 = {
𝑥1+𝑦1
2
,
𝑥2+𝑦2
2
,
𝑥3+𝑦3
2
, …
𝑥 𝑛+𝑦 𝑛
2
}
 BLX-α Crossover
𝐴 = {𝑎1, 𝑎2, 𝑎3, … 𝑎 𝑛} B = 𝑏1, 𝑏2, 𝑏3, … 𝑏 𝑛
where
 {𝒂𝒊, 𝒃𝒊}⁡∈ 𝑪 𝒎𝒊𝒏 − 𝜶 · 𝑰, 𝑪 𝒎𝒂𝒙 + 𝜶 · 𝑰
 𝐼 = 𝐶 𝑚𝑎𝑥 − 𝐶 𝑚𝑖𝑛
 𝐶 𝑚𝑖𝑛 = min⁡{ 𝑎𝑖, 𝑏𝑖} 𝐶 𝑚𝑎𝑥 = max⁡{ 𝑎𝑖, 𝑏𝑖}
2

Crossover Operators
Permutation Coding
3
Parent 1 Parent 2
Child 1 Child 2
Order

Mutation
Must allow to reach any point at the search space
Variation size must be controlled
Must produce feasible solutions
Is applied with low probability over each individual
in the offspring obtained after the crossover

Mutation Operators
 Uniform Mutation
 Interchange (“any” codification):
 Gaussian Mutation (real coding):
 𝑥′
= 𝑥 + 𝑁(0, 𝜎)

Replacement
 The way in which individuals are replaced by new
offspring affects the selective pressure
 Deterministic or randomized replacement
methods can be used
 It can be decided that the best individual (or
individuals) are not replaced  Elitism
1

Replacement
 In a Steady-State Model, it can be replaced
 The worst individual in the population
 The most similar (from N) individual
 The worst individual among a the set of the N most
similar
 The most similar parent
2

Stopping Criteria
When the optimum is reached
Limited CPU resources:
 Maximum number of generations
 Limited amount of execution time
After a certain number of generations without
improvements found

Considerations
Execute more than one time
 Use statistical measures (mean, deviation,…)
Easy to parallelize
Every search method needs equilibrium among:
 Exploring the search space
 Explode promising zones in the search space
Genetic Algorithms are general purpose search
methods. Genetic operators are used to maintain
this equilibrium

Considerations
Two opposite factors:
 Convergence: to focus the search in promising regions
by selective pressure
 Diversity: to avoid premature convergence
Selective Pressure: allow best individuals to be
selected to be crossed.

Considerations
Diversity
 It is associated with differences between individuals in
the population
Low diversity: all the individuals are quite similar between
them
Low diversity  premature convergence
Solutions:
 To include diversity mechanisms in the process
 To reinitialize once premature convergence is reached

Considerations
Diversity
 With Mutation operator
Probability adaptation
 To reduce it as the process run
 Apply high probability to bad solutions and low probability to good
solutions
 With the pairing for Crossover operator
Not cross individuals with themselves, their parents,
children,…
Incest prohibition  to cross only if the are different enough

Considerations
Diversity
 With the Crossover operator
Crossover operators with multiple parents
Crossover operators with multiple childs

Extensions
Multimodal problems
 Multiple solutions must be returned
 Niching technique to converge to diverse local optima
Multi-objective problems
 Multiple objectives must be satisfied
 Mutually excluyent objectives
Quality – Prize
Power – Consumption
Accuracy - Complexity
 There is not unique solution

Thank you very much
Any Question?

2015 Artificial Intelligence Techniques at Engineering Seminar - Chapter 2 - Part 2: Genetic Algorithms

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2015 Artificial Intelligence Techniques at Engineering Seminar - Chapter 2 - Part 2: Genetic Algorithms