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Genetic Algorithms

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Title: What is evolutionary computation? Author: Julie Leung Last modified by: hzhang Created Date: 1/21/2000 5:16:11 AM Document presentation format – PowerPoint PPT presentation

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Title: Genetic Algorithms


1
Genetic Algorithms
  • 22c 145, Chapter 4

2
It is a Search Technique
3
Natural Selection
  • Limited number of resources
  • Competition results in struggle for existence
  • Success depends on fitness --
  • fitness of an individual how well-adapted an
    individual is to their environment. This is
    determined by their genes (blueprints for their
    physical and other characteristics).
  • Successful individuals are able to reproduce and
    pass on their genes

4
When changes occur ...
  • Previously fit (well-adapted) individuals will
    no longer be best-suited for their environment
  • Some members of the population will have genes
    that confer different characteristics than the
    norm. Some of these characteristics can make
    them more fit in the changing environment.

5
Genetic Change in Individuals
  • Mutation in genes
  • may be due to various sources (e.g. UV rays,
    chemicals, etc.)
  • Start
  • 1001001001001001001001

Location of Mutation
After Mutation 1001000001001001001001
6
Genetic Change in Individuals
  • Recombination (Crossover)
  • occurs during reproduction -- sections of genetic
    material exchanged between two chromosomes

7
Recombination (Crossover)
8
Why Evolution Proves to be a Good Model for
Solving these Types of Problems
  • Evolution is a method of searching for an
    (almost) optimal solution
  • Possibilities -- all individuals
  • Best solution -- the most fit or well-adapted
    individual
  • Evolution is a parallel process
  • Testing and changing of numerous species and
    individuals occur at the same time (or, in
    parallel)
  • Evolution can be seen as a method that designs
    new (original) solutions to a changing environment

9
The Metaphor
  • EVOLUTION
  • Individual
  • Fitness
  • Environment
  • PROBLEM SOLVING
  • Candidate Solution
  • Quality
  • Problem

10
Genetic Algorithms
  • Closely follows a biological approach to problem
    solving
  • A simulated population of randomly selected
    individuals is generated then allowed to evolve

11
Encoding the Problem
  • Example Looking for a new site which is closest
    to several nearby cities.
  • Express the problem in terms of a bit string

z (1001010101011100)
where the first 8 bits of the string represent
the X-coordinate and the second 8 bits represent
the Y-coordinate
12
Basic Genetic Algorithm
  • Step 1. Generate a random population of n
    individuals
  • Step 2. Assign a fitness value to each individual
  • Step 3. Repeat until n children have been
    produced
  • Choose 2 parents based on fitness proportional
    selection
  • Apply genetic operators to copies of the parents
  • Produce new chromosomes

13
Fitness Function
  • For each individual in the population, evaluate
    its relative fitness
  • For a problem with m parameters, the fitness can
    be plotted in an m1 dimensional space

14
Genetic algorithms for 8-Queen Problem
6,7,2,4,7,5,8,8 7,5,2,5,1,4,4,7
6,7,2,5,1,4,4,7
15
Genetic algorithms
  • Fitness function number of non-attacking pairs
    of queens, the higher, the better (min 0, max
    8 7/2 28)
  • 24/(24232011) 31
  • 23/(24232011) 29 etc

16
Sample Search Space
  • A randomly generated population of individuals
    will be randomly distributed throughout the
    search space

17
An Abstract Example
Distribution of Individuals in Generation 0
Distribution of Individuals in Generation N
18
Genetic Operators
  • Cross-over
  • Mutation

19
Production of New Chromosomes
  • 2 parents give rise to 2 children

20
Generations
  • As each new generation of n individuals is
    generated, they replace their parent generation
  • To achieve the desired results, typically 500 to
    5000 generations are required

21
The Evolutionary Cycle
Selection
Recombination
Mutation
Replacement
22
Ultimate Goal
  • Each subsequent generation will evolve toward the
    global maximum (or minimum)
  • After sufficient generations a near optimal
    solution will be present in the population of
    chromosomes

23
Example Find the max value of f(x1, , x100).
  • Population real vectors of length 100.
  • Mutation randomly replace a value in a vector.
  • Combination Take the average of two vectors.

24
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

25
Representation
  • Representation is an ordered list of city
  • numbers known as an order-based GA.
  • 1) London 3) Dunedin 5) Beijing 7)
    Tokyo
  • 2) Venice 4) Singapore 6) Phoenix 8)
    Victoria
  • CityList1 (3 5 7 2 1 6 4 8)
  • CityList2 (2 5 7 6 8 1 3 4)

26
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)
  • Copy a randomly selected portion of Parent1 to
    Child
  • Fill the blanks in Child with those numbers in
    Parent2 from left to right, as long as there are
    no duplication in Child.
  • This operator is called the Order1 crossover.

27
Mutation
  • Mutation involves swapping two numbers of the
    list

  • Before (5 8 7 2 1 6 3 4)
  • After (5 8 6 2 1 7 3 4)

28
TSP Example 30 Cities
29
Solution i (Distance 941)
30
Solution j(Distance 800)
31
Solution k(Distance 652)
32
Best Solution (Distance 420)
33
Overview of Performance
34
Discrete Recombination
  • Similar to crossover of genetic algorithms
  • Equal probability of receiving each parameter
    from each parent
  • (8, 12, 31, ,5) (2, 5, 23, , 14)
  • (2, 12, 31, , 14)

35
Intermediate Recombination
  • Often used to adapt the strategy parameters
  • Each child parameter is the mean value of the
    corresponding parent parameters
  • (8, 12, 31, ,5) (2, 5, 23, , 14)
  • (5, 8.5, 27, , 9.5)

36
Tuning a GA
  • Typical tuning parameters for a small problem
  • Other concerns
  • population diversity
  • ranking policies
  • removal policies
  • role of random bias

Population size 50 100
Children per generation population size
Crossovers 0 3
Mutations lt 5
Generations 20 20,000
37
Domains of Application
  • Numerical, Combinatorial Optimization
  • System Modeling and Identification
  • Planning and Control
  • Engineering Design
  • Data Mining
  • Machine Learning
  • Artificial Life

38
Drawbacks of GA
  • Difficult to find an encoding for a problem
  • Difficult to define a valid fitness function
  • May not return the global maximum

39
Why use a GA?
  • requires little insight into the problem
  • the problem has a very large solution space
  • the problem is non-convex
  • does not require derivatives
  • objective function need not be smooth
  • variables do not need to be scaled
  • fitness function can be noisy (e.g. process data)
  • when the goal is a good solution

40
When NOT to use a GA?
  • if global optimality is required
  • if problem insight can
  • significantly impact algorithm performance
  • simplify problem representation
  • if the problem is highly constrained
  • if the problem is smooth and convex
  • use a gradient-based optimizer
  • if the search space is very small
  • use enumeration

41
Online Searching (section 4.5)
  • An online search agent operates by interleaving
    computation and action. First, it takes action,
    then it observes the environment and computes the
    next action.
  • However, there is a penalty for sitting around
    and computing too long. This is why we need
    efficient methods.
  • Usually used in exploration situations.

42
Offline Search vs. Online Search
  • Offline Search
  • Knows the map of the situation
  • Basically finds the shortest path knowing the
    whole layout of the situation
  • Works like a GPS navigation system
  • Online Search
  • Doesnt know the map of the situation
  • Has to explore and find out where to go, then
    determine the shortest path
  • Works like a Roomba

43
Search Patterns
  • Often, online search agents search using a
    depth-first search pattern. This is usually the
    most logical search method for an online search.
  • The search pattern must include whether or not
    the state space is safely explorable. That is,
    are there cliffs our robot friend will fall off?
  • Random walk method works, but not very well. It
    takes exponentially many steps to find the goal.
  • Hill climbing search is by default an online
    search method, but only keeps one state in memory
    and cant go back. Depth-first is more efficient.
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