04 1 evolution

2
Overview
 Introduction to Evolutionary Computation
– Biological Background
– Evolutionary Computation
 Genetic Algorithm
 Genetic Programming
 Summary
– Applications of EC
– Advantage & disadvantage of EC
 Further Information

3
Biological Basis
 Biological systems adapt themselves to a new
environment by evolution.
– Generations of descendants are produced that
perform better than do their ancestors.
 Biological evolution
– Production of descendants changed from their
parents
– Selective survival of some of these descendants to
produce more descendants

4
Evolutionary Computation
 What is the Evolutionary Computation?
– Stochastic search (or problem solving) techniques
that mimic the metaphor of natural biological
evolution.
 Metaphor
EVOLUTION
Individual
Fitness
Environment
PROBLEM SOLVING
Candidate Solution
Quality
Problem

5
General Framework of EC
Generate Initial Population
Evaluate Fitness
Select Parents
Generate New Offspring
Termination Condition?
Yes
No
Fitness Function
Crossover, Mutation
Best Individual

6
Geometric Analogy - Mathematical Landscape

7
Paradigms in EC
 Evolutionary Programming (EP)
– [L. Fogel et al., 1966]
– FSMs, mutation only, tournament selection
 Evolution Strategy (ES)
– [I. Rechenberg, 1973]
– Real values, mainly mutation, ranking selection
 Genetic Algorithm (GA)
– [J. Holland, 1975]
– Bitstrings, mainly crossover, proportionate selection
 Genetic Programming (GP)
– [J. Koza, 1992]
– Trees, mainly crossover, proportionate selection

8
(Simple) Genetic Algorithm (1)
 Genetic Representation
– Chromosome
 A solution of the problem to be solved is normally
represented as a chromosome which is also called an
individual.
 This is represented as a bit string.
 This string may encode integers, real numbers, sets, or
whatever.
– Population
 GA uses a number of chromosomes at a time called a
population.
 The population evolves over a number of generations
towards a better solution.

9
Genetic Algorithm (2)
 Fitness Function
– The GA search is guided by a fitness function which
returns a single numeric value indicating the fitness of
a chromosome.
– The fitness is maximized or minimized depending on
the problems.
– Eg) The number of 1's in the chromosome
Numerical functions

10
 Selection
– Selecting individuals to be parents
– Chromosomes with a higher fitness value will have a
higher probability of contributing one or more
offspring in the next generation
– Variation of Selection
 Proportional (Roulette wheel) selection
 Tournament selection
 Ranking-based selection

11
 Genetic Operators
– Crossover (1-point)
 A crossover point is selected at random and parts of the two
parent chromosomes are swapped to create two offspring with
a probability which is called crossover rate.
 This mixing of genetic material provides a very efficient and
robust search method.
 Several different forms of crossover such as k-points, uniform

12
– Mutation
 Mutation changes a bit from 0 to 1 or 1 to 0 with a
probability which is called mutation rate.
 The mutation rate is usually very small (e.g., 0.001).
 It may result in a random search, rather than the guided
search produced by crossover.
– Reproduction
 Parent(s) is (are) copied into next generation without
crossover and mutation.

13
Example of Genetic Algorithm

14
Genetic Programming
 Genetic programming uses variable-size tree-
representations rather than fixed-length strings of
binary values.
 Program tree
= S-expression
= LISP parse tree
 Tree = Functions (Nonterminals) + Terminals

15
GP Tree: An Example
 Function set: internal nodes
– Functions, predicates, or actions which take one or
more arguments
 Terminal set: leaf nodes
– Program constants, actions, or functions which take
no arguments
S-expression: (+ 3 (/ ( 5 4) 7))
Terminals = {3, 4, 5, 7}
Functions = {+, , /}

16
Setting Up for a GP Run
 The set of terminals
 The set of functions
 The fitness measure
 The algorithm parameters
– population size, maximum number of generations
– crossover rate and mutation rate
– maximum depth of GP trees etc.
 The method for designating a result and the criterion
for terminating a run.

17
Crossover: Subtree Exchange
+
b
 
a b
+
b
+

a
+

a b

 
a b
+
b
+

a
b


 
a b

18
Mutation

a b
+
b
/

a
+

b
+
b
/

a
-
b a

19
Example: Wall-Following Robot
 Program Representation in GP
– Functions
 AND (x, y) = 0 if x = 0; else y
 OR (x, y) = 1 if x = 1; else y
 NOT (x) = 0 if x = 1; else 1
 IF (x, y, z) = y if x = 1; else z
– Terminals
 Actions: move the robot one cell to each direction
{north, east, south, west}
 Sensory input: its value is 0 whenever the coressponding
cell is free for the robot to occupy; otherwise, 1.
{n, ne, e, se, s, sw, w, nw}

21
Evolving a Wall-Following Robot
 Experimental Setup
– Population size: 5,000
– Fitness measure: the number of cells next to the wall
that are visited during 60 steps
 Perfect score (320)
– One Run (32)  10 randomly chosen starting points
– Termination condition: found perfect solution
– Selection: tournament selection

22
 Creating Next Generation
– 500 programs (10%) are copied directly into next
generation.
 Tournament selection
– 7 programs are randomly selected from the population 5,000.
– The most fit of these 7 programs is chosen.
– 4,500 programs (90%) are generated by crossover.
 A mother and a father are each chosen by tournament
selection.
 A randomly chosen subtree from the father replaces a
randomly selected subtree from the mother.
– In this example, mutation was not used.

23
Two Parents Programs and Their
Children

24
Result (1)
 Generation 0
– The most fit program (Fitness = 92)

25
Result (2)
 Generation 2
– The most fit program (fitness = 117)
 Smaller than the best one of generation 0, but it does get
stuck in the lower-right corner.

26
Result (3)
 Generation 6
 Following the wall perfectly but still gets stuck in the
bottom-right corner.

27
Result (4)
 Generation 10
 Following the wall around clockwise and moves south to
the wall if it doesn’t start next to it.

28
Result (5)
 Fitness Curve
– Fitness as a function of generation number
 The progressive (but often small) improvement from
generation to generation

29
Applications of EC
 Numerical, Combinatorial Optimization
 System Modeling and Identification
 Planning and Control
 Engineering Design
 Data Mining
 Machine Learning
 Artificial Life

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Advantages of EC
 No presumptions w.r.t. problem space
 Widely applicable
 Low development & application costs
 Easy to incorporate other methods
 Solutions are interpretable (unlike NN)
 Can be run interactively, accommodate user proposed
solutions
 Provide many alternative solutions

31
Disadvantages of EC
 No guarantee for optimal solution within finite time
 Weak theoretical basis
 May need parameter tuning
 Often computationally expensive, i.e. slow

32
Further Information on EC
 Conferences
– IEEE Congress on Evolutionary Computation (CEC)
– Genetic and Evolutionary Computation Conference (GECCO)
– Parallel Problem Solving from Nature (PPSN)
– Int. Conf. on Artificial Neural Networks and Genetic Algorithms
(ICANNGA)
– Int. Conf. on Simulated Evolution and Learning (SEAL)
 Journals
– IEEE Transactions on Evolutionary Computation
– Evolutionary Computation
– Genetic Programming and Evolvable Machines
– Evolutionary Optimization

33
Assignments:
 Draw the tree structure of the program in figure 4.8 on
page 68.
 Write a program to implement the backpropagation
algorithm for a neural network with two hidden
layers ( C++, Matlab ).
Mail your source code to
lqzhang@sjtu.edu.cn

04 1 evolution

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04 1 evolution