For Monday Nothing due Chris and Rons project talks Program 4 - - PowerPoint PPT Presentation

For Monday

• Nothing due
• Chris and Ron’s project talks

Program 4 Discussion

Demo

• http://math.hws.edu/xJava/GA/
• http://www.dieslunae.net/tsp/
• http://www.sambee.co.th/MazeSolver/mazeg

a.htm

• http://www.ads.tuwien.ac.at/raidl/tspga/TSP

GA.html

Representation

ANTENNA DESIGN

ANTENNA DESIGN

• The problem (Altshuler and Linden 1998) is to

determine the x-y-z coordinates of the 3- dimensional position of the ends (X1, Y1, Z1, X2, Y2, Z2,… , X7, Y7, Z7) of 7 straight wires so that the resulting 7-wire antenna satisfies certain performance requirements

• The first wire starts at feed point (0, 0, 0) in the

middle of the ground plane

• The antenna must fit inside the 0.5 cube

ANTENNA GENOME

• 105-bit chromosome (genome)
• Each x-y-z coordinate is represented by 5 bits (4-

bit granularity for data plus a sign bit)

• Total chromosome is 3  7  5 = 105 bits

X1 Y1 Z1 X2 Y2 Z2 … +0010 -1110 +0001 +0011

• 1011

+0011 …

ANTENNA FITNESS

• Antenna is for ground-to-satellite

communications for cars and handsets

• We desire near-uniform gain pattern 10

above the horizon

• Fitness is measured based on the antenna's

radiation pattern. The radiation pattern is simulated by National Electromagnetics Code (NEC)

ANTENNA FITNESS

• Fitness is sum of the squares of the

difference between the average gain and the antenna's gain

• Sum is taken for angles  between -90 and

+90 and all azimuth angles  from 0 to 180

• The smaller the value of fitness, the better

Alternatives

• Neural Networks (SANE)
• Structured Representations

Genetic Programming

• Applying genetic algorithms to automatic

programming

A COMPUTER PROGRAM

A COMPUTER PROGRAM IN C

int foo (int time) { int temp1, temp2; if (time > 10) temp1 = 3; else temp1 = 4; temp2 = temp1 + 1 + 2; return (temp2); }

OUTPUT OF C PROGRAM

Time Output 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 7 12 7

PROGRAM TREE

(+ 1 2 (IF (> TIME 10) 3 4))

CREATING RANDOM PROGRAMS

CREATING RANDOM PROGRAMS

• Available functions

F = {+, -, *, %, IFLTE}

• Available terminals

T = {X, Y, Random-Constants}

• The random programs are:

– Of different sizes and shapes – Syntactically valid – Executable

GP GENETIC OPERATIONS

• Reproduction
• Mutation
• Crossover (sexual recombination)
• Architecture-altering operations

MUTATION OPERATION

MUTATION OPERATION

• Select 1 parent probabilistically based on fitness
• Pick point from 1 to NUMBER-OF-POINTS
• Delete subtree at the picked point
• Grow new subtree at the mutation point in same

way as generated trees for initial random population (generation 0)

• The result is a syntactically valid executable

program

• Put the offspring into the next generation of the

population

CROSSOVER OPERATION

CROSSOVER OPERATION

• Select 2 parents probabilistically based on fitness
• Randomly pick a number from 1 to NUMBER-OF-POINTS

for 1st parent

• Independently randomly pick a number for 2nd parent
• Identify the subtrees rooted at the two picked points
• Exchange the subtrees
• The result is a syntactically valid executable program
• Put the offspring into the next generation of the population

REPRODUCTION OPERATION

• Select parent probabilistically based on

fitness

• Copy it (unchanged) into the next

generation of the population

FIVE MAJOR PREPARATORY STEPS FOR GP

• Determining the set of terminals
• Determining the set of functions
• Determining the fitness measure
• Determining the parameters for the run
• Determining the method for designating a result and the

criterion for terminating a run

ILLUSTRATIVE GP RUN

SYMBOLIC REGRESSION

Independent variable X Dependent variable Y

• 1.00

1.00

• 0.80

0.84

• 0.60

0.76

• 0.40

0.76

• 0.20

0.84 0.00 1.00 0.20 1.24 0.40 1.56 0.60 1.96 0.80 2.44 1.00 3.00

PREPARATORY STEPS

Objective: Find a computer program with one input (independent variable X) whose output equals the given data 1 Terminal set: T = {X, Random-Constants} 2 Function set: F = {+, -, *, %} 3 Fitness: The sum of the absolute value of the differences between the candidate program’s

• utput

and the given data (computed over numerous values of the independent variable x from –1.0 to +1.0) 4 Parameters: Population size M = 4 5 Termination: An individual emerges whose sum of absolute errors is less than 0.1

SYMBOLIC REGRESSION POPULATION OF 4 RANDOMLY CREATED INDIVIDUALS FOR GENERATION 0

SYMBOLIC REGRESSION x2 + x + 1 FITNESS OF THE 4 INDIVIDUALS IN GEN 0

x + 1 x2 + 1 2 x 0.67 1.00 1.70 2.67

SYMBOLIC REGRESSION x2 + x + 1 GENERATION 1

Copy of (a) Mutant of (c) picking “2” as mutation point First offspring of crossover of (a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points Second offspring

• f crossover of

(a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points

CLASSIFICATION

GP TABLEAU – INTERTWINED SPIRALS

Objective: Create a program to classify a given point in the x-y plane to the red or blue spiral 1 Terminal set: T = {X,Y,Random-Constants} 2 Function set: F = {+,-,*,%,IFLTE,SIN,COS} 3 Fitness: The number of correctly classified points (0 – 194) 4 Parameters: M = 10,000. G = 51 5 Termination: An individual program scores 194

Demos

• http://www.cs.northwestern.edu/~fjs750/netl
• go/final/gpdemo.html
• http://www.3dprintingtechnologies.com/ndst

uff/Research/WutheringHeights/Page1.htm