Tutorial 5
Q1.
Consider a population of chromosomes in a genetic algorithm with their fitness values
specified as below:
Chromosome
A
11100101
B
11001100
C
11000101
D
01100111
E
11100110
F
00101110
Fitness value
9
7
10
7
5
9
If fitness sharing is applied
Part 4 : Modifications on
Simple GA
City University of Hong Kong
Simple Genetic Algorithm
Binary representation
Roulette Wheel Selection
Single Point Crossover
Bit Mutation
High crossover rate and
low mutation rate
Generational Replacement
Policy
/ GA str
Part 3: Theory and Hypothesis
City University of Hong Kong
Mathematical Models for GA
Macroscopic models
Focus on the
properties of a
large set of
individuals
Microscopic models
Focus on the
properties of a
single string
Hyperplanes
Assume that we have a
Part 2: Basic Genetic Algorithm
City University of Hong Kong
Genetic Algorithm
Natural selection:
Survival of the fittest
DNA structures
A
C
T
G
Nucleotides
AAA
CGA
ATC
Codons
. A A A C G A A T C .
Genes
AAAC GAAT C
DNA
Biological DNA Double Helix
From
Part 1:
Optimization - Problems and Classical Methods
City University of Hong Kong
Optimization Problems
Find the best solution from all feasible
solutions for a problem
Best for a function, cost,
Examples:
Dimensions of Antenna
Wireless network layout
P
This supplementary note is to further explain the example given in page 8 in Part 4.
Consider schemata with order 3, the disruptive rate is 0.75 with a uniform crossover operation.
For one-point crossover, to have a disruptive rate of 0.75, the defining l
Answer of Tutorial 5
6
7
Q1.
The derated fitness of chromosome A = 3
Q2.
Note: In this question, the Euclidean distance is used and it can be computed by:
d ij = ( xi x j ) 2 + ( y i y j ) 2 + ( z i z j ) 2
Chromosome
s(d )
Derated Fitness
(1, 1, 1)
(2,
Answer of Tutorial 4
Q1. S p =
Ts 10000
=
= 8.696
T p 1150
Q2. (a, b)
Chromosome
A
(a) Fonseca-Flemings rank
5 (B,D,E,F are better than A)
B
3 (D,F are better than B)
C
3 (D,E are better than C)
D
E
F
1
1
1
Chromosome
A
B
C
D
E
F
Goldbergs ranking
1
2
1
3
Part 5: Advantages
City University of Hong Kong
Strength of GA
Handle multi-modal problems
Handle multi-objective problems
Parallelism
Handle constrained problems
Multi-objective Problems
Linear combination
Nonlinear combination
Pareto-based approach
Pare
Pareto-based fitness assignment
(Fonseca and Fleming) with goal
Case 3: F(Ia) partially meets the goals V
Without loss of generality, let
k [1, m) , i 1, , k , j (k 1), , m
f i ( I a ) vi f j ( I a ) v j
Goals (1 k)
are not
F(Ia)
met.
Goals (k+1 m) are
Part 6: Problems and Difficulties
City University of Hong Kong
Problem 1:
Premature Convergence and Genetic Drift
Stochastic errors in sampling caused by small population
sizes
Genetic Drift: Population converges on a single peak
without differential ad
Tutorial 4
Q1.
Consider a Farmer-and-Workers Model for a parallel genetic algorithm. Assuming that
there are 100 offspring to be evaluated in each generation, and there are 10 processing
units (1 Farmer and 9 Workers). Each processor can handle computatio
Tutorial 3
Q1.
Consider the following two parents (each represented by a chromosome in 12-bits):
0100 0100 1111
1100 1101 0011
Construct the two offspring by
(a) performing the one-point crossover with crossover point at 6th site
(b) performing the two-po
Tutorial 2
Q1.
What are the order and the defining length of the following schemata?
(a)
(b)
(c)
Q2.
10*00*110
*00101*1
000111000111
Consider a chromosome constructed as a string of 5 bits,
(a)
(b)
(c)
How many schemata in total?
How many order-3 schemata
Tutorial 1
Q1.
Describe the genetic cycle for a conventional genetic algorithm.
Q2. Consider a population of 4 chromosomes with their fitness specified in the table.
Chromosome
A
B
C
D
Fitness
10
4
1
5
Roulette Wheel Selection is performed twice to select
Pseudo code of Migration GA
initialize P demes of size N each
generation = 1
while (NOT terminated)
cfw_
for each deme /* do in parallel */
cfw_
/* migration */
if mod(generation, frequency) = 0
cfw_
send K<N best individuals to a neighbouring deme
receiv
Course:
EE4047 - Genetic Algorithms and Their Applications
Objectives
1. To let students be familiar with the GA concept and procedures
2. To visualize the effect of parameter setting on the performance of a GA
3. To design GA to solve specified optimizat
Part 7: Advanced Designs in GA
(I) Hybrid Design
City University of Hong Kong
Example: Cloth Cutting
fabric
Used
length
r4
r1
r2
Rectangular
pieces
r3
Objective
Fabric in a long roll
Cloth cutting = 2-D strip packing
Objective: Allocate rectangular pieces
Answer of Tutorial 1 Q1. You are to describe the genetic cycle (shown below) in word
Population (chromosomes)
PhenoType
Selection
Fitness
Replacement
M ating Pool (parents)
Objective Function
Genetic Operations
Fitness
Sub-population (offspring)
PhenoType
Test Questions in Past Few Years Question 5 The yellow region is for the goals. Those meet all the goals will fall inside.
To build the table using Fonseca and Fleming approach with goal attainment, you should consider three cases (see the notes). Case 1:
Part 8: Advanced GA Designs
(I) Hierarchical Chromosome Structure
City University of Hong Kong
Biological Inspiration
Regulatory Sequences and Structural Genes
tran-acting factor transcription initiation site
A promoter
B
C
structural genes
mRNA
transcrip
Part 7: Problems and Difficulties
City University of Hong Kong
Problem 1:
Premature Convergence and Genetic Drift
Stochastic errors in sampling caused by small population sizes Genetic Drift: Population converges on a single peak without differential adva
Part 6: Advantages
City University of Hong Kong
Strength of GA
Handle multi-modal problems Handle multi-objective problems Parallelism Handle constrainted problems
1
Multi-objective Problems
Linear combination Nonlinear combination Pareto-based approach
P
Part 5: Modification on Simple GA
City University of Hong Kong
Simple Genetic Algorithm
Binary representation Roulette Wheel Selection Single Point Crossover Bit Mutation High crossover rate and low mutation rate Generational Replacement Policy
1
Chromo
Part 4: Theory and Hypothesis
City University of Hong Kong
Hyperplanes
Assume that we have a problem, where the solution can be encoded in 3 bits (X1,X2,X3)
X2
010 110
011 000 001
111 100
X1
101
X3
*1
1
Terminology
Schema: binary string may contain * (don
Part 2: Basic Genetic Algorithm
City University of Hong Kong
Genetic Algorithm
Natural selection: Survival of the fittest DNA structures
A C T G Nucleotides AAA CGA Codons . A A A C G A A T C . Genes ATC
AAA C GAAT C
DNA
1
Biological DNA Double Helix
From
Part 1: Optimization Problems and Classical Methods
City University of Hong Kong
Optimization Problems
Find the best solution from all feasible solutions for a problem Best for a function, cost, Examples:
Dimensions of Antenna Wireless network layout Para