AST21111
Discrete Mathematics
2. Logic II
1
Conditional Statements
Given propositions p and q, the compound proposition
p q is called the conditional statement. p is called the
antecedent ( ) and q is called the consequent ( ).
p q is read p implies q.
e.
EE4047 Genetic Algorithms and Their Applications (40 marks) Name:_ Q1.
Class Exercise 1
Student I.D.:_
Consider a population of chromosomes in a genetic algorithm for a maximization problem with their fitness values specified as below. Chromosome No. 1 2
Answer of Tutorial 5
Q1. (56,4,6,9) Q2. 1 0 1 0 0 0 56 12 4 23 6 9
Phenotype: (56,4) 0 0 1 1 1 1 36 54 3 12 0 5
Phenotype: (3,12,0,5) Q3. r z q y p x a w b v c u g d h e i f j t k s l n
Q4. a b c g d e f h i j k l
Q5. f y x w v u t s r q d e
Answer of Tutorial 4 Q1. Speed up = 8.696 Q2. (a, b)
Chromosome A B C D E F (a) Fonseca-Flemings rank 5 3 3 1 1 1 (b) Glodbergs ranking 3 2 2 1 1 1
Q3, Q4.
Chromosome A B C D E F Q3 Glodbergs ranking 1 2 1 3 2 3 Q4. Fonseca-Flemings rank 1 2 1 4 3 3
35 18
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
Appendix 1: Project list of Lab1.m % Lab1.m % % This script implements the Simple Genetic Algorithm for CASE 1 % Binary representation for the individuals is used. % NIND = 10; MAXGEN = 100; NVAR = 1; PRECI = 22; GGAP = .4; % % % % % Number of individuals
Part 7: Advanced Designs in GA
(I) Hybrid Design
City University of Hong Kong
Example: Cloth Cutting
fabric
Used length
r1 r2
r4
Rectangular pieces r3
1
Objective
Fabric in a long roll Cloth cutting = 2-D strip packing Objective: Allocate rectangular piec
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 adva
Part 5: 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 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
1
Chro
EE4047 Genetic Algorithms and Their Applications Q1.
Class Exercise 2
Q2. Offspring 1 Offspring 2 Q3. Q4.
Chromosome Number Processing time (sec) Cost (HK$) Rank
I F
D G
K L
A I
G D
F A
H E
E C
L K
C H
B B
J J
(1+2+3)44 = 96
94
92
1 2 3 4 5 6 7
5.0 7.0 7.
EE4047 Genetic Algorithms and Their Applications (Total: 35 marks) Name:_ Q1
Class Exercise 2
Student I.D.:_
Figure 1 depicts the corresponding values of f 1 ( x) and f 2 ( x) for all the possible x in the searching domain of a multi-objective optimizatio
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
CGE 13204
Food and
Health
Unit 1: Overview and
nutrition
About the lecturer
Name: Dr Christy Lau C. C.
Consultation Hour:
17:00-18:00 on Every Monday at CityU campus
16:00-17:00 on Every Tuesday at Telford Annex
By appointments on Thursday and Friday at
C
AST21111
Discrete Mathematics
3. Methods of Mathematical
Proof and Elementary Number
Theory
1
Mathematical Proofs
A mathematical proof is a valid argument that shows the truth
of a mathematical statement is deduced from the truth of
premises in the argume
AST21111
Discrete Mathematics
2. Logic III
1
Predicates
In English grammar, the word predicate refers to the part
of a sentence that gives information about the subject.
In the sentence Vincent Kwan is a teacher at CCCU. The
words Vincent Kwan is the subj
AST21111
Discrete Mathematics
2. Logic I
1
Propositions
Mathematics involves mathematical propositions.
A proposition ( ) is a sentence that is either true or false but
not both.
e.g.
Vincent Kwan is a teacher. is a proposition as it is truth-bearing.
Wha
Major commands in the GA toolbox that will be used crtbp pp. 2-8 bs2rv pp. 2-5 recombine pp. 2-33 mut pp. 2-14 mutate pp. 2-16 reins pp.2-34 rep pp.2-37 rws pp. 2-38 ranking pp. 2-20 scaling pp. 2-40 select pp. 2-41 sus pp. 2-44 xovdp pp. 2-46 xovdps pp.
1 Tutorial
MATLAB has a wide variety of functions useful to the genetic algorithm practitioner and those wishing to experiment with the genetic algorithm for the rst time. Given the versatility of MATLABs high-level language, problems can be coded in m-le
Course:
Objectives
EE4047 - Genetic Algorithms and Their Applications
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 a simple GA to solve specified
Tutorial 5 Q1. A hierarchical chromosome structure has the following form: control gene 1 0 1 0 1 1 56 12 parametric gene 4 23 6 9
where an 1 will activate the corresponding parametric gene. What is the phenotype of the chromosome? Q2. If a uniform crosso
Tutorial 4 Q1. Consider a Farmer-and-Worker 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). It takes 100ms to evaluate the fitnes
Tutorial 3 Q1. Consider the following two parents: 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-point crossover with the crossover points at 3rd
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