Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
Introduction:
Professor John Holland in 1975 proposed
an attractive class of computational models,
called Genetic Algorithms (GA), that simulate
the biological evolution process for solving
problems in a wide domain. GA has three main
applications, namely, intelligent search, optimization and machine and
robot learning. Currently, GA is used along with neural nets and fuzzy
logic for solving more complex problems. Because of their joint usage in
many problems, these together are often referred to by a generic name:
“soft-computing”.
2.1Genetic Algorithm:
Genetic algorithms are adaptive heuristic search algorithm
premised on the Darwin’s evolutionary ideas of natural selection and
genetic. The basic concept of genetic algorithms is designed to simulate
processes in natural system necessary for evolution. Strength of Genetic
Algorithm comes from:
1. Genetic algorithms are intrinsically parallel. They can explore the
solution space in multiple directions at once. So convergence to an
optimal solution does not depend on the chosen initial solution.
2. They are well-suited to solving problems having huge search space.
3. They perform well in problems for which the fitness landscape is
complex - where the function is discontinuous, noisy, changes over time,
or has many local optima.
Genetic algorithm maintains a population of individuals, for
generation. Each individual represents a potential solution to the problem.
Each individual is evaluated to give some measure of its fitness. Some
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
individuals undergo random transformations by means of genetic
operations to form new individuals. There are two type of transformation:
Mutation, which forms new individuals by making changes in a single
individual, and Crossover, which forms new individuals by combining
parts from two individuals.
The new individuals, called offspring , are then evaluated. A new
population is formed by selecting the more fit individuals from the parent
population and offspring population transformation.
After several generations, genetic algorithm converges to the best
individual, which represents an optimal or suboptimal solution to the
problem. The flowchart of a GA work is presented below in fig.1
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
2.2 Standard Genetic Algorithm(Simple genetic Algorithm):
Algorithm SGA
- Initial (population);
- Evaluation (population);
- Gen = 0;
- Do
- Selected_parents ← selection (population);
- Created_offspring ← crossover (selected_parents);
- Mutation (created_offspring);
- Population ← created_offspring;
- Evaluation (population);
- Gen ← gen+1;
- Until stop_criterion
Basic concepts:
2.2.1The population size :
is the number of individuals that are allowed in the population
maintained by a GA. If the population size is too large, the GA tends to
takes longer to converge upon a solution. However, if the population size
is too small, the GA is in danger of premature convergence upon a
suboptimal solution. This is primarily because there may not be enough
diversity in the population to allow the GA to escape local optima.
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
2.2.2 Encoding:
Encoding the solutions of the problem into chromosomes is a main
issue when using genetic algorithms. One excellent problem related with
encoding is that some individuals correspond to infeasible or illegal
solutions to a given problem. The difference between two concepts:
infeasibility and illegality, is shown in fig.2.
Infeasibility mean that a solution decoded from chromosome is
outside the feasible area of given problem. Illegality mean that a
chromosome does not represent a solution to a given problem. According
to what kind of a gene, the encoding methods are the following:
1. Binary encoding.
2. Real-number encoding.
3. Integer or literal permutation encoding.
a) Binary Encoding:
Binary encoding (i.e., the bit strings) are the most common
encoding used for several of reasons. Holland and his students
concentrated on such encodings. Binary encoding for function
optimization problems is know to severe drawbacks due to the existence
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
of Hamming cliffs, pairs of encoding having a large Hamming distance
(The Hamming distance between two bit strings is defined as the number
of corresponding positions in these bit strings where the bits have a
different value) while belonging to points of minimal distance in
phenotype space.
The bit strings 1000 and 0111 differ in every single bit, therefore having
maximal hamming distance of four, but encode the two adjacent integers
8 and 7. This adverse encoding may prevent the GA from converging to
the global optimum in case it is located at a so-called Hamming cliff, like
the one above.
GAs employ a Gray code which guarantees that adjacent integers
are represented by bit strings which only differ in a single bit and
therefore avoid Hamming cliffs. Given a binary string si,...,s„ coding
integers in the standard way, the conversion formula for obtaining the
corresponding Gray-coded string gi,...,gn is the following:
s1
if k =1
gk =
sk+1 XOR
sk
if k >1
The inverse conversion is defined by means of the following expression:
Table 1 compares the coding of integers 0 to 7 using binary and Gray
codes. Notice that strings encoding adjacent integers have a minimal
hamming distance of 1. Nevertheless, even for a Gray code, a single
mutation may still result in a large change of the integer value depending
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
on the position of the reversed bit. In general, mutation in binary-coded
GAs lacks the ability to strictly focus the search on solutions that are
located close to its parents in phenotype space.
Table 1 Comparison of binary and Gray codes.
integer
0
1
2
3
4
5
6
7
Binary
000
001
010
011
100
101
110
111
Gray
Code
000
001
011
010
110
111
101
100
Exercise: encode binary code for numbers(11-20)using gray code.
b) Integer or Literal Permutation Encoding:
Integer encoding is best used for combinational optimization
problems because to search for the best permutation or combination of
items subject to constrains. This mean that each gene is integer number
therefore a chromosome consists of string of integers.
Encoding
binary
Integer
Parent
Chromosome
1 | 00 010 001
0 | 01 110 000
4|
2 1
1|
6 0
Offspring Chromosome
101
000
4 6
1 2
110 000
010 001
0
1
value
560
021
460
121
Comparison between binary encoding and integer encoding.
c) Real Number Encoding:
Real number encoding is best used for function optimization
problems. It has been widely verified that real number encoding perform
better than binary encoding for function optimization and constrained
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Babylon university-uloom college for women- advanced intelligent applicationsGenetic Algorithms----------------4TH class---------------------- zainab falah
optimizations problems. In real number encoding, the structure of
genotype space is identical to that of the phenotype. Each gene is real
number and chromosome is string of real numbers. such as chromosome
is 0.0 1.4 3.5 4.4 9.1
Exercise: give chromosome with length 8 genes encding in real form.
Next lecture spooler:
After knowledge of the genetic algorithm , in the next lecture , we shall
know the evaluation of chromosomes and selection of chromosomes to
next generation.
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