generic optimization techniques lecture slides

Genetic Algorithms
Natural Evolution
 Charles Darwin presented his theory of evolution before
the Linnean Society of London. This day marks the
beginning of a revolution in biology.
 Darwin’s classical theory of evolution, together with
Weismann’s theory of natural selection and Mendel’s
concept of genetics, now represent the neo-Darwinian
paradigm.

 Neo-Darwinism is based on processes of
reproduction, mutation, competition and selection.
 The power to reproduce appears to be an essential
property of life.
 The power to mutate is also guaranteed in any living
organism that reproduces itself in a continuously
changing environment.
 Processes of competition and selection normally
take place in the natural world, where expanding
populations of different species are limited by a
finite space.
Natural Evolution

 Evolution can be seen as a process leading to the
maintenance of a population’s ability to survive
and reproduce in a specific environment. This
ability is called evolutionary fitness.
 Evolutionary fitness can also be viewed as a
measure of the organism’s ability to anticipate
changes in its environment.
 The fitness, or the quantitative measure of the
ability to predict environmental changes and
respond adequately, can be considered as the
quality that is optimized in natural life.
Natural Evolution

 If two parents have superior fitness, there is a good
chance that a combination of their genes will
produce an offspring with even higher fitness.
 Genetic Algorithms follow the idea of
SURVIVAL OF THE FITTEST- Better and better
solutions evolve from previous generations until
a near optimal solution is obtained.

Natural Evolution

Natural Evolution
 All methods of evolutionary computation simulate
natural evolution by
 creating a population of individuals,
 evaluating their fitness,
 generating a new population through genetic
operations,
 And repeating this process a number of times.

The evolution by GA works on the principles of
biology
Organisms (animals or plants) produce a number
of offspring which are almost, but not entirely, like
themselves Variation may be due to sexual
reproduction (offspring have some characteristics
from each parent) in GA it is Cross Over.
INTELLIGENT EVOLUTION?

Random changes
Variation may be due mutation
Some of these offspring may survive to produce
offspring of their own, others may not . .
The “better adapted” offspring are more likely to
survive
Over time, later generations become better and
better adapted
The idea of Genetic Algorithms is based on
the same process to “evolve” better
programs

 Intelligence can be defined as the capability of a
system to adapt its behavior to ever-changing
environment.
 Evolutionary computation simulates evolution on a
computer. The result of such a simulation is a series
of optimization algorithms, usually based on a
simple set of rules. Optimization iteratively
improves the quality of solutions until an
optimal, or at least feasible, solution is found.

 The behavior of an individual organism is an inductive
inference about some yet unknown aspects of its
environment. If, over successive generations, the
organism survives, we can say that this organism is
capable of learning to predict changes in its
environment.
 The evolutionary approach is based on
computational models of natural selection and
genetics. We call them evolutionary computation, a
term that combines genetic algorithms, evolution
strategies and genetic programming.

GENETIC ALGORITHMS
An algorithm is a set of instructions that is
repeated to solve a problem.
A genetic algorithm conceptually follows steps
inspired by the biological processes of evolution.

GENETIC ALGORITHMS
Also known as evolutionary algorithms, genetic algorithms
demonstrate self organization and adaptation similar to the
way that the fittest biological organism survive and
reproduce.
A genetic algorithm is an iterative procedure that represents
its candidate solutions as strings of genes called
chromosomes.
Genetic Algorithms are often used to improve the
performance of other AI methods such as expert systems or
neural networks.
The method learns by producing offspring that are better
and better as measured by a fitness function, which is a
measure of the objective to be obtained (maximum or
minimum).

GENETIC ALGORITHMS
It’s a class of probabilistic optimization algorithms
Inspired by the biological evolution process
Uses concepts of “Natural Selection” and “Genetic
Inheritance”
Particularly well suited for hard problems where little is
known about the underlying search space
It is now Widely-used in business, science and
engineering
A genetic algorithm maintains a population of candidate
solutions for the problem at hand, and makes it evolve by
iteratively applying a set of stochastic operators

GENETIC ALGORITHMS AS
OPTIMIZATION TECHNIQUE
Search Techniqes
Guided Random
Search Techniqes
Evolutionary
Algorithms
Genetic
Algorithms

Stochastic operators
Selection replicates the most successful
solutions found in a population at a rate
proportional to their relative quality
Recombination decomposes two distinct
solutions and then randomly mixes their
parts to form novel solutions
Mutation randomly perturbs a candidate
solution

BIOLOGICAL Analogies with GA’s
Nature
Genetic
Algorithm
Environment
Optimization problem
Individuals living in that
environment
Feasible solutions
Individual’s degree of adaptation
to its surrounding environment
Solutions quality
(fitness function)

BIOLOGICAL Analogies with ga’s
Nature
Genetic
Algorithm
A population of organisms
(species)
A set of feasible solutions
Selection, recombination and
mutation in nature’s
evolutionary process
Stochastic operators
Evolution of populations to
suit their environment
Iteratively applying a set of
stochastic operators on a set
of feasible solutions

Nature
Genetic Algorithm
Gene
Each bit in chromosomes
Chromosomes
A string of bits
Population
A set of chromosomes
BIOLOGICAL ANALOGIES WITH GA’s

Genotypes and phenotypes?
Genes are the basic “instructions” for building
an organism
A chromosome is a sequence of genes
Biologists distinguish between an organism’s
genotype (the genes and chromosomes) and
its phenotype (what the organism actually is
like)
“Genes” may describe a possible solution to a
problem, without actually being the solution

Genotype space
Phenotype space
Encoding
Decoding
011101001
010001001
10010010
10010001
Genotypes and phenotypes?

Genotypes and Phenotypes?
Phenotype: the "outward, physical manifestation" of an organism.
The physical parts, the sum of the
atoms, molecules, macromolecules, cells, structures, metabolism,
energy utilization, tissues, organs, reflexes and behaviors;
anything that is part of the observable structure, function or
behavior of a living organism.
Genotype: This is the "internally coded, heritable information"
carried by all living organisms. This stored information is used as a
"blueprint" or set of instructions for building and maintaining a
living creature.

Encoding
Bit strings
Real numbers
Permutations of element
Lists of rules
Program elements
Any data structure
REPRESENTATION

Representing the Genotype Candidate Solutions
GAs can have the following types of representations:
Binary-Coded;
Encoding as Vectors of integers;
Vectors of real numbers;
Vectors of binary bits;
Combination of the previous types;
Binary-Coded GAs must decode a chromosome into a candidate
solution (CS), evaluate the CS and return the resulting fitness
back to the binary-coded chromosome representing the
evaluated CS.

Use a data structure as close as possible to the
natural representation
Write appropriate genetic operators as needed
If possible, ensure that all genotypes correspond
to feasible solutions
If possible, ensure that genetic operators reserve
feasibility
While choosing an encoding method keep the
following key ideas in consideration
Representing the Genotype Candidate Solutions

Process of Genetic Algorithm
• Produce an initial population of individuals
• Evaluate the fitness of all individuals
• while termination condition not met do
• Select fitter individuals for reproduction
• Recombine between individuals
• Mutate individuals
• Evaluate the fitness of the modified individuals
• Generate a new population
• End while

Process of Genetic Algorithm
 Problem Definition input
 Encoding principles (gene, chromosome)
 Initialization procedure (creation)
 Selection of parents (reproduction)
 Genetic operators (mutation, recombination)
 Evaluation function (environment)
 Termination condition

The crossover operator exchanges parts of two single
chromosomes, and the mutation operator changes the gene
value in some randomly chosen location of the chromosome.
GA OPERATOR
The fitness of a chromosome determines how likely it is that it will
reproduce.
Fitness is usually measured in terms of how well the chromosome
solves some goal problem.
E.g., if the genetic algorithm is to be used to sort numbers
then the fitness of a chromosome will be determined by how
close to a correct sorting it produces.
Can be applied as objective fitness level and also by subjectively
by using a human operator In GA – Fitness metric is
essential

SELECTION OF INITIAL POPULATION
Roulette-wheel Selection
Proportionate Selection
Linear Ranking
Tournament Selection

Crossover Example
Suppose an “organisms” consist of 32-bit computer
words, and we want a string with all the bits as ones
How can we do it?
Create 100 randomly generated computer words
Repeatedly do the following:
Count the 1 bits in each word
Exit if any of the words have all 32 bits set to 1
Keep the ten words that have the most 1s (discard the rest)
From each word, generate 9 new words as follows:
Choose one of the other words
Take the first half of this word and combine it with the
second half of the other word

Example cntd
1. Half from one, half from the other:
0110 1001 0100 1110 1010 1101 1011 0101
1101 0100 0101 1010 1011 0100 1010 0101
0110 1001 0100 1110 1011 0100 1010 0101
2. Choose “genes” (bits) randomly:
0110 1001 0100 1110 1010 1101 1011 0101
1101 0100 0101 1010 1011 0100 1010 0101
0100 0101 0100 1010 1010 1100 1011 0101
3. Consider a “gene” to be a larger unit:
0110 1001 0100 1110 1010 1101 1011 0101
1101 0100 0101 1010 1011 0100 1010 0101
1101 1001 0101 1010 1010 1101 1010 0101

Example
In the simple example (trying to get all 1s):
The sexual (two-parent, no mutation) approach, if it succeeds, is likely
to succeed much faster
Because up to half of the bits change each time, not just one bit
However, with no mutation, it may not succeed at all
By pure bad luck, maybe none of the first (randomly
generated) words have (say) bit 17 set to 1
Then there is no way a 1 could ever occur in this position
Another problem is lack of genetic diversity
Maybe some of the first generation did have bit 17 set to
1, but none of them were selected for the second
generation
The best technique in general turns out to be reproduction operation
with a small probability of mutation operation

Example: Curve fitting with reproduction operator
Consider y = ax2 + bx + c
“genes” are a, b, c
“chromosome” is the array [a, b, c]
What’s the best way to combine two chromosomes into one?
We could choose the first half of one and the second
half of the other: [a, b, c] We can choose
genes randomly: [a, b, c] You could compute “gene
averages:”
[(a+a)/2, (b+b)/2, (c+c)/2]

Basic Components of GA
Encoded representation.
binary encoding, real number encoding, integer encoding, data structure encoding.
Generating initial population.
random initialization, patterned initialization.
Evaluation of design fitness.
Need a consistent means of determining which designs are “better” than others.
Operators for producing and selecting new designs.
Ex. selection, crossover, mutation.
Values for the other parameters.
Ex. How much crossover and mutation, how big is population.

Basic genetic algorithms
Step 1: Represent the problem variable domain as
a chromosome of a fixed length, choose the size
of a chromosome population N, the crossover
probability pc and the mutation probability pm.
Step 2: Define a fitness function to measure the
performance, or fitness, of an individual
chromosome in the problem domain. The fitness
function establishes the basis for selecting
chromosomes that will be mated during
reproduction.

Step 3: Randomly generate an initial population of
chromosomes of size N:
x1, x2 , . . . , xN
Step 4: Calculate the fitness of each individual
chromosome:
f (x1), f (x2), . . . , f (xN)
Step 5: Select a pair of chromosomes for mating
from the current population. Parent
chromosomes are selected with a probability
related to their fitness.

Step 6: Create a pair of offspring chromosomes by
applying the genetic operators - crossover and
mutation.
Step 7: Place the created offspring chromosomes
in the new population.
Step 8: Repeat Step 5 until the size of the new
chromosome population becomes equal to the
size of the initial population, N.
Step 9: Replace the initial (parent) chromosome
population with the new (offspring) population.
Step 10: Go to Step 4, and repeat the process until the
termination criterion is satisfied.

Genetic algorithms
GA is essentially iterative process. Each iteration is
called a generation. The entire set of generations is
called a run.
A common practice is to terminate a GA after a specified
number of generations and then examine the best
chromosomes in the population. If no satisfactory
solution is found, the GA is restarted.
Because GAs use a stochastic search method, the fitness
of a population may remain stable for a number of
generations before a superior chromosome appears.

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