UNIT -7

Genetic Algorithms: Representation of Hypothesis as GA,, Genetic

Operators,
Fitness function and Selection, Hypothesis Space search, Genetic
Programming,
Models of Evolution and Learning, Parallelizing GA, Different search
methods for
Induction

1Genetic Algorithms



Genetic Algorithms(GAs) are adaptive heuristic search algorithms

that belong to the larger part of evolutionary algorithms. Genetic
algorithms are based on the ideas of natural selection and
genetics. These are intelligent exploitation of random searches
provided with historical data to direct the search into the region of
better performance in solution space. They are commonly used
to generate high-quality solutions for optimization
problems and search problems.
Genetic algorithms simulate the process of natural
selection which means those species that can adapt to changes
in their environment can survive and reproduce and go to the
next generation. In simple words, they simulate “survival of the
fittest” among individuals of consecutive generations to solve a
problem. Each generation consists of a population of
individuals and each individual represents a point in search
space and possible solution. Each individual is represented as a
string of character/integer/float/bits. This string is analogous to
the Chromosome.
Foundation of Genetic Algorithms
Genetic algorithms are based on an analogy with the genetic
structure and behavior of chromosomes of the population.
Following is the foundation of GAs based on this analogy –
1. Individuals in the population compete for resources and
mate

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 2. Those individuals who are successful (fittest) then mate to
create more offspring than others
3. Genes from the “fittest” parent propagate throughout the
generation, that is sometimes parents create offspring
which is better than either parent.
4. Thus each successive generation is more suited for their
environment.
Search space
The population of individuals are maintained within search space.
Each individual represents a solution in search space for given
problem. Each individual is coded as a finite length vector
(analogous to chromosome) of components. These variable
components are analogous to Genes. Thus a chromosome
(individual) is composed of several genes (variable components).

Fitness Score
A Fitness Score is given to each individual which shows the
ability of an individual to “compete”. The individual having
optimal fitness score (or near optimal) are sought.
The GAs maintains the population of n individuals
(chromosome/solutions) along with their fitness scores.The
individuals having better fitness scores are given more chance to
reproduce than others. The individuals with better fitness scores
are selected who mate and produce better offspring by
combining chromosomes of parents. The population size is static
so the room has to be created for new arrivals. So, some
individuals die and get replaced by new arrivals eventually
creating new generation when all the mating opportunity of the
old population is exhausted. It is hoped that over successive
generations better solutions will arrive while least fit die.
Each new generation has on average more “better genes” than
the individual (solution) of previous generations. Thus each new
generations have better “partial solutions” than previous
generations. Once the offspring produced having no significant
difference from offspring produced by previous populations, the
population is converged. The algorithm is said to be converged to
a set of solutions for the problem.
Operators of Genetic Algorithms

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Once the initial generation is created, the algorithm evolves the
generation using following operators –
1) Selection Operator: The idea is to give preference to the
individuals with good fitness scores and allow them to pass their
genes to successive generations.
2) Crossover Operator: This represents mating between
individuals. Two individuals are selected using selection operator
and crossover sites are chosen randomly. Then the genes at
these crossover sites are exchanged thus creating a completely
new individual (offspring). For example –

3) Mutation Operator: The key idea is to insert random genes

in offspring to maintain the diversity in the population to avoid
premature convergence. For example –

The whole algorithm can be summarized as –

1) Randomly initialize populations p
2) Determine fitness of population
3) Until convergence repeat:
a) Select parents from population
b) Crossover and generate new population
c) Perform mutation on new population
d) Calculate fitness for new population

Example problem and solution using Genetic

Algorithms
Given a target string, the goal is to produce target string starting
from a random string of the same length. In the following
implementation, following analogies are made –
 Characters A-Z, a-z, 0-9, and other special symbols are
considered as genes
 A string generated by these characters is considered as
chromosome/solution/Individual
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Fitness score is the number of characters which differ from
characters in target string at a particular index. So individual
having lower fitness value is given more preference.
 C++
 Java
 Python3
 C#
 Javascript

// C++ program to create target string, starting from

// random string using Genetic Algorithm

#include <bits/stdc++.h>
using namespace std;

// Number of individuals in each generation

#define POPULATION_SIZE 100

// Valid Genes
const string GENES =
"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP"\
"QRSTUVWXYZ 1234567890, .-;:_!\"#%&/()=?@${[]}";

// Target string to be generated

const string TARGET = "I love GeeksforGeeks";

// Function to generate random numbers in given range

int random_num(int start, int end)
{
int range = (end-start)+1;
int random_int = start+(rand()%range);
return random_int;
}

// Create random genes for mutation

char mutated_genes()
{
int len = GENES.size();
int r = random_num(0, len-1);
return GENES[r];
}

// create chromosome or string of genes

string create_gnome()
{

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 int len = TARGET.size();
string gnome = "";
for(int i = 0;i<len;i++)
gnome += mutated_genes();
return gnome;
}

// Class representing individual in population

class Individual
{
public:
string chromosome;
int fitness;
Individual(string chromosome);
Individual mate(Individual parent2);
int cal_fitness();
};

Individual::Individual(string chromosome)
{
this->chromosome = chromosome;
fitness = cal_fitness();
};

// Perform mating and produce new offspring

Individual Individual::mate(Individual par2)
{
// chromosome for offspring
string child_chromosome = "";

int len = chromosome.size();

for(int i = 0;i<len;i++)
{
// random probability
float p = random_num(0, 100)/100;

// if prob is less than 0.45, insert gene

// from parent 1
if(p < 0.45)
child_chromosome += chromosome[i];

// if prob is between 0.45 and 0.90, insert

// gene from parent 2
else if(p < 0.90)
child_chromosome += par2.chromosome[i];

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 // otherwise insert random gene(mutate),
// for maintaining diversity
else
child_chromosome += mutated_genes();
}

// create new Individual(offspring) using

// generated chromosome for offspring
return Individual(child_chromosome);
};

// Calculate fitness score, it is the number of

// characters in string which differ from target
// string.
int Individual::cal_fitness()
{
int len = TARGET.size();
int fitness = 0;
for(int i = 0;i<len;i++)
{
if(chromosome[i] != TARGET[i])
fitness++;
}
return fitness;
};

// Overloading < operator

bool operator<(const Individual &ind1, const Individual
&ind2)
{
return ind1.fitness < ind2.fitness;
}

// Driver code
int main()
{
srand((unsigned)(time(0)));

// current generation
int generation = 0;

vector<Individual> population;
bool found = false;

// create initial population

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 for(int i = 0;i<POPULATION_SIZE;i++)
{
string gnome = create_gnome();
population.push_back(Individual(gnome));
}

while(! found)
{
// sort the population in increasing order of fitness
score
sort(population.begin(), population.end());

// if the individual having lowest fitness score ie.

// 0 then we know that we have reached to the target
// and break the loop
if(population[0].fitness <= 0)
{
found = true;
break;
}

// Otherwise generate new offsprings for new

generation
vector<Individual> new_generation;

// Perform Elitism, that mean 10% of fittest

population
// goes to the next generation
int s = (10*POPULATION_SIZE)/100;
for(int i = 0;i<s;i++)
new_generation.push_back(population[i]);

// From 50% of fittest population, Individuals

// will mate to produce offspring
s = (90*POPULATION_SIZE)/100;
for(int i = 0;i<s;i++)
{
int len = population.size();
int r = random_num(0, 50);
Individual parent1 = population[r];
r = random_num(0, 50);
Individual parent2 = population[r];
Individual offspring = parent1.mate(parent2);
new_generation.push_back(offspring);
}
population = new_generation;

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 cout<< "Generation: " << generation << "\t";
cout<< "String: "<< population[0].chromosome <<"\t";
cout<< "Fitness: "<< population[0].fitness << "\n";

generation++;
}
cout<< "Generation: " << generation << "\t";
cout<< "String: "<< population[0].chromosome <<"\t";
cout<< "Fitness: "<< population[0].fitness << "\n";
}

Output:
Generation: 1 String: tO{"-?=jH[k8=B4]Oe@} Fitness: 18
Generation: 2 String: tO{"-?=jH[k8=B4]Oe@} Fitness: 18
Generation: 3 String: .#lRWf9k_Ifslw #O$k_ Fitness: 17
Generation: 4 String: .-1Rq?9mHqk3Wo]3rek_ Fitness: 16
Generation: 5 String: .-1Rq?9mHqk3Wo]3rek_ Fitness: 16
Generation: 6 String: A#ldW) #lIkslw cVek) Fitness: 14
Generation: 7 String: A#ldW) #lIkslw cVek) Fitness: 14
Generation: 8 String: (, o x _x%Rs=, 6Peek3 Fitness: 13
.
.
.
Generation: 29 String: I lope Geeks#o, Geeks Fitness: 3
Generation: 30 String: I loMe GeeksfoBGeeks Fitness: 2
Generation: 31 String: I love Geeksfo0Geeks Fitness: 1
Generation: 32 String: I love Geeksfo0Geeks Fitness: 1
Generation: 33 String: I love Geeksfo0Geeks Fitness: 1
Generation: 34 String: I love GeeksforGeeks Fitness: 0
Note: Every-time algorithm start with random strings, so output
may differ
As we can see from the output, our algorithm sometimes stuck at
a local optimum solution, this can be further improved by
updating fitness score calculation algorithm or by tweaking
mutation and crossover operators.
Why use Genetic Algorithms
 They are Robust
 Provide optimisation over large space state.
 Unlike traditional AI, they do not break on slight change in
input or presence of noise
Application of Genetic Algorithms
Genetic algorithms have many applications, some of them are –
 Recurrent Neural Network
 Mutation testing
 Code breaking
 Filtering and signal processing

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  Learning fuzzy rule base etc
2Genotype representing
Genotype representation is very important during the
implementation of a genetic algorithm, as it directly
impacts the performance of the genetic algorithm. A
proper representation is where the phenotype and the
genotype mappings have proper spaces between them.

The most common representation methods for GA are as

follows:

1. Binary representation
Binary representation is one of the most common
methods of representing GA.

The genotype in this method consists of bit strings. In the

case of a Knapsack problem, where the solution space
consists of Boolean decision variables, the binary
representation is natural.

For other problems, which may deal with numbers, we

represent the numbers with their binary representation.
The only drawback in this situation is that different bits
have different meanings, which results in undesired
consequences for the mutation and crossover operators.

2. Integer representation
In the case of discrete-valued genes, we cannot always
limit the results to binary, so instead, we use integer
representation. For example, if we had to encode the
three directions, we could have encoded them as:
{1,2,3,4}, and represented using integer representation.

3. Permutation representation

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Whenever the solutions are represented by an order of
elements we can use permutation representation. We can
take the same example of TSP, let us assume the person
has to travel all the cities, visiting one city at a time, and
then comes back to the source city. As we can see the
order of the TSP is naturally becoming a permutation,
therefore we can use the permutation representation.

4. Real valued representation

In the problems where we require to define the genes
using continuous variables, we use real-valued
representation.
3 Genetic Algorithms: Fitness Function and
Selection

The fitness function can be defined as a particular solution

to a particular problem through corresponding input and
produces output as to how good the solution is with
respect to the given problem.

The fitness value calculation is done repeatedly in a

genetic algorithm and that is why it must be fast enough.
Slow problem-solving computation can have an effect on
the genetic algorithm and can make it too slow to
execute.

In some cases, the genetic fitness function and function

objects are nearly equal or the same because the function
objective is to either minimize or maximize some complex
computation problems with multiple constraints. A
designer algorithm must be used to have a different
fitness function.

The following characteristics must be produced by the

fitness function :

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 1. It must be fast to easily solve or compute complex problems.
2. It must measure in quantity how good or fit the function
provided or how much good can it provide individuals from the
particular solution.

Some cases may happen that a fitness function cannot

calculate the given complex problem directly thereafter
approximation of fitness function may be used to get with
the correct solution, and that problem may occur because
of inherit in complexities of the problem.

USES OF GENETIC FITNESS FUNCTIONS:

1. We test with complex problems and come up with the best
case solution.
2. Each solution is given a particular approximation to check
whether it is near the original value or not.

REQUIREMENTS OF A FITNESS FUNCTION :

1. It must be clearly defined so that it can be understood how
efficiently the fitness is being calculated.
2. It must be efficiently produced executed or implemented. If the
function becomes the congestion of the algorithm then the
efficiency of the overall algorithm may be lowered.
3. The particular fitness function must produce an approximated
solution.

TO OVERCOME A PARTICULAR FITNESS FUNCTION FOR A

GIVEN PROBLEM :
Every particular problem has its own fitness function.
There is no particular rule to use a fitness function.
However, a few methods are being adopted by scientists
that deal with data.

For optimization of a particular complex problem,

functions that are basic must be used such as the total set
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of calculations of parameters that are directly associated
with the complexity of the problem and its domain can be
used to solve in a fitness function.

A fitness function must be such a kind of function that can

measure how fast or better it can produce solutions for a
given set of problems. For example, suppose a fitness
function is almost zero unless a function produces it is
correct or not is not better, since it does not provide the
data how approximate is the solution to the correct
answer.

Similarly, a fitness function that is increasing in nature will

give solutions better but it would not identify or reallocate
the solution which is best is not approximately close
enough to the actual answer.

Thus, the fitness function is also known as the evaluation

function which evaluates how close or approximate it is or
how nearly it is to the original solution.

4.Genetic algorithm:
Hypothesis space search
As already understood from our illustrative example, it is
clear that genetic algorithms employ a randomized beam
search method to seek maximally fit hypotheses. In the
hypothesis space search method, we can see that the
gradient descent search in backpropagation moves
smoothly from one hypothesis to another. On the other
hand, the genetic algorithm search can move much more
abruptly. It replaces the parent hypotheses with an
offspring that can be very different from the parent. Due
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to this reason, genetic algorithm search has lower
chances of it falling into the same kind of local minima
that plaques the gradient descent methods.

There is one practical difficulty that is often encountered

in genetic algorithms, it is crowding. Crowding can be
defined as the phenomenon in which some individuals
that are more fit in comparison to others, reproduce
quickly, therefore the copies of this individual take over a
larger fraction of the population. Most of the strategies
used in the genetic algorithms are inspired by biological
evolution. One such other strategy used is fitness sharing,
in which the measured fitness of an individual is
decreased by the presence of another individual of a
similar kind. The third method is to restrict all the
individuals to combine to form offspring. To better
understand we can say that by allowing individuals of the
same kind to recombine, clusters of similar individuals are
formed, forming multiple subspecies in the population.
Another method would be to spatially distribute
individuals and allow only nearby individuals to combine.

Population evolution and schema theorem.

The schema theorem of Holland is used to mathematically
characterize the evolution over time of the population
with respect to time. It is based on the concept of schema.
So, what is schema? Schema is any string composed of 0s,
and 1s, and *s, where * represents null, so a schema
0*10, is the same as 0010 and 0110. The schema theorem
characterizes the evolution within a genetic algorithm on
the basis of the number of instances representing each
schema. Let us assume the m(s, t) to denote the number
of instances of schema denoted by ‘s’, in the population at
the time ‘t’, the expected value in the schema theorem is
described as m(s, t+1), in terms of m(s, t), and the other
parameters of the population, schema, and GA.

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In a genetic algorithm, the evolution of the population
depends on the selection step, the recombination step,
and the mutation step. The schema theorem is one of the
most widely used theorems in the characterization of
population evolution within a genetic algorithm. If it fails
to consider the positive effects of crossover and mutation,
it is in a way incomplete. There are many other recent
theoretical analyses that have been proposed, many of
these analogies are based on models such as Markov
chain models and the statistical mechanical model.

5Genetic Algorithms and Genetic

Programming for Advanced Problem Solving



Genetic algorithms (GAs) and genetic programming (GP) are
branches of evolutionary computing, a subset of artificial
intelligence where solutions evolve over time to fit a given set
of parameters or solve specific problems. These techniques are
inspired by the biological concepts of reproduction, mutation,
and natural selection.
This article explores some intriguing and practical
applications of genetic algorithms and genetic
programming across various industries.
Table of Content
 Introduction to Genetic Algorithms
 Introduction to Genetic Programming
 Key Principles of Evolutionary Algorithms
 Examples in Optimization Problems
 Real-World Applications of Genetic Algorithms and
Genetic Programing
 Tools and Libraries for Genetic Algorithms in Python
 Conclusion
Introduction to Genetic Algorithms
Genetic Algorithms (GAs) are optimization techniques inspired
by the principles of natural selection and genetics. They
operate on a population of potential solutions, evolving these
solutions through processes analogous to biological evolution,
such as selection, crossover (recombination), and mutation.
Key Components of Genetic Algorithms

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 1. Population: A set of candidate solutions.
2. Chromosomes: Data structures representing solutions,
typically encoded as strings of binary or other types of
genes.
3. Fitness Function: A function that evaluates how good
a solution is with respect to the problem being solved.
4. Selection: The process of choosing the fittest
individuals to reproduce.
5. Crossover: The process of combining two parent
solutions to produce offspring.
6. Mutation: The process of making random alterations to
offspring to maintain genetic diversity.
6.Introduction to Genetic Programming
Genetic Programming (GP) extends the concept of genetic
algorithms to evolve programs or expressions. Instead of
evolving a set of parameters or solutions, GP evolves entire
programs or expressions that can perform a task or solve a
problem.
Key Components of Genetic Programming
1. Population: A set of programs or expressions.
2. Fitness Function: A measure of how well a program or
expression performs a given task.
3. Selection, Crossover, and Mutation: Similar to GAs,
but applied to program structures or expressions.
Key Principles of Evolutionary Algorithms
Evolutionary Algorithms (EAs), including GAs and GP, are based
on several fundamental principles:
1. Natural Selection: The idea that better solutions are
more likely to be selected for reproduction.
2. Genetic Variation: Diversity in the population is
introduced through crossover and mutation to explore a
wider solution space.
3. Survival of the Fittest: Solutions are evaluated based
on a fitness function, and the fittest solutions are more
likely to be selected for the next generation.
These principles ensure that the algorithm explores a variety of
solutions and converges towards optimal or near-optimal
solutions.
Examples in Optimization Problems
1. Knapsack Problem

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The Knapsack Problem is a classic optimization problem where
the goal is to maximize the total value of items placed in a
knapsack without exceeding its weight capacity.
GA Approach:
1. Representation: Items are represented as binary
strings, where each bit indicates whether an item is
included.
2. Fitness Function: Evaluates the total value of selected
items while penalizing solutions that exceed the weight
limit.
3. Crossover and Mutation: Involve swapping items
between solutions or flipping bits to introduce variation.
Example: Solving the 0/1 Knapsack Problem using GAs can
yield good approximations even for large instances where exact
methods become computationally infeasible.
2. Traveling Salesman Problem (TSP)
The Traveling Salesman Problem involves finding the shortest
possible route that visits a set of cities and returns to the origin
city.
GA Approach:
1. Representation: Routes are represented as
permutations of city indices.
2. Fitness Function: Measures the total distance of the
route.
3. Crossover and Mutation: Involves techniques like
order crossover (OX) and swap mutation to preserve the
feasibility of routes.
Example: GAs can effectively solve TSP instances with
hundreds of cities, providing near-optimal solutions in a
reasonable time frame.
3. Scheduling Problems
Scheduling Problems involve assigning resources to tasks over
time, aiming to optimize certain criteria like minimizing
completion time or maximizing resource utilization.
GA Approach:
1. Representation: Schedules are represented as
sequences or matrices of tasks and resources.
2. Fitness Function: Measures the quality of the
schedule based on criteria like total completion time or
resource conflicts.
3. Crossover and Mutation: Involve swapping tasks or
adjusting schedules to explore different configurations.

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Example: GAs are used in job-shop scheduling to minimize
makespan or in timetabling to ensure conflicts are resolved
efficiently.
7.Real-World Applications of Genetic Algorithms and Genetic
Programing
1. Optimizing Complex Systems
One of the classic applications of genetic algorithms is in
optimizing complex systems where traditional approaches
might fail due to the vastness of the solution space. For
example, GAs have been effectively used in airline industry for
scheduling flights and crew assignments, considering numerous
constraints and objectives. Similarly, they have been applied to
optimize the layout of components on a computer chip, which
involves a highly complex configuration space.
2. Automated Design and Creativity
In the field of automated design, GAs can generate innovative
solutions to engineering problems. For instance, NASA has used
genetic algorithms to design antennae for spacecrafts. These
algorithms generated unconventional, asymmetric designs that
performed better than the traditional symmetrical ones.
Similarly, in architecture, GAs have helped in creating novel
building layouts that optimize space utilization and
environmental factors like sunlight and airflow.
3. Financial Market Analysis
Genetic algorithms have found a niche in the financial sector
for portfolio optimization and algorithmic trading. By simulating
numerous investment scenarios, GAs help in identifying the
best allocation of assets that maximizes returns and minimizes
risks. Moreover, they are used in trading algorithms to predict
market movements and execute trades at optimal times.
4. Game Development and AI
In game development, genetic programming has been
employed to evolve behaviors for non-player characters (NPCs),
making them more challenging and realistic opponents. For
example, GAs have been used to develop strategic behaviors in
games like chess and Go, where the vast number of possible
moves makes brute force approaches impractical.
5. Machine Learning and Data Mining
GAs are increasingly integrated into machine learning
workflows, particularly in feature selection and model
optimization. By selecting the most relevant features from large
datasets, GAs improve the efficiency and accuracy of predictive
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models. Additionally, they are used to optimize neural network
architectures in deep learning without human intervention.
6. Robotics and Autonomous Vehicles
In robotics, genetic programming can automate the design of
control systems for autonomous robots, enabling them to adapt
to new environments and perform complex tasks without
explicit programming. This approach has been instrumental in
developing autonomous vehicles, where GAs optimize driving
strategies based on real-time data.

8GENETIC ALGORITHM: MODELS OF EVOLUTION

A genetic algorithm is a search type that was totally

inspired by the theory of Charles Darwin, the theory of
natural evolution-it covers the process of selection
naturally where the individuals fit get selected for
reproduction for the production of offspring to the next
generation.
Genetic algorithm covers the Darwinian model of
evolution which states that natural selection can be
possible as well as genetic mutation variation through
reallocating and process of mutation.
However there are other models of evolution and lifetime
adaption, they are as follows :
1. Lamarckian model and
2. Baldwinian model.

LAMARCKIAN MODEL :
The Lamarckian model defines that the traits of an
individual get his or her lifetime can also be passed to its
further offspring. It was then named after the French
biologist – Jean Baptiste Lamarck. Though natural biology
has excluded or disregarded the Lamarckism theory we
know that only the information in a particular genotype
can be transmitted.
But from a computation point of view, it has also been
stated that the Lamarckian model also gives better results
for some kinds of problems.

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In the Lamarckian model, there is a local search operator
which examines the neighbors getting new traits, and if a
good chromosome is found then it itself becomes the
offspring.

BALDWINIAN MODEL :
It was named after James Mark Baldwin in 189. It was an
intermediate idea. As per the Baldwininan model, a
chromosome can have the superficiality of encoding
learning beneficial behavior types. Unlike the Lamarckian
model, here it does not transmit the traits acquired to the
next generation, and neither it completely ignores the
traits acquired by the Darwinian model.
The Baldwinian model out of these extremes of two has
the tendency of such kind of an individual for acquiring
traits that are encoded except the traits of themselves.
In the Baldwinian model, there is a local search operator
that exists that examines the neighbor on acquiring new
traits, and if a good chromosome is found at the step, it
then assigns only the improved fitness factor to the
particular chromosomes and it does not modify the
chromosome itself. The ability on acquiring the trait
though it does not get passed directly on to the fur=ture
generations.
Therefore we often see a genetic algorithm with local
search which is similar to the Memetic algorithm. Hence,
one always must choose the correct and suitable models,
either Lamarckian or Baldwinian to get decided what the
individuals generate after a normal local search.
Therefore, it generally follows the non-Darwinian theory or
methodology of computing evolutionary procedures in
machine learning for the guide of new individuals.
The networks which are neurally generated from
Lamarckian theory states that they are small but require
less time and to get designed. Thus, from every point of
view, the Lamarckian operator gets improved by the
fitness functions if used in early agreements. It was due to
some part which gets passed to the next individuals which
are fit and therefore the Lamarckian model is more
suitable.

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Parallelizing GA
Parallelizing a Genetic Algorithm (GA) can significantly improve its performance by
spreading the computational workload across multiple processors. Here's a high-level
overview of the steps involved in parallelizing a GA:

1. Divide the Population: Split the population of individuals into sub-populations, which
can be processed in parallel. Each sub-population will undergo the selection,
crossover, and mutation processes independently.
2. Evaluate Fitness: Evaluate the fitness of individuals within each sub-population using
parallel processors. This step is often the most computationally intensive and benefits
greatly from parallelization.
3. Migration: Periodically, exchange individuals between sub-populations. This helps
maintain genetic diversity and prevents sub-populations from converging to local
optima. There are different migration strategies, such as ring topology, fully connected
topology, and others.
4. Master-Slave Model: Alternatively, use a master-slave model where a master process
handles the population and distributes tasks (like fitness evaluation) to slave processes.
The master gathers results and performs genetic operations.
5. Synchronization: Ensure that the parallel processes are synchronized at key points in
the algorithm, such as after each generation. This isn't always necessary and depends
on the specific implementation.
6. Implementation Tools: Use parallel computing libraries or frameworks such as MPI
(Message Passing Interface), OpenMP, or even GPU-based libraries like CUDA for
implementation

Different search methods for Induction

Induction is a vital concept in various fields, especially in machine
learning and logic. Here are some different search methods for
induction:

1. Greedy Search
Greedy search is a straightforward search method that builds up
the solution piece by piece, always choosing the next piece that
offers the most immediate benefit.
2. Beam Search
Beam search is an optimization of the greedy search that keeps
track of multiple top candidates at each step, balancing between
diversity and best score among the candidates.
3. Random Search

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 As the name suggests, random search involves randomly
selecting possible solutions and evaluating them. It's less
structured but can be useful for exploring large, unknown spaces.
4. Genetic Algorithms
Inspired by the process of natural selection, genetic algorithms
are used to find approximate solutions by mimicking processes
like mutation, crossover, and natural selection.

5. Simulated Annealing

Simulated annealing is a probabilistic technique that searches for

a global optimum in a large solution space. It simulates the
physical process of heating a material and then slowly lowering
the temperature to decrease defects, thus minimizing the system's
energy.

6. Search Light Induction

This method involves iteratively testing hypotheses and adjusting

the search "light" to hone in on the most promising areas of the
search space.

7. Monty Carlo Tree Search (MCTS)

MCTS is a heuristic search algorithm often used in game playing

and decision processes, balancing exploration and exploitation
by randomly sampling the search space in a controlled manner.
8. Brute-force Search
Although computationally expensive, brute-force search tries all
possible combinations or solutions to find the best one. It's
thorough but typically impractical for large problem spaces.
9. A Search Algorithm*
A* is a popular algorithm in pathfinding and graph traversal,
which combines the benefits of both Dijkstra's algorithm and
greedy best-first search to find the most efficient path.
10. Probabilistic Search

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 This method weights the probability of success in certain paths and
selects the paths with higher probabilities, often used when dealing
with uncertainty and incomplete information.

Applications
These methods are highly applicable in various domains like
machine learning, artificial intelligence, game development, and
more. Understanding and choosing the right one can significantly
impact the efficiency and effectiveness of the induction process.

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