Evolutionary Algorithms

‫مهندس‬‫شرفی‬
‫مصنوعی‬‫هوش‬ ‫دکتری‬ ‫دانشجوی‬(‫تحقیقات‬ ‫و‬ ‫علوم‬ ‫واحد‬ ‫آزاد‬ ‫دانشگاه‬)
‫تکاملی‬ ‫پردازش‬(‫سازی‬ ‫بهینه‬)

Nature-Inspired Optimization Algorithms
Cat Swarm Optimization
Cuckoo Optimization Algorithm
Grey Wolf Optimization
Genetic Algorithm
Differential Evolution

2015 Workshop on Soft Computing and Big Data, ECE Dept. of K. N. Toosi University of Technology, Tehran.

Search space
x
y
(x,y) = (9.039, 8.668)
f(x,y) = -8.5547
9.039 8.668

7 .425 0.118
2.324 1.0
4.5 8.6
1.257 6.364
1.23 5.3
2.34 9.1
9.039 8.668
x y
( x* , y* )
. . .
Population

Population- based
Evolutionary Computation
Evolutionary Algorithms
RandomSwarm intelligence

Swarm intelligence

Genetic Algorithm

Genetic Algorithm Cycle

Genetic Algorithm

The first paper based on cats’ behavior problems was
published in 2006 by Chu and Tsai to resolve continuous
optimization. They investigated cats’ behavior in two
modes, namely seeking and tracing modes. Cats are
always categorized into one of the aforementioned modes.
That what ratio of all cats (mixture ratio) exists in each
mode is considered as a crucial parameter which can be a
subject of discussion.
Seeking mode(Exploration)
Tracing mode(Exploitation)
MixtureRate (MR)

The seeking mode process
SMP(Seeking Memory Pool)
SRD(Seeking Range of the selected Dimension)
CDC(Counts of Dimension to Change)
SPC(Self-Position Considering)

The seeking mode process

The tracing mode process
Global best
Velocity
New Position
Current Position
acceleration
coefficient
best
position
velocity
inertia
weight
Random
[0,1]
position
resultant

The tracing mode process

pseudo code of cat swarm optimization algorithm

Grey wolf (Canis lupus) belongs to Canidae family
Grey wolves mostly prefer to live in a pack
The Group size is 5–12 on average
Hierarchy of grey wolf (dominance decreases from top down)

wolvesalphas
The leaders are a male and a female, called alphas. The
alpha is mostly responsible for making decisions about
hunting, sleeping place, time to wake, and so on.
The alpha’s decisions are dictated to the pack.
Interestingly, the alpha is not necessarily the strongest
member of the pack but the best in terms of managing the
pack. This shows that the organization and discipline of a
pack is much more important than its strength.

Beta wolves
The second level in the hierarchy of grey wolves is beta. The
betas are subordinate wolves that help the alpha in
decision-making or other pack activities.
The beta wolf can be either male or female, and he/she is
probably the best candidate to be the alpha in case one of
the alpha wolves passes away or becomes very old.
The beta wolf should respect the alpha, but commands the
other lower-level wolves as well. It plays the role of an
advisor to the alpha and discipliner for the pack. The beta
reinforces the alpha’s commands throughout the pack and
gives feedback to the alpha

wolvesomega
The lowest ranking grey wolf is omega. The omega plays the
role of scapegoat. Omega wolves always have to submit to
all the other dominant wolves.
They are the last wolves that are allowed to eat.
It may seem the omega is not an important individual in the
pack, but it has been observed that the whole pack face
internal fighting and problems in case of losing the omega.
This is due to the venting of violence and frustration of all
wolves by the omega(s). This assists satisfying the entire
pack and maintaining the dominance structure. In some
cases the omega is also the babysitters in the pack.

wolvesDelta
If a wolf is not an alpha, beta, or omega, he/she is called
subordinate (or delta in some references). Delta wolves have
to submit to alphas and betas, but they dominate the
omega.
Scouts, sentinels, elders, hunters, and caretakers belong to
this category.
Scouts are responsible for watching the boundaries of the territory and
warning the pack in case of any danger. Sentinels protect and guarantee
the safety of the pack. Elders are the experienced wolves who used to be
alpha or beta. Hunters help the alphas and betas when hunting prey
and providing food for the pack. Finally, the caretakers are responsible
for caring for the weak, ill, and wounded wolves in the pack.

The main phases of grey wolf hunting
are as follows:
Tracking, chasing, and approaching the prey.
Pursuing, encircling, and harassing the prey until it
stops moving.
Attack towards the prey.

Hunting behavior of grey wolves: (A) chasing, approaching,
and tracking prey

Hunting behavior of grey wolves: (B–D) pursuiting,
harassing, and encircling

Hunting behavior of grey wolves: (E) stationary situation
and attack

Mathematical model and algorithm
Social hierarchy
In order to mathematically model the social hierarchy of
wolves when designing GWO, we consider the fittest
solution as the alpha (α). Consequently, the second and
third best solutions are named beta (β) and delta ( )
respectively. The rest of the candidate solutions are
assumed to be omega (ω). In the GWO algorithm the
hunting (optimization) is guided by α, β, and . The ω
wolves follow these three wolves.

2D and 3D position vectors and their possible next locations

Hunting
Grey wolves have the ability to recognize the location of prey
and encircle them. The hunt is usually guided by the alpha.
The beta and delta might also participate in hunting
occasionally. However, in an abstract search space we have
no idea about the location of the optimum (prey). In order to
mathematically simulate the hunting behavior of grey
wolves, we suppose that the alpha (best candidate solution)
beta, and delta have better knowledge about the potential
location of prey. Therefore, we save the first three best
solutions obtained so far and oblige the other search agents
(including the omegas) to update their positions according to
the position of the best search agents.

Position updading in GWO

The following formulas are proposed in this regard.

Attacking prey (exploitation)

Search for prey (exploration)

There are other birds that
dispense with every convention of
home making and parenthood,
and resort to cunning to raise
their families
These are the “brood parasites,”
birds which never build their own
nests and instead lay their eggs in
the nest of another species,
leaving those parents to care for
its young

The cuckoo is the best known brood parasite, an expert in
the art of cruel deception. Its strategy involves stealth,
surprise and speed.
The mother removes one egg laid by the host mother, lays
her own and flies off with the host egg in her bill. The
whole process takes barely ten seconds.

Cuckoos parasitize the nests of a large variety of bird
species and carefully mimic the color and pattern of their
own eggs to match that of their hosts.
Many bird species learn to recognize a cuckoo egg dumped
in their own nest and either throw out the strange egg or
desert the nest to start afresh.
So the cuckoo constantly tries to improve its mimicry of its
hosts’ eggs, while the hosts try to find ways of detecting the
parasitic egg
For the cuckoos suitable habitat provides a source of food
(principally insects and especially caterpillars) and a place
to breed, for brood parasites the need is for suitable
habitat for the host species.

Like other evolutionary algorithms, the proposed
algorithm starts with an initial population of cuckoos.
These initial cuckoos have some eggs to lay in some host
birds’ nests
Some of these eggs which are more similar to the host
bird’s eggs have the opportunity to grow up and become a
mature cuckoo
Other eggs are detected by host birds and are killed.
After remained eggs grow and turn into a mature cuckoo,
they make some societies. Each society has its habitat
region to live in. The best habitat of all societies will be
the destination for the cuckoos in other societies. Then
they immigrate toward this best habitat.

Generating initial cuckoo habitat
In order to solve an optimization problem, it’s necessary
that the values of problem variables be formed as an
array. In GA and PSO terminologies this array is called
“Chromosome” and “Particle Position”, respectively. But
here in Cuckoo Optimization Algorithm(COA) it is called
“habitat”.
In nature, each cuckoo lays from 5 to 20 eggs.
These values are used as the upper and lower limits of
egg dedication to each cuckoo at different iterations

maximum range will be called “Egg Laying Radius (ELR)”
In an optimization problem with upper limit of variable
High and lower limit of variable Low for variables, each
cuckoo has an egg laying radius (ELR) which is
proportional to the total number of eggs, number of
current cuckoo’s eggs and also variable limits of variable
High and variable Low. So ELR is defined as:

Random egg laying in ELR, central red star is the initial
habitat of the cuckoo with 5 eggs; pink stars are the eggs’
new nest

Each cuckoo starts laying eggs randomly in some other
host birds’ nests within her ELR.
After all cuckoos’ eggs are laid in host birds’ nests, some
of them that are less similar to host birds’ own eggs, are
detected by host birds and though are thrown out of the
nest. So after egg laying process,
p% of all eggs (usually 10%)
Rest of the eggs grow in host nests, hatch and are fed by
host birds.

Another interesting point about laid cuckoo eggs is that
only one egg in a nest has the chance to grow. This is
because when cuckoo egg hatches and the chicks come out,
she throws the host bird’s own eggs out of the nest. In case
that host bird’s eggs hatch earlier and cuckoo egg hatches
later, cuckoo’s chick eats most of the food host bird brings
to the nest (because of her 3 times bigger body, she pushes
other chicks and eats more). After couple of days the host
bird’s own chicks die from hunger and only cuckoo chick
remains in the nest

Immigration of cuckoos
When young cuckoos grow and become mature, they live in their own
area and society for sometime. But when the time for egg laying
approaches they immigrate to new and better habitats with more
similarity of eggs to host birds and also with more food for new
youngsters.

When mature cuckoos live in all over the environment it’s
difficult to recognize which cuckoo belongs to which group.
To solve this problem, the grouping of cuckoos is done with
K-means clustering method (k of 3–5 seems to be sufficient
in simulations).
When all cuckoos immigrated toward goal point and new
habitats were specified, each mature cuckoo is given some
eggs. Then considering the number of eggs dedicated to
each bird, an ELR is calculated for each cuckoo. Afterward
new egg laying process restarts.

Eliminating cuckoos in worst habitats
Due to the fact that there is always equilibrium in birds’
population so a number of Nmax controls and limits the
maximum number of live cuckoos in the environment. This
balance is because of food limitations, being killed by
predators and also inability to find proper nest for eggs. In
the modeling proposed here in this paper, only those Nmax
number of cuckoos survive that have better profit values,
others demise.
Convergence of more than 95% of all cuckoos to the same
habitat puts an end to Cuckoo Optimization Algorithm
(COA).

Flowchart of Cuckoo Optimization Algorithm

Pseudo-code for Cuckoo Optimization Algorithm

𝐺𝑟𝑖𝑒𝑤𝑎𝑛𝑘(𝒏 = 𝟐𝟎𝟎)

Evolutionary Algorithms

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