Essay: Artificial intelligence techniques

Introduction
In these days, Artificial intelligence (AI) techniques have become widely used in power system problems. AI techniques work in off line and have the ability to give better results. The increase in size and complexity of electric power systems along with increase in power demand makes it a great need to use AI techniques. These techniques are applied widely in many fields such as planning, operation, and control. The controllers are designed based on AI techniques have proved sufficient efficiency and adaptability. From time to time, show a new way of AI techniques. There are different types of AI techniques used in power system problems such as GA, PSO, BFOA, Fuzzy Logic Controllers, ACO, ABC, ICA, BIA and GSA. This chapter will concentrate on ICA, BIA and GSA which are proposed in this thesis.
4.2 Overview of Imperialist Competitive Algorithm
The imperialist competitive algorithm (ICA) is constructed on idea of the imperialistic competition process. The countries in the world are the initial population of the algorithm at the start and each country represent an individual population. The imperialists are represented by the best countries in the population and the colonies of these imperialists are formed by the rest of countries. The colonies are distributed between the imperialists based on their fitness and moves to join their relevant imperialist country. The fitness of an empire equal the fitness of imperialist country plus a percentage of mean fitness of its colonies. After this the imperialistic competition starts between all empires. If the fitness of an empire not able to increase in this competition, this empire will be eliminated. The fitness of powerful empires increase and the fitness of weaker ones decrease gradually in the imperialistic competition. The decrease in fitness of weak empires makes them lose their power and at the end they will collapse. The movement of colonies and the collapse mechanism are the main idea to cause all the countries to converge to one empire in the world. All the other countries in this new ideal world are colonies of that empire. The position and fitness of colonies in this new ideal world the same as the imperialist. The steps of ICA will be illustrated in the following sections.
4.2.1 Initial empires generation
The optimal solution in terms of problem variables is the goal of optimization. These variables which need to be optimized are formed in an array with dimension 1×Nvar. Where Nvar is the optimization problem dimension. This array is called country and defined by,
(4.1)
The values of the country variables are represented as floating point numbers. The fitness of a country is a function in the variables and evaluated by,
(4.2)
In the start of optimization the initial population of size Npop is defined and the most powerful countries Nimp is selected to form the empires. The colonies Ncol which belongs to an empire are the remaining of the population. Then there are two types of countries are named imperialist and colony. By dividing the colonies between imperialists based on their fitness the initial empires are formed. This initial colonies number of an empire proportionate directly to its fitness. The colonies are divided between imperialists proportionally. The normalized fitness of an imperialist is defined by
(4.3)
Where
Fn : Normalized fitness of all imperialists
fn : Fitness of nth imperialist
Then for each imperialist the normalized power of is calculated by
(4.4)
Equation (4.4) shows that the normalized power of an imperialist is the container of colonies that belong to that imperialist. The initial number of colonies of an empire is selected randomly by
(4.5)
Where
Ncol : Number of all colonies
4.2.2 Moving mechanism of the colonies toward the imperialist
The imperialists countries improve their colonies by moving of colony toward the imperialist with x units as shown in Figure 4.1. Where x is a random variable with uniform distribution and defined by
(4.6)
Where
: A number > 1 to make the colonies closer to the imperialist state from both sides
d : Distance between imperialist and colony
Figure 4.1 Colonies moving to their relevant imperialist.
A random deviation θ to the direction of movement is added to search different points around the imperialist. The new direction is shown in Figure 4.2. The random deviation θ is calculated by the following uniform distribution function
(4.7)
Where
: A limit angle that adjust the deviation from the original direction
Figure 4.2 Colonies moving to their relevant imperialist with randomly deviated direction.
If the colony moved toward the imperialist and its fitness decreased in the new position, the imperialist position and colony position will Share with some. The total power of an empire is a function in the fitness of imperialist country and its colonies, defined by
(4.8)
Where
: A positive number < 1
4.2.3 Collapse mechanism
This mechanism is carried by the competition between the imperialistic. In the collapse mechanism the fitness of weaker empires decrease and the fitness of more powerful ones increase. The competition start by finding the possession probability of each empire to the colonies of the weaker empire based on its total fitness. The normalized total fitness of nth empire is calculated by
(4.9)
Hence the possession probability of each empire is presented by
(4.10)
A vector P is formed to divide the mentioned colonies between empires based on the possession probability of them, , then a vector R whose elements are uniformly distributed random numbers is formed with the same size as P,
.
Where
(4.11)
Therefore, a vector D is formed by simply subtracting R from P.
(4.12)
By referring to the vector D, the mentioned colonies is handed to the empire with maximum relevant index in D . after the weaker empires collapse and from the most powerful one, all the colonies will be under the control of this most powerful empire. All the colonies and imperialist will have the same positions and same fitness in this ideal new world. At achieving this condition the imperialistic competition stop and the algorithm ends. Figure 4.3 show the flowchart of the ICA.