Experiment No:-

TITLE:-Study of MATLAB.

AIM:-Study of Genetic Algorithm application used in MATLAB.

REQUIRED S/W:- MATLAB 7.5.

THERORY:-

1. MATLAB:-

MATLAB is a high-performance language for technical computing. It integratescomputation, visualization, and programming in an easy-to-use environmentwhere problems and solutions are expressed in familiar mathematical notation.

1.1 Typical uses include-

Math and computation Algorithm development Data acquisition Modeling, simulation, and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development, including graphical user interfacebuilding

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technicalcomputing problems, especially those with matrix and vector formulations,in a fraction of the time it would take to write a program in a scalar noninteractivelanguage such as C or Fortran.The name MATLAB stands for matrix laboratory. MATLABwas originally written to provide easy access to matrix software developedby the LINPACK and EISPACK projects. Today, MATLAB engines incorporate theLAPACK and BLAS libraries, embedding the state of the art in software formatrix computation. MATLAB has evolved over a period of years with input from many users.In university environments, it is the standard instructional tool for introductoryand advanced courses in mathematics, engineering, and science. In industry,MATLAB is the tool of choice for high-productivity research, development,and analysis. MATLAB features a family of add-on application-specific solutions called toolboxes.Very important to most users of MATLAB, toolboxes allow you to learn and apply specializedtechnology. Toolboxes are comprehensive collections of MATLAB functions (M-files)that extend the MATLAB environment to solve particular classes of problems.Areas in which toolboxes are available include signal processing, controlsystems, neural networks, fuzzy logic, wavelets, simulation, and many others.

1.2 The MATLAB System:-The MATLAB system consists of these main parts:

I) Desktop Tools and Development Environment-This is the set of tools and facilities that help you use MATLAB functions and

files. Many of these tools are graphical user interfaces. It includes the MATLAB desktop and Command Window, a command history, an editor and debugger, a code analyzer and other reports, and browsers for viewing help, the workspace, files, and the search path.

II) The MATLAB Mathematical Function Library-This is a vast collection of computational algorithms ranging from elementary

functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

III) The MATLAB Language-This is a high-level matrix/array language with control flow statements, functions,

data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create large and complex application programs.

IV) Graphics-MATLAB has extensive facilities for displaying vectors and matrices as graphs,

as well as annotating and printing these graphs. It includes high-level functions for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It also includes low-level functions that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your MATLAB applications.

1.3 MATLAB Documentation-MATLAB provides extensive documentation, in both printable and HTML format, to

help you learn about and use all of its features. If you are a new user, start with this Getting Started book. It covers all the primar MATLAB features at a high level, including many examples.

To view the online documentation, select MATLAB Help from the Help menu in MATLAB. Online help appears in the Help browser, providing task-oriented and reference information about MATLAB features. For more information about using the Help browser, including typographical conventions used in the documentation.

1.3.1 The MATLAB documentation is organized into these main topics:

Desktop Tools and Development Environment — Startup and shutdown, the desktop, and other tools that help you use MATLAB.

Mathematics —Mathematical operations. DataAnalysis — Data analysis, including data fitting, Fourier analysis,and time-

series tools. Programming —The MATLAB language and how to develop MATLAB

applications. Graphics —Tools and techniques for plotting, graph annotation, printing, and

programming with Handle Graphics 3-D. Visualization — Visualizing surface and volume data, transparency,and viewing

and lighting techniques. CreatingGraphical User Interfaces — GUI-building tools and how to

writecallback functions External. Interfaces — MEX-files, the MATLAB engine, and interfacingto Java, COM,

and the serial port.

1.3.2 MATLAB also includes reference documentation forall MATLAB functions:

Functions — By Category —Lists all MATLAB functions grouped into categories.

Handle GraphicsProperty Browser — Provides easy access to descriptions ofgraphics object properties.

Cand Fortran API Reference — Covers those functionsused by the MATLAB external interfaces, providing information on syntax inthe calling language, description, arguments, return values, and examples.

1.3.3 The MATLAB onlinedocumentation also includes :

Examples —An index of examples included in the documentation. ReleaseNotes — New features, compatibility considerations, and bugreports.`

Printable Documentation —PDF versions of the documentation suitable for printing.

In addition to the documentation, you can access demos from the Helpbrowser by clicking the Demos tab. Run demos tolearn about key functionality of Math Works products and tools.

2. Genetic Algorithm-The genetic algorithm is a method for solving both constrained and

unconstrainedoptimization problems that is based on natural selection, the process thatdrives biological evolution. The genetic algorithm repeatedly modifies a populationof individual solutions. At each step, the genetic algorithm selects individualsat random from the current

population to be parents and uses them to producethe children for the next generation. Over successive generations, the population"evolves" toward an optimal solution. You can apply the genetic algorithmto solve a variety of optimization problems that are not well suited for standardoptimization algorithms, including problems in which the objective functionis discontinuous, nondifferentiable, stochastic, or highly nonlinear.

The genetic algorithm uses three main types of rules at each step tocreate the next generation from the current population-

Selection rules select the individuals,called parents, that contribute to the population atthe next generation.

Crossover rules combine two parents toform children for the next generation. Mutation rules apply random changes toindividual parents to form children.

The genetic algorithm differs from a classical, derivative-based, optimizationalgorithm

2.1 Calling the Function ga at the Command Line-

To use the genetic algorithm at the command line, call the genetic algorithmfunction ga with the syntax

[xfval] = ga(@fitnessfun, nvars, options)

Where @fitnessfun is a handle to the fitnessfunction. nvars is the number of independent variablesfor the fitness function. options is a structure containing optionsfor the genetic algorithm.If you do not pass in

this argument, ga usesits default options.The results are given

byx — Point at which the final valueis attained fval — Final value of the fitnessfunction

Using the function ga is convenient if you wantto Return results directly to the MATLAB workspace Run the genetic algorithm multiple times with different options,by calling ga from an M-

file

Figure 1 : Opening Window of Matlab

Figure 2 :Open Demos-Genetic Algorithm-Custom data type optimization

Figure 3 :Opening Coding window of example

3. Coding :-

load('usborder.mat','x','y','xx','yy');plot(x,y,'color','green'); hold on;

cities = 10;locations = zeros(cities,2);n = 1;while (n <= cities)xp = rand*1.5;yp = rand;ifinpolygon(xp,yp,xx,yy)locations(n,1) = xp;locations(n,2) = yp; n = n+1;endendplot(locations(:,1),locations(:,2),'mh');

distances = zeros(cities);for count1=1:cities,for count2=1:count1,x1 = locations(count1,1); y1 = locations(count1,2);x2 = locations(count2,1); y2 = locations(count2,2);distances(count1,count2)=sqrt((x1-x2)^2+(y1-y2)^2);distances(count2,count1)=distances(count1,count2);end;

end;

typecreate_permutations.mtypecrossover_permutation.mtypemutate_permutation.mtypetraveling_salesman_fitness.mFitnessFcn = @(x) traveling_salesman_fitness(x,distances);typetraveling_salesman_plot.m

my_plot = @(options,state,flag) traveling_salesman_plot(options, ...state,flag,locations);

options = gaoptimset('PopulationType', 'custom','PopInitRange', ... [1;cities]);

options = gaoptimset(options,'CreationFcn',@create_permutations, ... 'CrossoverFcn',@crossover_permutation, ... 'MutationFcn',@mutate_permutation, ... 'PlotFcn', my_plot, ... 'Generations',500,'PopulationSize',60, ... 'StallGenLimit',200,'Vectorized','on');

numberOfVariables = cities;[x,fval,reason,output] = ga(FitnessFcn,numberOfVariables,options)

displayEndOfDemoMessage(mfilename)

Figure 4 :Coding of Program

Figure 5 :After running it shows the map of Program

Figure 6 :Output Window