MATLAB Examples

# Simple EMOO Problem

This code is an applicatino of EMOO by using Genetic algorithms to solve the following simple constrained problem: Draw the biggest possible circle in a 2D space filled with stars without enclosing any of them.

Author: Wesam ELSHAMY

Electrical Engineering Dept., Cairo University, Egypt

wesamelshamy@ieee.org

## Initializing parameters

```clear; stars = 30; iterations = 500; population = 100; mutation = 0.7; mutation_step = 0.8; grid_size = 10; ```

## Building the stars

```for i = 1:stars for j = 1:2 star(i,j) = rand(1)*grid_size; end end plot(star(:,1),star(:,2),'x') hold on ```

## Cearting initial population

```for i = 1:population for j = 1:2 cit(i,j)= rand(1)*grid_size; end end ```

## Initial Population Fitness Assignment

```for j = 1:population for k = 1:stars d(k) = sqrt((star(k,1)-cit(j,1))^2 + (star(k,2)-cit(j,2))^2); end d(stars+1) = cit(j,1); d(stars+2) = grid_size - cit(j,1); d(stars+3) = cit(j,2); d(stars+4) = grid_size - cit(j,2); d = sort(d); cit(j,3) = d(1); end cit = sortrows(cit,-3); cit(1,:) cit(:,3) = cit(:,3)/cit(1,3); ```
```ans = 2.6457 7.1843 1.7186 ```

## The Iterations

```for i = 1:iterations %--------------- Mating Selection ----------------- cit(:,3) = cit(:,3)/cit(1,3); pool = []; for l = 1:population if rand(1)<cit(l,3),pool=[pool;cit(l,:)];,end end %--------------- Crossover ------------------ s = size(pool,1); if s/2 - round(s/2) ~=0 , pool = pool(1:s-1,:); , s = size(pool,1); , end for m = 1:2:s pool = [ pool ; [pool(m,1) , pool(m+1,2) , 0]]; pool = [ pool ; [pool(m+1,1) , pool(m,2) , 0]]; end %--------------- Mutation ------------------- s = size(pool,1); for m = 1:s if ((rand < mutation) & (pool(m,1) < grid_size - mutation_step)) , pool(m,1)=pool(m,1)+(2*rand - 1)*mutation_step;,end if ((rand < mutation) & (pool(m,2) < grid_size - mutation_step)) , pool(m,2)=pool(m,2)+(2*rand - 1)*mutation_step;,end end %--------------- Invironmental Selection------------ temp = [cit ; pool]; ts = size(temp,1); for j = 1:ts for k = 1:stars d(k) = sqrt((star(k,1)-temp(j,1))^2 + (star(k,2)-temp(j,2))^2); end d(stars+1) = temp(j,1); d(stars+2) = grid_size - temp(j,1); d(stars+3) = temp(j,2); d(stars+4) = grid_size - temp(j,2); d = sort(d); temp(j,3) = d(1); end temp = sortrows(temp,-3); cit = temp(1:population,:); end xc = cit(1,1); yc = cit(1,2); r = cit(1,3); x = (xc-r) : 0.05 : (xc+r); for i = 1:size(x,2) y(i) = yc + sqrt(r^2-(x(i)-xc)^2); end plot (x,y) for i = 1:size(x,2) y(i) = yc - sqrt(r^2-(x(i)-xc)^2); end plot (x,y) hold off ```