Code covered by the BSD License

### Highlights fromNSGA - II: A multi-objective optimization algorithm

from NSGA - II: A multi-objective optimization algorithm by Aravind Seshadri
A function for multi-objective optimization using evolutionary algorithms

initialize_variables

## function f = initialize_variables(N, M, V, min_tange, max_range)

This function initializes the chromosomes. Each chromosome has the following at this stage * set of decision variables * objective function values

where, N - Population size M - Number of objective functions V - Number of decision variables min_range - A vector of decimal values which indicate the minimum value for each decision variable. max_range - Vector of maximum possible values for decision variables.

```min = min_range;
max = max_range;

% K is the total number of array elements. For ease of computation decision
% variables and objective functions are concatenated to form a single
% array. For crossover and mutation only the decision variables are used
% while for selection, only the objective variable are utilized.

K = M + V;
```

## Initialize each chromosome

For each chromosome perform the following (N is the population size)

```for i = 1 : N
% Initialize the decision variables based on the minimum and maximum
% possible values. V is the number of decision variable. A random
% number is picked between the minimum and maximum possible values for
% the each decision variable.
for j = 1 : V
f(i,j) = min(j) + (max(j) - min(j))*rand(1);
end
% For ease of computation and handling data the chromosome also has the
% vlaue of the objective function concatenated at the end. The elements
% V + 1 to K has the objective function valued.
% The function evaluate_objective takes one chromosome at a time,
% infact only the decision variables are passed to the function along
% with information about the number of objective functions which are
% processed and returns the value for the objective functions. These
% values are now stored at the end of the chromosome itself.
f(i,V + 1: K) = evaluate_objective(f(i,:), M, V);
end
```