crossover_ga_binary

Arguments

Indiv1

A string

the first individual (here a binary code) to be crossed-over.

Indiv2

A string

the second individual to be crossed-over.

param

a list of parameters.

• "binary_length": an integer, the length of the binary code (default 8).

• "multi_cross": a boolean. If %T then we allow several cuts in the binary code (default %F).

• "multi_cross_nb": an integer, the number of cuts in the binary code. Only used when multi_cross is set to %T (default 2).

Crossed_Indiv1

A string

The first individual obtained by the cross-over function.

Crossed_Indiv2

A string

The second individual obtained by the cross-over function.

mix

A vector of integers

The positions the crossover occurred.

Description

This function implements a classical binary cross-over.

crossover_ga_binary(Indiv1, Indiv2) generates the crossover between Indiv1 and Indiv2 by merging the characters from each string.

A position i is chosen randomly between 1 and the length of the binary code.

Then Indiv1 and Indiv2 are split in two parts: the first i characters (the head), and the remaining characters (the tail). The crossover swaps the tails of the binary codes.

The following schema presents the crossover:

Indiv1=[H1 T1]
Indiv2=[H2 T2]
Crossed_Indiv1=[H1 T2]
Crossed_Indiv2=[H2 T1]

The behaviour of the function can be modified with the use of param:

binary_length

changes the minimal length of the binary code, by default 8 characters.

Binary code for Indiv1 or Indiv2 of lower length are zero padded to the right to be of binary_length length or max([length(Indiv1), length(Indiv2)]) whichever is greater.

multi_cross

if set to %T multiple crossovers can happen (default %F)

multi_cross_nb

the number of locations for crossovers. (default 2 if multi_cross is set to %T, 1 otherwise)

Random number generator

crossover_ga_binary is based on grand for generating the random samples. Use grand("setsd", seed) to change the seed for crossover_ga_binary.

seed = getdate("s");
grand("setsd", seed); //sets the seed to current date

seed = 0;
grand("setsd", seed); //sets the seed to default value

Examples

A = "11100000"
B = "00011111"
[A_crossed, B_crossed, mix] = crossover_ga_binary(A, B)

C = dec2bin(2^16 - 1, 16)
D = "0"
param = init_param();
param = add_param(param, "binary_length", 16);  // Code of length 16
param = add_param(param, "multi_cross", %T);    // Multiple Crossover
param = add_param(param, "multi_cross_nb", 3);  // Occurs over 3 locations

[C_crossed, D_crossed, mix] = crossover_ga_binary(C, D, param)

See also

• crossover_ga_binary — A crossover function for binary code
• crossover_ga_default — A crossover function for continuous variable functions
• mutation_ga_binary — A function which performs binary mutation
• optim_ga — A flexible genetic algorithm
• grand — Random numbers