ga

Syntax

x = ga(@func,nVars)

x = ga(@func,nVars,A,b)

x = ga(@func,nVars,A,b,Aeq,beq)

x = ga(@func,nVars,A,b,Aeq,beq,lb,ub)

x = ga(@func,nVars,A,b,Aeq,beq,lb,ub,nonlcon)

x = ga(@func,nVars,A,b,Aeq,beq,lb,ub,nonlcon,options)

x = ga(@func,nVars,A,b,Aeq,beq,dv)

x = ga(@func,nVars,A,b,Aeq,beq,dv,nonlcon)

x = ga(@func,nVars,A,b,Aeq,beq,dv,nonlcon,options)

[x,fval,info,output] = ga(...)

Inputs

func

The function to minimize.

nVars

The number of variables in the domain.

A

A matrix used to compute A*x for inequality constraints.

Use [ ] if unneeded.

b

The upper bound of the inequality constraints A*x<=b.

Use [ ] if unneeded.

Aeq

A matrix used to compute Aeq*x for equality constraints.

Use [ ] if unneeded.

beq

The upper bound of the equality constraints Aeq*x=beq.

Use [ ] if unneeded.

lb

The continuous design variable lower bounds.

Use [ ] if unbounded. Support for this option is limited. See Comments.

ub

The continuous design variable upper bounds.

Use [ ] if unbounded. Support for this option is limited. See Comments.

dv

The discrete design variable value options.

Each element of the cell array contains a vector of possible values for each of the nVars design variable.

Type: cell

Dimension: vector

nonlcon

The nonlinear constraints function.

The function signature is as follows:

function [c, ceq] = ConFunc(x)

, where

c and ceq contain inequality and equality contraints, respectively. The ceq output can be omitted if it is empty.

Inequality constraints are assumed to have upper bounds of 0, and equality constraints are equal to 0. For constraints of the form g(x) < b, where b ~= 0, the recommended best practice is to write the constraint as (g(x) - b) / abs(b) < 0.

Use [ ] if unused and the options argument is needed.

options

A struct containing option settings.

See gaoptimset for details.

Outputs

x

The location of the function minimum.

fval

The minimum of the function.

info

The convergence status flag.

info = 3

Converged with a constraint violation within tolCon.

info = 1

Function value converged to within tolFun.

info = 0

Reached maximum number of iterations or function calls.

info = -2

The function did not converge.

output

A struct containing generation details. The members are as follows:

generations

The number of generations.

xgen

The candidate solution for each generation.

fvalgen

The objective function value for each iteration.

congen

The constraint values for each iteration. The columns contain the constraint function values in the following order: linear inequality contraints, linear equality constraints, nonlinear inequality contraints, nonlinear equality constraints.

Example 1

function obj = ObjFunc(x)
    obj = 2*(x(1)-3)^2 - 5*(x(1)-3)*(x(2)-2) + 4*(x(2)-2)^2 + 6;
end

n = 2;
A = [-1, -4];
b = [-27];
lb = [-10, -10];
ub = [10, 10];
[x,fval] = ga(@ObjFunc,2,A,b,[],[],lb,ub)

x = [Matrix] 1 x 2
6.93843  4.98382
fval = 13.8773516

function obj = ObjFunc(x,offset)
    obj = 2*(x(1)-3)^2 - 5*(x(1)-3)*(x(2)-2) + 4*(x(2)-2)^2 + offset;
end
handle = @(x) ObjFunc(x,7);
[x,fval] = ga(handle,2,A,b,[],[],lb,ub)

x = [Matrix] 1 x 2
6.88378  4.99563
fval = 14.8908606

function obj = ObjFunc(x)

function obj = ObjFunc(x)
	obj = 8*x(1) + 11*x(2) + 6*x(3) + 4*x(4);
	obj = -obj;    % reframe as a minimization problem
end

% cost coefficients and limit
A = [5, 7, 4, 3];
b = 14;

% 0-1 knapsack problem values
dv = {};
dv{1,1} = [0,1];
dv{1,2} = [0,1];
dv{1,3} = [0,1];
dv{1,4} = [0,1];

options = gaoptimset('TolCon', 0.1, 'Seed', 2013);

[x,value,info] = ga(@ObjFunc,4,A,b,[],[],dv,[],options);
x
value = -value
info
cost = A * x'

x = [Matrix] 1 x 4
0  1  1  1
value = 21
info = 1
cost = 14

Comments

Options are specified with gaoptimset.

The initial design variable values can be specified with a vector using the InitialPopulation option.

The design variable ranges can be specified as a 2xN matrix using the PopInitRange option.

Unbounded limits design variable limits are not fully supported and are set to -1000 and 1000. Use of large limits is discouraged due to the size of the search area.

To pass additional parameters to a function argument, use an anonymous function.