Find minimum of function using genetic algorithm
x = ga(fun,nvars)
x = ga(fun,nvars,A,b)
x = ga(fun,nvars,A,b,Aeq,beq)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options)
x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon)
x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon,options)
x = ga(problem)
[x,fval]
= ga(___)
[x,fval,exitflag,output]
= ga(___)
[x,fval,exitflag,output,population,scores]
= ga(___)
finds a local unconstrained minimum, x
= ga(fun
,nvars
)x
, to the objective
function, fun
. nvars
is the dimension (number
of design variables) of fun
.
Passing Extra Parameters (Optimization Toolbox) explains how to pass extra parameters to the objective function and nonlinear constraint functions, if necessary.
subjects the minimization to the constraints defined in x
= ga(fun
,nvars
,A
,b
,Aeq
,beq
,lb
,ub
,nonlcon
)nonlcon
.
The function nonlcon
accepts x
and returns
vectors C
and Ceq
, representing the nonlinear
inequalities and equalities respectively. ga
minimizes the
fun
such that
C(x)
≤ 0
and
Ceq(x) = 0
. (Set lb=[]
and
ub=[]
if no bounds exist.)
or
x
= ga(fun
,nvars
,A
,b
,[],[],lb
,ub
,nonlcon
,IntCon
)
requires that the variables listed in x
= ga(fun
,nvars
,A
,b
,[],[],lb
,ub
,nonlcon
,IntCon
,options
)IntCon
take integer
values.
When there are integer constraints, ga
does not
accept linear or nonlinear equality constraints, only inequality
constraints.
ga
The ps_example.m
file ships with your software. Plot the function.
xi = linspace(6,2,300); yi = linspace(4,4,300); [X,Y] = meshgrid(xi,yi); Z = ps_example([X(:),Y(:)]); Z = reshape(Z,size(X)); surf(X,Y,Z,'MeshStyle','none') colormap 'jet' view(26,43) xlabel('x(1)') ylabel('x(2)') title('ps\_example(x)')
Find the minimum of this function using ga
.
rng default % For reproducibility x = ga(@ps_example,2)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
x = 1×2
4.6793 0.0860
Use the genetic algorithm to minimize the ps_example
function on the region x(1) + x(2) >= 1
and x(2) <= 5 + x(1)
.
First, convert the two inequality constraints to the matrix form A*x <= b
. In other words, get the x
variables on the lefthand side of the inequality, and make both inequalities less than or equal:
x(1) x(2) <= 1
x(1) + x(2) <= 5
A = [1,1; 1,1]; b = [1;5];
Solve the constrained problem using ga
.
rng default % For reproducibility fun = @ps_example; x = ga(fun,2,A,b)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
x = 1×2
0.9991 0.0000
The constraints are satisfied to within the default value of the constraint tolerance, 1e3
. To see this, compute A*x'  b
, which should have negative components.
disp(A*x'  b)
0.0009 5.9991
Use the genetic algorithm to minimize the ps_example
function on the region x(1) + x(2) >= 1
and x(2) == 5 + x(1)
.
First, convert the two constraints to the matrix form A*x <= b
and Aeq*x = beq
. In other words, get the x
variables on the lefthand side of the expressions, and make the inequality into less than or equal form:
x(1) x(2) <= 1
x(1) + x(2) == 5
A = [1 1]; b = 1; Aeq = [1 1]; beq = 5;
Solve the constrained problem using ga
.
rng default % For reproducibility fun = @ps_example; x = ga(fun,2,A,b,Aeq,beq)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
x = 1×2
2.0000 2.9990
Check that the constraints are satisfied to within the default value of ConstraintTolerance
, 1e3
.
disp(A*x'  b)
1.0000e03
disp(Aeq*x'  beq)
9.9997e04
Use the genetic algorithm to minimize the ps_example
function on the region x(1) + x(2) >= 1
and x(2) == 5 + x(1)
. In addition, set bounds 1 <= x(1) <= 6
and 3 <= x(2) <= 8
.
First, convert the two linear constraints to the matrix form A*x <= b
and Aeq*x = beq
. In other words, get the x
variables on the lefthand side of the expressions, and make the inequality into less than or equal form:
x(1) x(2) <= 1
x(1) + x(2) == 5
A = [1 1]; b = 1; Aeq = [1 1]; beq = 5;
Set bounds lb
and ub
.
lb = [1 3]; ub = [6 8];
Solve the constrained problem using ga
.
rng default % For reproducibility fun = @ps_example; x = ga(fun,2,A,b,Aeq,beq,lb,ub)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
x = 1×2
1.0001 5.9992
Check that the linear constraints are satisfied to within the default value of ConstraintTolerance
, 1e3
.
disp(A*x'  b)
5.9993
disp(Aeq*x'  beq)
9.4902e04
ga
Use the genetic algorithm to minimize the ps_example
function on the region $2{\mathit{x}}_{1}^{2}+{\mathit{x}}_{2}^{2}\le 3$ and $$({x}_{1}+1{)}^{2}=({x}_{2}/2{)}^{4}$$.
To do so, first write a function ellipsecons.m
that returns the inequality constraint in the first output, c
, and the equality constraint in the second output, ceq
. Save the file ellipsecons.m
to a folder on your MATLAB® path.
type ellipsecons
function [c,ceq] = ellipsecons(x) c = 2*x(1)^2 + x(2)^2  3; ceq = (x(1)+1)^2  (x(2)/2)^4;
Include a function handle to ellipsecons
as the nonlcon
argument.
nonlcon = @ellipsecons; fun = @ps_example; rng default % For reproducibility x = ga(fun,2,[],[],[],[],[],[],nonlcon)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance and constraint violation is less than options.ConstraintTolerance.
x = 1×2
0.9766 0.0362
Check that the nonlinear constraints are satisfied at x
. The constraints are satisfied when c
≤ 0 and ceq
= 0 to within the default value of ConstraintTolerance
, 1e3
.
[c,ceq] = nonlcon(x)
c = 1.0911
ceq = 5.4645e04
Use the genetic algorithm to minimize the ps_example
function on the region x(1) + x(2) >= 1
and x(2) == 5 + x(1)
using a constraint tolerance that is smaller than the default.
First, convert the two constraints to the matrix form A*x <= b
and Aeq*x = beq
. In other words, get the x
variables on the lefthand side of the expressions, and make the inequality into less than or equal form:
x(1) x(2) <= 1
x(1) + x(2) == 5
A = [1 1]; b = 1; Aeq = [1 1]; beq = 5;
To obtain a more accurate solution, set a constraint tolerance of 1e6
. And to monitor the solver progress, set a plot function.
options = optimoptions('ga','ConstraintTolerance',1e6,'PlotFcn', @gaplotbestf);
Solve the minimization problem.
rng default % For reproducibility fun = @ps_example; x = ga(fun,2,A,b,Aeq,beq,[],[],[],options)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
x = 1×2
2.0000 3.0000
Check that the linear constraints are satisfied to within 1e6
.
disp(A*x'  b)
9.9986e07
disp(Aeq*x'  beq)
9.9565e07
Use the genetic algorithm to minimize the ps_example
function subject to the constraint that x(1)
is an integer.
IntCon = 1; rng default % For reproducibility fun = @ps_example; A = []; b = []; Aeq = []; beq = []; lb = []; ub = []; nonlcon = []; x = ga(fun,2,A,b,Aeq,beq,lb,ub,nonlcon,IntCon)
Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance and constraint violation is less than options.ConstraintTolerance.
x = 1×2
5.0000 0.0000
Use to genetic algorithm to minimize an integerconstrained nonlinear problem. Obtain both the location of the minimum and the minimum function value.
IntCon = 1; rng default % For reproducibility fun = @ps_example; A = []; b = []; Aeq = []; beq = []; lb = []; ub = []; nonlcon = []; [x,fval] = ga(fun,2,A,b,Aeq,beq,lb,ub,nonlcon,IntCon)
Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance and constraint violation is less than options.ConstraintTolerance.
x = 1×2
5.0000 0.0000
fval = 1.9178
Compare this result to the solution of the problem with no constraints.
[x,fval] = ga(fun,2)
Optimization terminated: maximum number of generations exceeded.
x = 1×2
4.7121 0.0051
fval = 1.9949
Use the genetic algorithm to minimize the ps_example
function constrained to have x(1)
integervalued. To understand the reason the solver stopped and how ga
searched for a minimum, obtain the exitflag
and output
results. Also, plot the minimum observed objective function value as the solver progresses.
IntCon = 1; rng default % For reproducibility fun = @ps_example; A = []; b = []; Aeq = []; beq = []; lb = []; ub = []; nonlcon = []; options = optimoptions('ga','PlotFcn', @gaplotbestf); [x,fval,exitflag,output] = ga(fun,2,A,b,Aeq,beq,lb,ub,nonlcon,IntCon,options)
Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance and constraint violation is less than options.ConstraintTolerance.
x = 1×2
5.0000 0.0000
fval = 1.9178
exitflag = 1
output = struct with fields:
problemtype: 'integerconstraints'
rngstate: [1x1 struct]
generations: 96
funccount: 3881
message: 'Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance...'
maxconstraint: 0
Use the genetic algorithm to minimize the ps_example
function constrained to have x(1)
integervalued. Obtain all outputs, including the final population and vector of scores.
IntCon = 1; rng default % For reproducibility fun = @ps_example; A = []; b = []; Aeq = []; beq = []; lb = []; ub = []; nonlcon = []; [x,fval,exitflag,output,population,scores] = ga(fun,2,A,b,Aeq,beq,lb,ub,nonlcon,IntCon);
Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance and constraint violation is less than options.ConstraintTolerance.
Examine the first 10 members of the final population and their corresponding scores. Notice that x(1)
is integervalued for all these population members. The integer ga
algorithm generates only integerfeasible populations.
disp(population(1:10,:))
5.0000 0.0000 5.0000 0.0000 5.0000 0.0014 6.0000 0.0008 13.0000 0.0124 10.0000 0.0011 4.0000 0.0010 0 0.0072 4.0000 0.0010 5.0000 0.0000
disp(scores(1:10))
1.9178 1.9178 1.9165 1.0008 64.0124 25.0011 1.5126 2.5072 1.5126 1.9178
fun
— Objective functionObjective function, specified as a function handle or function name. Write the objective
function to accept a row vector of length
nvars
and return a scalar
value.
When the 'UseVectorized'
option is true
, write
fun
to accept a
pop
bynvars
matrix, where pop
is the current
population size. In this case,
fun
returns a vector the same
length as pop
containing the
fitness function values. Ensure that
fun
does not assume any
particular size for pop
, since
ga
can pass a single
member of a population even in a vectorized
calculation.
Example: fun = @(x)(x[4,2]).^2
Data Types: char
 function_handle
 string
nvars
— Number of variablesNumber of variables, specified as a positive integer. The solver passes row vectors of length
nvars
to fun
.
Example: 4
Data Types: double
A
— Linear inequality constraintsLinear inequality constraints, specified as a real matrix. A
is an M
bynvars
matrix, where M
is the number of inequalities.
A
encodes the M
linear inequalities
A*x <= b
,
where x
is the column vector of nvars
variables x(:)
, and b
is a column vector with M
elements.
For example, to specify
x_{1} + 2x_{2} ≤ 10
3x_{1} + 4x_{2} ≤ 20
5x_{1} + 6x_{2} ≤ 30,
give these constraints:
A = [1,2;3,4;5,6]; b = [10;20;30];
Example: To specify that the control variables sum to 1 or less, give the constraints
A = ones(1,N)
and b = 1
.
Data Types: double
b
— Linear inequality constraintsLinear inequality constraints, specified as a real vector. b
is an M
element vector related to the A
matrix. If you pass b
as a row vector, solvers internally convert b
to the column vector b(:)
.
b
encodes the M
linear inequalities
A*x <= b
,
where x
is the column vector of N
variables x(:)
, and A
is a matrix of size M
byN
.
For example, to specify
x_{1} + 2x_{2} ≤ 10
3x_{1} + 4x_{2} ≤ 20
5x_{1} + 6x_{2} ≤ 30,
give these constraints:
A = [1,2;3,4;5,6]; b = [10;20;30];
Example: To specify that the control variables sum to 1 or less, give the constraints
A = ones(1,N)
and b = 1
.
Data Types: double
Aeq
— Linear equality constraintsLinear equality constraints, specified as a real matrix. Aeq
is an Me
bynvars
matrix, where Me
is the number of equalities.
Aeq
encodes the Me
linear equalities
Aeq*x = beq
,
where x
is the column vector of N
variables x(:)
, and beq
is a column vector with Me
elements.
For example, to specify
x_{1}
+ 2x_{2} +
3x_{3} =
10
2x_{1}
+ 4x_{2} +
x_{3} =
20,
give these constraints:
Aeq = [1,2,3;2,4,1]; beq = [10;20];
Example: To specify that the control variables sum to 1, give the constraints Aeq =
ones(1,N)
and beq = 1
.
Data Types: double
beq
— Linear equality constraintsLinear equality constraints, specified as a real vector. beq
is an Me
element vector related to the Aeq
matrix. If you pass beq
as a row vector, solvers internally convert beq
to the column vector beq(:)
.
beq
encodes the Me
linear equalities
Aeq*x = beq
,
where x
is the column vector of N
variables x(:)
, and Aeq
is a matrix of size Meq
byN
.
For example, to specify
x_{1}
+ 2x_{2} +
3x_{3} =
10
2x_{1}
+ 4x_{2} +
x_{3} =
20,
give these constraints:
Aeq = [1,2,3;2,4,1]; beq = [10;20];
Example: To specify that the control variables sum to 1, give the constraints Aeq =
ones(1,N)
and beq = 1
.
Data Types: double
lb
— Lower bounds[]
(default)  real vector or arrayLower bounds, specified as a real vector or array of doubles. lb
represents
the lower bounds elementwise in
lb
≤ x
≤ ub
.
Internally, ga
converts an array lb
to the
vector lb(:)
.
Example: lb = [0;Inf;4]
means x(1) ≥ 0
, x(3) ≥ 4
.
Data Types: double
ub
— Upper bounds[]
(default)  real vector or arrayUpper bounds, specified as a real vector or array of doubles. ub
represents
the upper bounds elementwise in
lb
≤ x
≤ ub
.
Internally, ga
converts an array ub
to the
vector ub(:)
.
Example: ub = [Inf;4;10]
means x(2) ≤ 4
, x(3) ≤ 10
.
Data Types: double
nonlcon
— Nonlinear constraintsNonlinear constraints, specified as a function handle or function name.
nonlcon
is a function that accepts a vector or array
x
and returns two arrays, c(x)
and
ceq(x)
.
c(x)
is the array of nonlinear inequality
constraints at x
. ga
attempts to satisfy
c(x) <= 0
for all entries of c
.
ceq(x)
is the array of nonlinear equality
constraints at x
. ga
attempts to satisfy
ceq(x) = 0
for all entries of ceq
.
For example,
x = ga(@myfun,4,A,b,Aeq,beq,lb,ub,@mycon)
where mycon
is a MATLAB^{®} function such
as
function [c,ceq] = mycon(x) c = ... % Compute nonlinear inequalities at x. ceq = ... % Compute nonlinear equalities at x.
To learn how to use vectorized constraints, see Vectorized Constraints.
ga
does not enforce nonlinear constraints to be
satisfied when the PopulationType
option is set to
'bitString'
or
'custom'
.
If IntCon
is not empty, the second output of
nonlcon
(ceq
) must be an empty
entry ([]
).
For information on how ga
uses
nonlcon
, see Nonlinear Constraint Solver Algorithms.
Data Types: char
 function_handle
 string
options
— Optimization optionsoptimoptions
 structureOptimization options, specified as the output of
optimoptions
or a structure.
Create options
by using optimoptions
(recommended) or
by exporting options from the Optimization app. For details, see Importing and Exporting Your Work (Optimization Toolbox).
optimoptions
hides the options listed in
italics. See Options that optimoptions Hides.
Values in {}
denote the default value.
{}*
represents the default when there are
linear constraints, and for MutationFcn
also when
there are bounds.
I* indicates that
ga
handles options for integer constraints
differently; this notation does not apply to
gamultiobj
.
NM indicates that the option does
not apply to gamultiobj
.
Options for ga
, Integer ga
,
and gamultiobj
Option  Description  Values 

ConstraintTolerance  Determines the feasibility with respect to nonlinear constraints. Also,
For an options
structure, use  Positive scalar  
 I* Function that creates the initial population. Specify as a name of a builtin creation function or a function handle. See Population Options. 

 I* Function that the algorithm uses to create crossover children. Specify as a name of a builtin crossover function or a function handle. See Crossover Options. 

 The fraction of the population at the next generation, not including elite children, that the crossover function creates.  Positive scalar  
 Level of display. 

 Function that computes distance measure of individuals. Specify as a name of a builtin
distance measure function or a function handle. The value applies to
decision variable or design space (genotype) or to function space
(phenotype). The default For an options structure, use a function handle, not a name. 

 NM Positive integer
specifying how many individuals in the current generation are guaranteed
to survive to the next generation. Not used in  Positive integer  
 NM If the fitness function
attains the value of  Scalar  
 Function that scales the values of the fitness function. Specify as a name of a
builtin scaling function or a function handle. Option unavailable for


FunctionTolerance  The algorithm stops if the average relative change in the best fitness function value
over For
For an options structure, use
 Positive scalar  
 I* Function that continues the optimization after
Alternatively, a cell array specifying the hybrid function and its options. See ga Hybrid Function. For  Function name or handle  or 1by2 cell array
 
InitialPenalty  NM I* Initial value of penalty parameter  Positive scalar  
 Initial population used to seed the genetic algorithm. Has up to
For an options structure, use
 Matrix  
 Matrix or vector specifying the range of the individuals in the initial population.
Applies to For an options structure, use
 Matrix or vector  
 I* Initial scores used to determine fitness. Has up to
For an
options structure, use  Column vector for single objective  matrix for multiobjective
 
 Maximum number of iterations before the algorithm halts. For an options
structure, use  Positive integer  
 The algorithm stops if the average relative change in the best fitness function value
over For
For an options structure, use
 Positive integer  
 NM The algorithm stops if there is no improvement in
the objective function for For an
options structure, use  Positive scalar 
 The algorithm stops after running after For an options structure,
use  Positive scalar  
MigrationDirection  Direction of migration. See Migration Options 

MigrationFraction  Scalar from 0 through 1 specifying the fraction of individuals in each subpopulation that migrates to a different subpopulation. See Migration Options  Scalar  
MigrationInterval  Positive integer specifying the number of generations that take place between migrations of individuals between subpopulations. See Migration Options.  Positive integer  
 I* Function that produces mutation children. Specify as a name of a builtin mutation function or a function handle. See Mutation Options. 

 Nonlinear constraint algorithm. See Nonlinear Constraint Solver Algorithms. Option unchangeable for
For an options structure,
use 

 Functions that For an options structure,
use  Function handle or cell array of function handles 

 Scalar from 0 through 1 specifying the fraction of individuals to keep on the first
Pareto front while the solver selects individuals from higher fronts, for
 Scalar  
PenaltyFactor  NM I* Penalty update parameter.  Positive scalar  
 Function that plots data computed by the algorithm. Specify as a name of a builtin plot function, a function handle, or a cell array of builtin names or function handles. See Plot Options. For an options
structure, use 

PlotInterval  Positive integer specifying the number of generations between consecutive calls to the plot functions.  Positive integer  
 Size of the population.  Positive integer  
 Data type of the population. Must be 

 I* Function that selects parents of crossover and mutation children. Specify as a name of a builtin selection function or a function handle.


StallTest  NM Stopping test type. 

UseParallel  Compute fitness and nonlinear constraint functions in parallel. See Vectorize and Parallel Options (User Function Evaluation) and How to Use Parallel Processing in Global Optimization Toolbox. 

 Specifies whether functions are vectorized. See Vectorize and Parallel Options (User Function Evaluation) and Vectorize the Fitness Function. For an options structure, use 

Example: optimoptions('ga','PlotFcn',@gaplotbestf)
IntCon
— Integer variablesInteger variables, specified as a vector of positive integers taking
values from 1
to nvars
. Each value
in IntCon
represents an x
component
that is integervalued.
When IntCon
is nonempty, Aeq
and beq
must be an empty entry
([]
), and nonlcon
must
return empty for ceq
. For more information on integer
programming, see Mixed Integer Optimization.
Example: To specify that the even entries in x
are
integervalued, set IntCon
to
2:2:nvars
Data Types: double
problem
— Problem descriptionProblem description, specified as a structure containing these fields.
fitnessfcn  Fitness functions 
nvars  Number of design variables 
Aineq 

Bineq 

Aeq 

Beq 

lb  Lower bound on 
ub  Upper bound on 
nonlcon  Nonlinear constraint function 
rngstate  Optional field to reset the state of the random number generator 
solver 

options  Options created using 
Create problem
by exporting a problem from the Optimization app, as described in Importing and Exporting Your Work (Optimization Toolbox).
Data Types: struct
x
— SolutionSolution, returned as a real vector. x
is the best
point that ga
located during its iterations.
fval
— Objective function value at the solutionObjective function value at the solution, returned as a real number. Generally, fval
= fun(x)
.
exitflag
— Reason ga
stoppedReason that ga
stopped, returned as an integer.
Exit Flag  Meaning 

1 
Without nonlinear
constraints — Average cumulative
change in value of the fitness function over

With nonlinear
constraints — Magnitude of the
complementarity measure (see Complementarity Measure) is less than
 
3 
Value of the fitness function did not change in

4 
Magnitude of step smaller than machine precision and
the constraint violation is less than

5 
Minimum fitness limit 
0 
Maximum number of generations

1 
Optimization terminated by an output function or plot function. 
2 
No feasible point found. 
4 
Stall time limit 
5 
Time limit 
When there are integer constraints, ga
uses the
penalty fitness value instead of the fitness value for stopping
criteria.
output
— Information about the optimization processInformation about the optimization process, returned as a structure with these fields:
problemtype
— Problem type, one
of:
'unconstrained'
'boundconstraints'
'linearconstraints'
'nonlinearconstr'
'integerconstraints'
rngstate
— State of the MATLAB random number generator, just before the algorithm
started. You can use the values in rngstate
to
reproduce the output of ga
. See Reproduce Results.
generations
— Number of generations
computed.
funccount
— Number of evaluations of the
fitness function.
message
— Reason the algorithm
terminated.
maxconstraint
— Maximum constraint
violation, if any.
population
— Final populationFinal population, returned as a
PopulationSize
bynvars
matrix.
The rows of population
are the individuals.
scores
— Final scoresFinal scores, returned as a column vector.
For noninteger problems, the final scores are the fitness
function values of the rows of
population
.
For integer problems, the final scores are the penalty fitness values of the population members. See Integer ga Algorithm.
In the Augmented Lagrangian nonlinear constraint solver, the complementarity measure is the norm of the vector whose elements are c_{i}λ_{i}, where c_{i} is the nonlinear inequality constraint violation, and λ_{i} is the corresponding Lagrange multiplier. See Augmented Lagrangian Genetic Algorithm.
To write a function with additional parameters to the independent variables
that can be called by ga
, see Passing Extra Parameters (Optimization Toolbox).
For problems that use the population type Double Vector
(the default), ga
does not accept functions whose inputs are
of type complex
. To solve problems involving complex data,
write your functions so that they accept real vectors, by separating the real
and imaginary parts.
For a description of the genetic algorithm, see How the Genetic Algorithm Works.
For a description of the mixed integer programming algorithm, see Integer ga Algorithm.
For a description of the nonlinear constraint algorithms, see Nonlinear Constraint Solver Algorithms.
[1] Goldberg, David E., Genetic Algorithms in Search, Optimization & Machine Learning, AddisonWesley, 1989.
[2] A. R. Conn, N. I. M. Gould, and Ph. L. Toint. “A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds”, SIAM Journal on Numerical Analysis, Volume 28, Number 2, pages 545–572, 1991.
[3] A. R. Conn, N. I. M. Gould, and Ph. L. Toint. “A Globally Convergent Augmented Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds”, Mathematics of Computation, Volume 66, Number 217, pages 261–288, 1997.
To run in parallel, set the 'UseParallel'
option to true
.
options = optimoptions('
solvername
','UseParallel',true)
For more information, see How to Use Parallel Processing in Global Optimization Toolbox.
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