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Find minimum of function using genetic algorithm

ConstraintTolerance

Determines the feasibility with respect to nonlinear constraints. Also,
max(sqrt(eps),ConstraintTolerance) determines
feasibility with respect to linear constraints.

For an options
structure, use TolCon.

Positive scalar | {1e-3}

CreationFcn

Function that creates the initial population. Specify as a name of a built-in creation
function or a function handle. See Population Options.

{'gacreationuniform'} |
{'gacreationlinearfeasible'}* |
'gacreationnonlinearfeasible' |
{'gacreationuniformint'}I* for ga |
{'gacreationsobol'}I* for gamultiobj | Custom creation
function

CrossoverFcn

Function that the algorithm uses to create crossover children. Specify as a name of a
built-in crossover function or a function handle. See Crossover Options.

{'crossoverscattered'} for ga,
{'crossoverintermediate'}* for
gamultiobj |
{'crossoverlaplace'}I* | 'crossoverheuristic' |
'crossoversinglepoint' |
'crossovertwopoint' |
'crossoverarithmetic' | Custom crossover
function

CrossoverFraction

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

Positive scalar | {0.8}

Display

Level of display.

'off' | 'iter' | 'diagnose' | {'final'}

DistanceMeasureFcn

Function that computes the distance measure of individuals. Specify as a name of a
built-in distance measure function or a function handle. The value applies
to the decision variable or design space (genotype) or to function space
(phenotype). The default 'distancecrowding' is in
function space (phenotype). For gamultiobj only. See
Multiobjective Options.

For
an options structure, use a function handle, not a name.

{'distancecrowding'} means the same as
{@distancecrowding,'phenotype'} |
{@distancecrowding,'genotype'} | Custom distance
function

EliteCount

NM Positive integer
specifying how many individuals in the current generation are guaranteed
to survive to the next generation. Not used in gamultiobj.

Positive integer | {ceil(0.05*PopulationSize)} | {0.05*(default
PopulationSize)}
for mixed-integer problems

FitnessLimit

NM If the fitness function
attains the value of FitnessLimit, the algorithm
halts.

Scalar | {-Inf}

FitnessScalingFcn

Function that scales the values of the fitness function. Specify as a name of a
built-in scaling function or a function handle. Option unavailable for
gamultiobj.

{'fitscalingrank'} | 'fitscalingshiftlinear' |
'fitscalingprop' | 'fitscalingtop'
| Custom fitness scaling
function

FunctionTolerance

The algorithm stops if the average relative change in the best fitness function value
over MaxStallGenerations generations is less than or
equal to FunctionTolerance. If
StallTest is 'geometricWeighted',
then the algorithm stops if the weighted average relative change is less
than or equal to FunctionTolerance.

For
gamultiobj, the algorithm stops when the geometric
average of the relative change in value of the spread over
options.MaxStallGenerations generations is less than
options.FunctionTolerance, and the final spread is
less than the mean spread over the past
options.MaxStallGenerations generations. See gamultiobj Algorithm.

For an options structure, use
TolFun.

Positive scalar | {1e-6} for ga, {1e-4} for gamultiobj

HybridFcn

I* Function that continues the optimization after
ga terminates. Specify as a name or a function
handle.

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Alternatively, a cell array specifying the hybrid
function and its options. See ga Hybrid Function.

For gamultiobj, the only hybrid
function is @fgoalattain. See gamultiobj Hybrid Function.

When the problem has integer constraints, you cannot use a
hybrid function.

See When to Use a Hybrid Function.

Function name or handle | 'fminsearch' | 'patternsearch' | 'fminunc' |
'fmincon' | {[]}

or

1-by-2 cell array
| {@solver, hybridoptions}, where solver =
fminsearch
, patternsearch,
fminunc, or fmincon
{[]}

InitialPenalty

NM
I* Initial value of the penalty
parameter

Positive scalar | {10}

InitialPopulationMatrix

Initial population used to seed the genetic algorithm. Has up to
PopulationSize rows and N columns,
where N is the number of variables. You can pass a
partial population, meaning one with fewer than
PopulationSize rows. In that case, the genetic
algorithm uses CreationFcn to generate the remaining
population members. See Population Options.

For an options structure, use
InitialPopulation.

Matrix | {[]}

InitialPopulationRange

Matrix or vector specifying the range of the individuals in the initial population.
Applies to gacreationuniform creation function.
ga shifts and scales the default initial range to
match any finite bounds.

For an options structure, use
PopInitRange.

Matrix or vector | {[-10;10]} for unbounded components,
{[-1e4+1;1e4+1]} for unbounded components of
integer-constrained problems, {[lb;ub]} for bounded
components, with the default range modified to match one-sided
bounds

InitialScoresMatrix

Initial scores used to determine fitness. Has up to PopulationSize
rows and Nf columns, where Nf is the
number of fitness functions (1 for
ga, greater than 1 for
gamultiobj). You can pass a partial scores matrix,
meaning one with fewer than PopulationSize rows. In that
case, the solver fills in the scores when it evaluates the fitness
functions.

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For an options structure, use
InitialScores.

Column vector for single objective | matrix for multiobjective
| {[]}

MaxGenerations

Maximum number of iterations before the algorithm halts.

For an options
structure, use Generations.

Positive integer |{100*numberOfVariables} for ga, {200*numberOfVariables} for gamultiobj

MaxStallGenerations

The algorithm stops if the average relative change in the best fitness function value
over MaxStallGenerations generations is less than or
equal to FunctionTolerance. If
StallTest is 'geometricWeighted',
then the algorithm stops if the weighted average relative change is less
than or equal to FunctionTolerance.

For
gamultiobj, the algorithm stops when the geometric
average of the relative change in value of the spread over
options.MaxStallGenerations generations is less than
options.FunctionTolerance, and the final spread is
less than the mean spread over the past
options.MaxStallGenerations generations. See gamultiobj Algorithm.

For an options structure, use
StallGenLimit.

Positive integer | {50} for ga, {100} for gamultiobj

MaxStallTime

NM The algorithm stops if there is no improvement in
the objective function for MaxStallTime seconds, as
measured by tic and toc.

For an
options structure, use StallTimeLimit.

Positive scalar | {Inf}

MaxTime

The algorithm stops after running for MaxTime seconds, as measured
by tic and toc. This limit is enforced
after each iteration, so ga can exceed the limit when
an iteration takes substantial time.

For an options structure,
use TimeLimit.

Positive scalar | {Inf}

MigrationDirection

Direction of migration. See Migration Options.

'both' | {'forward'}

MigrationFraction

Scalar from 0 through 1 specifying the fraction of individuals in each subpopulation
that migrates to a different subpopulation. See Migration Options.

Scalar | {0.2}

MigrationInterval

Positive integer specifying the number of generations
that take place between migrations of individuals between subpopulations.
See Migration Options.

Positive integer | {20}

MutationFcn

Function that produces mutation children. Specify as a name of a built-in mutation
function or a function handle. See Mutation Options.

{'mutationgaussian'} for ga without constraints
| {'mutationadaptfeasible'}* for
gamultiobj and for ga with
constraints | {'mutationpower'}I* | 'mutationpositivebasis' |
'mutationuniform' | Custom mutation function

NonlinearConstraintAlgorithm

Nonlinear constraint algorithm. See Nonlinear Constraint Solver Algorithms. Option unchangeable for
gamultiobj.

For an options structure,
use NonlinConAlgorithm.

{'auglag'} for ga, {'penalty'} for gamultiobj

OutputFcn

Functions that ga calls at each iteration. Specify as a function
handle or a cell array of function handles. See Output Function Options.

For an options structure,
use OutputFcns.

Function handle or cell array of function handles |
{[]}

ParetoFraction

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
gamultiobj only. See Multiobjective Options.

Scalar | {0.35}

PenaltyFactor

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NM I* Penalty
update parameter.

Positive scalar | {100}

PlotFcn

Function that plots data computed by the algorithm. Specify as a name of a built-in
plot function, a function handle, or a cell array of built-in names or
function handles. See Plot Options.

For an options
structure, use PlotFcns.

ga or gamultiobj: {[]} |
'gaplotdistance' | 'gaplotgenealogy' | 'gaplotselection' |
'gaplotscorediversity' |'gaplotscores' | 'gaplotstopping' |
'gaplotmaxconstr' |
Custom plot function

ga only:
'gaplotbestf' | 'gaplotbestindiv' | 'gaplotexpectation' |
'gaplotrange'

gamultiobj
only: 'gaplotpareto' | 'gaplotparetodistance' | 'gaplotrankhist' |
'gaplotspread'

PlotInterval

Positive integer specifying the number of generations
between consecutive calls to the plot functions.

Positive integer | {1}

PopulationSize

Size of the population.

Positive integer | {50} when numberOfVariables
<= 5
, {200} otherwise | {min(max(10*nvars,40),100)} for
mixed-integer problems

PopulationType

Data type of the population. Must be 'doubleVector' for
mixed-integer problems.

'bitstring' | 'custom' | {'doubleVector'}

ga ignores
all constraints when PopulationType is set to 'bitString' or 'custom'.
See Population Options.

SelectionFcn

Function that selects parents of crossover and mutation children. Specify as a name of
a built-in selection function or a function handle.

gamultiobj uses only
'selectiontournament'.

{'selectionstochunif'} for ga,
{'selectiontournament'} for
gamultiobj |
'selectionremainder' |
'selectionuniform' |
'selectionroulette' | Custom selection
function

StallTest

NM Stopping test type.

'geometricWeighted' | {'averageChange'}

UseVectorized

Specifies whether functions are vectorized. See Vectorize and Parallel Options (User Function Evaluation) and
Vectorize the Fitness Function.

For an options structure, use Vectorized
with the values 'on' or
'off'.

true | {false}

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