None of the optimizers in the optimization toolbox (except for intlinprog, which handles only linear problems, so it does not apply) can handle mixed integer problems. Binary variables are a subset of integer variables, so that rules out most of the solvers. That leaves you with only the tools in the global optimization toolbox.
help globaloptim
Global Optimization Toolbox
Version 4.8.1 (R2023a) 19-Nov-2022
Solvers
ga - Genetic algorithm solver.
gamultiobj - Multi-objective genetic algorithm solver.
GlobalSearch - A scatter-search based global optimization
solver.
MultiStart - A multi-start global optimization solver.
paretosearch - A patternsearch-based multi-objective solver.
particleswarm - Particle swarm solver.
patternsearch - Pattern search solver.
simulannealbnd - Simulated annealing solver.
surrogateopt - Surrogate optimization solver.
Accessing options
GlobalSearch - Get/set options for GlobalSearch solver.
MultiStart - Get/set options for MultiStart solver.
optimoptions - Create or alter optimization solver options.
Live Editor task and plot functions.
Optimize - Global Optimization Toolbox Live Editor task
(available in the Live Editor only).
Utility for GlobalSearch and MultiStart solvers
createOptimProblem - Create an optimization problem.
Start point sets for MultiStart solver
CustomStartPointSet - A start point set that contains custom start
points.
RandomStartPointSet - A random start point set.
Fitness scaling for genetic algorithm
fitscalingshiftlinear - Offset and scale fitness to desired range.
fitscalingprop - Proportional fitness scaling.
fitscalingrank - Rank based fitness scaling.
fitscalingtop - Top individuals reproduce equally.
Selection for genetic algorithm
selectionremainder - Remainder stochastic sampling without replacement.
selectionroulette - Choose parents using roulette wheel.
selectionstochunif - Choose parents using stochastic universal
sampling (SUS).
selectiontournament - Each parent is the best of a random set.
selectionuniform - Choose parents at random.
Crossover (recombination) functions for genetic algorithm.
crossoverheuristic - Move from worst parent to slightly past best
parent.
crossoverintermediate - Weighted average of the parents.
crossoverscattered - Position independent crossover function.
crossoversinglepoint - Single point crossover.
crossovertwopoint - Two point crossover.
crossoverarithmetic - Arithmetic mean between two parents satisfying
linear constraints and bound.
Mutation functions for genetic algorithm
mutationgaussian - Gaussian mutation.
mutationuniform - Uniform multi-point mutation.
mutationadaptfeasible - Adaptive mutation for linearly constrained
problems.
Distance function for multi-objective genetic algorithm
distancecrowding - Calculates crowding distance for individuals
Plot functions for genetic algorithm
gaplotbestf - Plots the best score and the mean score.
gaplotbestindiv - Plots the best individual in every generation
as a bar plot.
gaplotdistance - Plots average distance between some individuals.
gaplotexpectation - Plots raw scores vs the expected number of
offspring.
gaplotgenealogy - Plot the ancestors of every individual.
gaplotrange - Plots the min, mean, and max of the scores.
gaplotscorediversity - Plots a histogram of this generations scores.
gaplotscores - Plots the scores of every member of the population.
gaplotselection - Plots a histogram of parents.
gaplotstopping - Plots stopping criteria levels.
gaplotmaxconstr - Plots maximum nonlinear constraint violation
gaplotpareto - Plots Pareto front for a multi-objective GA
gaplotparetodistance - Plots distance measure of individuals on
Pareto front in multi-objective GA
gaplotrankhist - Plots histogram of rank of the population
gaplotspread - Plots spread of Pareto front in multi-objective
GA
Output functions for genetic algorithm
gaoutputfile - Writes iteration history of the genetic algorithm
solver to a file.
gaoutputfcntemplate - Template file for a custom output function.
Plot function for particle swarm optimization
pswplotbestf - Plots best function value.
Search methods for pattern search
searchlhs - Implements Latin hypercube sampling as a search
method.
searchneldermead - Implements Nelder-Mead simplex method
(FMINSEARCH) to use as a search method.
searchga - Implements genetic algorithm (GA) to use as a
search method.
searchfcntemplate - Template file for a custom search method.
Plot functions for pattern search
psplotbestf - Plots best function value.
psplotbestx - Plots current point in every iteration as a bar
plot.
psplotfuncount - Plots the number of function evaluation in every
iteration.
psplotmeshsize - Plots mesh size used in every iteration.
psplotmaxconstr - Plots maximum nonlinear constraint violation
Output functions for pattern search
psoutputfile - Writes iteration history of the pattern search
solver to a file.
psoutputfcntemplate - Template file for a custom output function.
Annealing functions for simulated annealing
annealingboltz - Boltzman annealing.
annealingfast - Fast annealing.
saannealingfcntemplate - Template file to write annealing function.
Acceptance functions for simulated annealing
acceptancesa - Simulated annealing acceptance function.
saacceptancefcntemplate - Template file to write acceptance function.
Temperature functions for simulated annealing
temperatureboltz - Boltzman annealing temperature function.
temperatureexp - Exponential annealing temperature function.
temperaturefast - Fast annealing temperature function.
satemperaturefcntemplate - Template file to write temperature function.
Plot functions for simulated annealing
saplotbestf - Plots best function value.
saplotbestx - Plots best point in every iteration as a bar plot.
saplotf - Plots current function value.
saplotx - Plots current point in every iteration as a bar plot.
saplotstopping - Plots stopping criteria levels.
saplottemperature - Plots mean temperature.
Global Optimization Toolbox Documentation
doc globaloptim
Folders named globaloptim
toolbox/globaloptim globaloptim/globaloptim
Of the solvers in that list of tools, besides GA, only SURROGATEOPT allows you to specify that some variables must be integer.
help surrogateopt
SURROGATEOPT The surrogateopt function is a global solver for
time-consuming objective functions. surrogateopt attempts to solve
problems of the form
minimize f(x)
subject to: lb <= x <= ub (bound constraints)
A*X <= B, Aeq*X = Beq (linear constraints)
c(x) <= 0 (nonlinear inequalities)
x(i) must be integer for i in intcon
The solver searches for the global minimum of a real-valued objective
function in multiple dimensions, subject to bounds, optional integer
constraints, and optional nonlinear inequality constraints. surrogateopt
is best suited to objective functions that take a long time to evaluate.
The objective function can be nonsmooth. The solver requires finite
bounds on all variables. The solver can optionally maintain a checkpoint
file to enable recovery from crashes or partial execution, or
optimization continuation after meeting a stopping condition.
x = SURROGATEOPT(fun,lb,ub) searches for a global minimum of fun(x) in
the region lb <= x <= ub.
fun accepts a single row vector argument x. fun can return either
* a real scalar fval = fun(x), or
* a structure. If the structure contains a field Fval, then
surrogateopt attempts to minimize fun(x).Fval. If the structure
contains a field Ineq, then surrogateopt attempts to make all of the
components of that field be nonpositive: fun(x).Ineq <= 0 for all
entries.
For information on converting nonlinear constraints between the
surrogateopt structure syntax and other solvers, see the packfcn
function reference page.
x = SURROGATEOPT(fun,lb,ub,intcon) requires that the variables listed
in intcon take integer values. pass intcon = [] if there are no integer
variables.
x = SURROGATEOPT(fun,lb,ub,intcon,A,B) finds a local minimum x
subject to the linear inequalities A*X <= B.
x = SURROGATEOPT(fun,lb,ub,intcon,A,B,Aeq,Beq) finds a local minimum x
subject to the linear equalities Aeq*X = Beq as well as A*X <= B. (Set
A=[] and B=[] if no inequalities exist.)
x = SURROGATEOPT(fun,lb,ub,intcon,A,B,Aeq,Beq,options) replaces
the default optimization parameters by values in options. Create
options using optimoptions.
x = SURROGATEOPT(PROBLEM) searches for a minimum for PROBLEM, a
structure with these fields:
objective: The objective (and constraint) function
lb: Lower bounds for x
ub: Upper bounds for x
intcon: Indices of variables that must be integer
Aineq: <A matrix for inequality constraints>
bineq: <B vector for inequality constraints>
Aeq: <A matrix for equality constraints>
beq: <B vector for equality constraints>
rngstate: Optional field to reset the state of RNG
options: Options created with OPTIMOPTIONS
solver: 'surrogateopt'
x = SURROGATEOPT(checkpointFile) continues running the optimization
from the state in a saved checkpoint file. checkpointFile is a path to
a checkpoint file, specified as a string or character vector. If you
specify a file name without a path, SURROGATEOPT uses a checkpoint file
in the current folder.
SURROGATEOPT creates a checkpoint file when it has a valid
CheckpointFile option.
The data in a checkpoint file is in .mat format. To avoid errors or
other unexpected results, do not modify the data before calling
surrogateopt.
x = SURROGATEOPT(checkpointFile,opts) continues running the
optimization from the state in a saved checkpoint file, and replaces
options in checkpointFile with those in opts. surrogateopt accepts
changes in the following options:
CheckpointFile
Display
MaxFunctionEvaluations
MaxTime
MinSurrogatePoints
ObjectiveLimit
OutputFcn
PlotFcn
UseParallel
UseVectorized
BatchUpdateInterval
[x,fval] = SURROGATEOPT(__) also returns the best (smallest) value of
the objective function found by the solver, using any of the input
argument combinations in the previous syntaxes.
[x,fval,exitflag] = SURROGATEOPT(__) also returns exitflag, an
integer describing the reason the solver stopped. Possible values of
exitflag and the corresponding exit conditions are listed below.
1 Best function value reached options.ObjectiveLimit
3 Feasible point but solver stopped (stalled) because no new points
were found.
10 Unique solution exist for the problem due to one of the following
reasons:
All lower bounds are same as corresponding upper bounds.
Unique solution due to linear equalities.
0 Number of function evaluations exceeded options.MaxFunctionEvaluations
or elapsed time exceeded options.MaxTime.
-1 Stopped by output/plot function.
-2 No feasible point found due to one or more of the following reasons:
One or more lower bound lb(i) exceeds a corresponding upper bound ub(i).
One or more ceil(lb(i)) exceeds a corresponding floor(ub(i)) for i in INTCON.
Linear constraints are infeasible.
No solution found that satisfies nonlinear constraints.
[x,fval,exitflag,output] = SURROGATEOPT(__) also returns output, a
structure with these fields:
rngstate: State of the random number generator before the solver started.
funccount: Total number of function evaluations.
message: Reason why SURROGATEOPT stopped.
elapsedtime: Time spent running the solver in seconds, as measured by tic/toc.
constrviolation: Maximum constraint violation due to nonlinear
inequalities at x.
ineq: Inequality constraints at the x.
[x,fval,exitflag,output,trials] = SURROGATEOPT(__) also returns a
structure containing all of the evaluated points (Npts) and the
function function values at those points. trials have these fields:
trials.X: Matrix of size Npts-by-Nvar.
Each row of trials.X represents one point that SURROGATEOPT
evaluated.
trials.Fval: A vector, where each entry is the objective function
value of the corresponding row of trials.X
trials.Ineq: A matrix in which rows are nonlinear inequalties of the
corresponding row of trials.X
Examples:
Find the minimum of a function subject to bounds.
Search for a minimum of the six-hump camel back function in the region
-2.1 <= x(i) <= 2.1. This function has two global minima with the
objective function value -1.0316284... and four local minima with
higher objective function values.
fun = @(x)(4*x(:,1).^2 - 2.1*x(:,1).^4 + x(:,1).^6/3 ...
+ x(:,1).*x(:,2) - 4*x(:,2).^2 + 4*x(:,2).^4);
lb = [-2.1,-2.1];
ub = -lb;
x = surrogateopt(fun,lb,ub)
Find the minimum of a function subject to nonlinear constraints.
Find the minimum of Rosenbrock's function 100(x(2)-x(1)2)2+(1-x(1))2
subject to the nonlinear constraint that the solution lies in a disk of
radius 1/3 around the point [1/3,1/3]: (x(1)-1/3)2+(x(2)-1/3)2 <= (1/3)2.
To do so, write a function fun(x) that returns the value of
Rosenbrock's function in a structure field Fval, and returns the
nonlinear constraint value in the form c(x) <= 0 in the structure field
Ineq.
function f = fun(x)
f.Fval = 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
f.Ineq = (x(1)-1/3)^2 + (x(2)-1/3)^2 - (1/3)^2;
Call surrogateopt using lower bounds of 0 on each component and upper
bounds of 2/3.
lb = [0,0];
ub = [2/3,2/3];
[x,fval,exitflag] = surrogateopt(@fun,lb,ub)
If objective and constraints are in separate function use this
convenienece function to return output as a struct.
objAndConstr = packfcn(@objective,@inequalities)
X = surrogateopt(objAndConstr, ...) % objAndConstr is a function handle
Find the minimum of a function subject to integer constraints
Find the minimum of the piecewiseFcn function for a two-dimensional
variable x whose first component is restricted to integer values, and
all components are between -5 and 5.
function f = piecewiseFcn(x)
f = zeros(1,size(x,1));
for i = 1:size(x,1)
if x(i,1) < -5
f(i) = (x(i,1)+5)^2 + abs(x(i,2));
elseif x(i,1) < -3
f(i) = -2*sin(x(i,1)) + abs(x(i,2));
elseif x(i,1) < 0
f(i) = 0.5*x(i,1) + 2 + abs(x(i,2));
elseif x(i,1) >= 0
f(i) = .3*sqrt(x(i,1)) + 5/2 +abs(x(i,2));
end
end
intcon = 1;
rng default % For reproducibility
fun = @piecewiseFcn;
lb = [-5,-5];
ub = [5,5];
x = surrogateopt(fun,lb,ub,intcon)
Restart from checkpoint file
To enable restarting surrogate optimization due to a crash or any other
reason, set a checkpoint file name.
Create an optimization problem and set a small number of function
evaluations.
rng default % For reproducibility
fun = @(x)(4*x(:,1).^2 - 2.1*x(:,1).^4 + x(:,1).^6/3 ...
+ x(:,1).*x(:,2) - 4*x(:,2).^2 + 4*x(:,2).^4);
lb = [-2.1,-2.1];
ub = -lb;
opts = optimoptions('surrogateopt','CheckpointFile','checkfile.mat');
opts.MaxFunctionEvaluations = 30;
[x,fval,exitflag,output] = surrogateopt(fun,lb,ub,opts)
Set options to use 100 function evaluations (which means 70 more than
already done) and restart the optimization.
opts.MaxFunctionEvaluations = 100;
[x2,fval2,exitflag2,output2] = surrogateopt('checkfile.mat',opts)
See also OPTIMOPTIONS, PATTERNSEARCH, FMINCON
Documentation for surrogateopt
doc surrogateopt
