How to generate the objconstr for multivariate surrogate optimization with nonlinear constraints?

Hello,

I am trying to use the surrogate optimization function in matlab to obtain the global minima of a problem with an objective function and several nonlinear constraints. My problem has been computed using symbolic variables, but I am not able to find the correct syntax of putting these symbolic cost functinos and nonlinear constraints into "matlabFunction" to obtain the function handle to use with surrogateopt.

***** Code example ********

symbolic_objective_function %computed from several operations

symbolic_nonlinear_constraints %computed after several operations

%% Is the below line of code the correct way to compute the objconstr for use in surrogateopt?

objconstr=matlabFunction([symbolic_objective_function], [symbolic_nonlinear_constraints],'vars',{x})

Answer 1

[Alan Weiss]

Try this:

obj = matlabFunction(symbolic_objective_function,'vars',{x});
constr = matlabFunction(symbolic_nonlinear_constraints,'vars',{x});
objconstr = @(x)struct('Fval',obj(x),'Ineq',constr(x));

Alan Weiss

MATLAB mathematical toolbox documentation

[Suhas Raghavendra Kulkarni]

Thank you for your resonse, Alan.

I tried your suggestion in the following format but received the error as highlighted. I am unsure what it means.

Code:

[func, constraint]=some_function(inputs a,b,c,d)

syms computations here

f=objective function output of syms computations

inequality_constraint=constraint output of syms computation

equality_constraint=constraint output of syms computation

func=matlabFunction(f,'vars',{symvar(f)});

constraint=matlabFunction(inequality_constraint,equality_constraint,'vars',{symvar(cons)});

%% note: symvar(f)=symvar(cons)=[x]

end

for the above code, i obtain

% func= @(in1).....

% constraint=@(in1)deal(zeros(0,0)).....

func and cons are passed to another function inside which the optimisation is formulated as follows

options=optimoptions(....)

lb=...

ub=...

objconstr = @(in1)struct('Fval',func(in1),'Ineq',constraint(in1));

[xfinal,fval] = surrogateopt(objconstr,lb,ub,options);

********************************************************************************************************************

**Running the above code results in the following error.

***************************************** ERROR BEGIN ********************************

Error using deal (line 37)

The number of outputs should match the number of inputs.

Error in symengine>@(in1)deal(zeros(0,0),[in1(:,1).*4.890738003669028e-1+(in1(:,1).*.................(very long expression that i have deleted for brevity)

Error in thetasol>@(in1)struct('Fval',func_0(in1),'Ineq',constraint_0(in1)) (line 25)

objconstr_0 = @(in1)struct('Fval',func_0(in1),'Ineq',constraint_0(in1));

Error in surrogateopt>expensiveModel (line 379)

temp = feval(objconstr,x);

Error in surrogateopt>@(x)expensiveModel(x,objfun) (line 367)

expensive = struct('model', @(x) expensiveModel(x,objfun), ...

Error in globaloptim.bmo.ModelManager>conditionalModelEvaluator (line 422)

out = feval(expensiveModel,Xin);

Error in globaloptim.bmo.ModelManager>@(trial)conditionalModelEvaluator(trial,output,self.varName,expensive.model,expensive.response) (line 61)

self.combinedModel = @(trial) conditionalModelEvaluator(trial, output, ...

Error in globaloptim.bmo.ModelManager/evaluateLocal (line 284)

self.pendingTrials(end).output = self.combinedModel(nextTrial);

Error in globaloptim.bmo.ModelManager/evaluate (line 109)

self.evaluateLocal(nextTrial);

Error in globaloptim.bmo.BlackboxModelOptimizer/optimize (line 162)

self.modelMgr.evaluate(nextTrial);

Error in surrogateopt (line 338)

controller = controller.optimize();

Error in thetasol (line 37)

[xfinal_0,fval_0] = surrogateopt(objconstr_0,lb,ub,options);

*************************** END ERROR **************************************************************

Thank you for any advice you may be able to provide

[Alan Weiss]

The problem as I understand it is that you have nonlinear equality constraints as well as nonlinear inequality constraints. Your constraint function should be for nonlinear inequality constraints only. It should not have a deal statement. It should accept the in1 argument and return a scalar or vector. Check that your nonlinear inequality constraint accepts one argument and returns one argument.

Alan Weiss

MATLAB mathematical toolbox documentation

[MohammadReza Jabbari (Jabari)]

Hi Alan Weiss,

How a nonlinear equality constraint can be fed to the Matlab Sover such as Surrogate?

[Alan Weiss]

As shown in the surrogateopt reference page, the solver does not accept nonlinear equality constraints. This example shows a potential workaround by using two inequality constraints to form an approximate equality constraint. However, this technique does not always work.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation