MATLAB: Can GA always find a smaller objective than SQP

gaGlobal Optimization ToolboxMATLABoptimizationsqp

Hi everyone,

These days I am using GA and SQP for optimization.

It is very strange that the result from SQP is smaller than GA, i.e., better results are from SQP.

I think my codes are all right, but I am not sure about the results.

It is said SQP can only find a local optimal result while GA can search for the global one.

But why this happens ?

Any help is greatly appreciated!

Cheers

Best Answer

The SQP method starts from a specified point and moves (almost) along local gradient to smaller function values. If the start point is inside a valley, which does not contain the global minimum there is only a tiny chance that the surrounding mountains are exceeded by accident.

GA uses a set of start points and the crossing over exceeds the search area during the processing. Therefore there is a larger chance to find a global optimum.

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MATLAB: Linprogr in Matlab not finding a solution when a solution exists

It looks to me LINPROG is flawed or buggy in your case. I try to remove suspected constraints and change beq so that the equality is satisfied by x, and LINPROG still fails.

load matrices
f=zeros(size(x,1),1);
Aeq = round(Aeq);
beq = Aeq*x;
keep = max(abs(Aineq),[],2)>1e-10;
all(x>=lb)
all(x<=ub)
all(Aineq*x<=bineq)
all(Aeq*x==beq)
% This will fail to return solution
options = optimoptions('linprog','Algorithm','interior-point','ConstraintTolerance',1e-3);
xlinprog = linprog(f,Aineq(keep,:),bineq(keep,:),Aeq,beq, lb, ub, options);

But if I call QUADPROG it will returns a solution

% This will returns a solution
H = sparse(size(x,1),size(x,1));
xquadprog = quadprog(H,f,Aineq(keep,:),bineq(keep,:),Aeq,beq, lb, ub);

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MATLAB: How to manually change MaxFunctionEvaluations in fmincon

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