Matlab optimization module problem

I am using matlab R2016a. I am using optimization module for my application 

trying to find the minimum in my function (below is the main optimization 

lines). There are two variables that I'm interested to optimize them to 

make the function minimum. The objective function has lots of local 

minimums. Unfortunately each run gave me different variables. Sometimes 

there's 30% or more difference between runs results. And sometimes the 

optimization module get stuck in one of the local minimums. I tried to tune 

every tolerance and step size but no success so far and I don't get a 

consistent final results for my two variables. Could you please help me how 

can I tune the Options to have a quicker and consistent result. ; options = 

optimoptions('fmincon','Display','iter','Algorithm',' 

sqp','MaxFunctionEvaluations',1500,'MaxIterations',1500,' 

ConstraintTolerance',1.0e-10,'OptimalityTolerance',1.0e-10,'StepTolerance',1.0e-10);; 

estparam=fmincon(@objfun,estparam0,A,b,Aeq,beq,lb,ub,[],options) 

Answer 1

[MathWorks Support Team]

If you have access to the Global Optimization Toolbox, you may use “GlobalSearch” or “MultiStart” features of the toolbox to obtain the global minimum to your problem.

https://www.mathworks.com/help/gads/globalsearch.html

https://www.mathworks.com/help/gads/multistart.html

 

In addition, another potential workaround is to use the function “patternsearch”

Example:

>> options = optimoptions('patternsearch','Display','iter','MaxFunctionEvaluations',1500,'MaxIterations',1500,'ConstraintTolerance',1.0e-10,'StepTolerance',1.0e-10);

>> estparam=patternsearch(@objfun,estparam0,A,b,Aeq,beq,lb,ub,[],options)

https://www.mathworks.com/help/gads/patternsearch.html

 

Finally, you may also try calling “fmincon” multiple times in a “for” or “parfor” loop, giving different initial guesses each time and keeping track of the best solution.  This will not necessarily guarantee a global minimum, but it will likely yield a better and more consistent answer.