How strict are constraints in the Global Optimization Toolbox?

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Joel Marchand 2016-12-20

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回答： Walter Roberson 2016-12-20

I am working on an optimization problem using the Global Optimization Toolbox; specifically, I am using the genetic algorithm (ga). I have some inequality constraints to help guide the optimization to physically realizable properties (for example, various thickness may not be negative). I allow for the possibility of zero thickness.

Consider the inequality Ax <= b (as in the ga documentation). If x represents three thicknesses A = [-1,0,0;0,-1,0;0,0,-1] and b = [0;0;0], then each of the three thicknesses should be allowed to go to zero but not below. However, I regularly get a thickness on the order of -1e-19 (meters) which raises an exception in my code. Note that I expect these dimensions to be on the order of millimeters to centimeters.

My question is this. Can I consider the inequality constraints, lower, and upper bounds to be strict? Is there an option that I am missing that can force these to be strict limits?

Running on MATLAB 2015B, Windows 7 Professional Service Pack 1

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David Barry 2016-12-20

Please remove the code formatting from your question so we can read it without getting RSI from scrolling.

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Answer 1

Walter Roberson 2016-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/317653-how-strict-are-constraints-in-the-global-optimization-toolbox#answer_248001

https://www.mathworks.com/help/gads/genetic-algorithm-options.html#bue6mgy-1

"The penalty algorithm uses the gacreationnonlinearfeasible creation function by default. This creation function uses fmincon to find feasible individuals. [...] You can specify tuning parameters for gacreationnonlinearfeasible using the following name-value pairs.

SolverOpts fmincon options, created using optimoptions or optimset."

https://www.mathworks.com/help/optim/ug/fmincon.html#inputarg_options

"ConstraintTolerance

Tolerance on the constraint violation, a positive scalar. The default is 1e-6. See https://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html Tolerances and Stopping Criteria>"