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Penalty and Barrier methods are normally used to solve Nonlinear Optimization
Problems constrained problems. The problems appear in areas such as
engineering and are often characterised by the fact that involved functions (objective
and constraints) are non-smooth and/or their derivatives are not know. This
means that optimization methods based on derivatives cannot net used. A Java based
API was implemented, including only derivative-free optimizationmethods, to solve
both constrained and unconstrained problems, which includes Penalty and Barriers
methods. In this work a new penalty function, based on Fuzzy Logic, is presented.
This function imposes a progressive penalization to solutions that violate the constraints.
This means that the function imposes a low penalization when the violation
of the constraints is low and a heavy penalisation when the violation is high. The
value of the penalization is not known in beforehand, it is the outcome of a fuzzy
inference engine. Numerical results comparing the proposed function with two of
the classic penalty/barrier functions are presented. Regarding the presented results
one can conclude that the prosed penalty function besides being very robust also
exhibits a very good performance.
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Springer