Evolutionary pattern search algorithms for unconstrained and linearly constrained optimization

Redescribe aconvergence theory forevolutionary pattern search algorithms (EPS.4S) ona broad class of unconstrained and linearlyconstrainedproblems. EPSAS adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAS is inspired by recent analysesof pattern search methods. Our analysis significantly extends the previous convergence theory for EPSAS. Our analysis applies to a broader class of EPS.AS,and it appliesto problemsthat are nonsmooth, have unbounded objective functions, and which are linearlyconstrained. Further,we describe a modest change to the algorithmicframeworkof EPSASfor whicha non-probablisticconvergencetheory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPS.4S. m d DISCLAIMER This report was prepared as an account of work sponsored by an agencyof the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal Iiabiiity or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. ‘