Computer-aided design and optimization for pharmaceutical ...

Bootstrap process for estimating the accuracy ofan optimal formulationBootstrap samples are generated by sampling with replacement from m the original dataset.The accuracy of bootstrap optimal solutions X * optim, , Y*optimcould be evaluated by their standard deviations.optimal solutions estimated from bootstrap samplesX * optim Y * optimy**Original dataOptimal solutionIs localy*Bootstrap re-samplingx*X *1 optim , Y*1 optimX *2 optim , Y*2 optimX *B optim , Y*B optimBootstrap re-samplingX *1 , Y *1 X *2 , Y *2 X *B , Y *Bnormal distribution ofbootstrap solutionsx**Optimal solutionIs globaly**X=(X 1 , X 2 ,…, X n )Y=(Y 1 , Y 2 ,…, Y m )bootstrap samplesoriginal datasetx**Risk of local optima involved in the optimizationprocess based on bootstrap methodm iOutput layerm i(t+1) = m i(t)) + α i(t)[x(t)-m i(t)]m i1m i2m i3…m inOptimal solutions obtainedby a bootstrap processBootstrap solutions classifiedinto several clustersx 1x 2x 3x nInput layerMixture of global optima and local optimain bootstrap solutionsKohonen’s s self-organizingmaps (SOM)T. Kohonen, “Self-Organization and Association Memory” Springer Series in Information Sciences, Vol. . 8, 1984.