| The purpose of this study was to develop methods for the use of parallel processing with nonlinear optimization to efficiently perform chemical process design. Sequential optimization was performed with the parallel calculation of multiple flash units. A more comprehensive study was then performed introducing parallelism into a sequential optimization subroutine to determine the potential for reducing the computational time involved with the optimization.; The sequential successive quadratic programming (SQP) algorithm was developed using the quadratic programming (EQP) formulation developed by Bartholomew-Biggs with the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) inverse Hessian matrix update. This algorithm was able to minimize 13 classical test problems and three small chemical process optimization problems.; Algorithms using a parallel finite difference Hessian (PH), Straeter's parallel variable metric (PVM) update, and Freeman's projected parallel variable (PPVM) metric update were investigated. The PPVM algorithm solved the 13 test problems in an average of 24.5 iterations and 1.18 seconds (versus 31.5 iterations and 0.82 seconds for BFGS) on an Alliant FX/8. The parallel task overhead and the extra calculations required were the major causes for the longer PPVM algorithm computation times. The PH and PVM algorithms solved 8 and 12 of the 13 problems, respectively.; Schnabel's parallel partial speculative gradient evaluation technique was used for the simultaneous determination of objective function values at x and other points during the line search for the later calculation of the numerical gradient. Computational time was reduced with increasing numbers of processors. The sequential algorithm performed the function evaluations for the gradient at the end of the iteration. Less time was required for the sequential algorithm because of the parallel task overhead.; Simultaneous function evaluations were performed in parallel at predetermined intervals during the line search. The sequential algorithm's quadratic interpolation was more efficient, however, with respect to number of iterations and computational time required.; Simultaneous minimizations at various initial guesses were performed with the sequential BFGS algorithm. The success of this algorithm shows potential for robust and reliable global minimization of complex multiextremal large scale design problems. |
