Combined stochastic and gradient-Based optimization

Chemical engineering plants and processes models are very often highly nonlinear and of large scale. Handling these systems is a difficult, onerous (?) and time-consuming activity. To facilitate the generation of the codes, the mathematical solution of the equation systems and the simulation and representation of the problems, the simulator DIVA [4] has been developed in our group since the middle 80’s. Today the package has already achieved the status of a very robust and flexible computer aided process engineering tool. One of the new steps being pursued in the last years in the integrated package is the implementation of dynamic and steady state optimization facilities. First attempts of implementing simple gradient-based algorithms leaded to solutions that strongly depend on the starting points (local-optima) and require high computation times [3]. In this contribution, the focus is on steady-state optimization. To cope with these problems we propose two different approaches using combined stochastic and gradient based optimization methods. The first generates feasible starting points stochastically and then performs a successive quadratic programming search (SQP). The second, a mixed-integer nonlinear programming algorithm, uses a simplex-simulated annealing approach [1] with the possibility of a SQP refinement step. To illustrate the capabilities of the algorithms two examples are presented. The first example is an analytical function consisting of a sum of cosine functions combined with a Gaussian distribution with many local optima and a known global optimum. The other example is the synthesis of a fluid-fluid two phase reactor network [2]. [1] M.F. Cardoso, R.L. Salcedo, S.F. de Azevedo and D. Barbosa: A Simulated Annealing Approach to the Solution of MINLP Problems. Comp. Chem. Engng, 21(12):1349-1364, 1997. [2] A.R.J. Esparta, T. Obertopp and E.D. Gilles: Synthesis of isothermal fluid-fluid two-phase CSTR networks. Comp. Chem. Engng, 22, Suppl.:S671-S674, 1998. [3] C.P. Majer: Erweiterung einer Simulationsumgebung für verfahrentechnische Prozesse zur Parameterschätzung, Versuchsplannung und Trajektorienoptimierung. VDI Fortschritt-Berichte Nr. 3/538, VDI-Verlag, Düsseldorf, 1998. [4] K.D. Mohl, A. Spieker, E. Stein, and E.D. Gilles: DIVA - Eine Umgebung zur Simulation, Analyse und Optimierung verfahrenstechnischer Prozesse. In A. Kuhn and S. Wenzel (Eds.): Simulationstechnik, 11. ASIM-Symposium in Dortmund, p. 278-283. Vieweg Verlag, Braunschweig/Wiesbaden, 1997