Modeling and solution strategies for large nonlinear production planning models.

摘要

This study focuses on large nonlinear models used in the Chemical and Process Industry. A transition path in modeling strategy is offered from the traditional linear models to the more general and more flexible nonlinear models. This approach is consistent with the changes within the industry that are pushing for the development of nonlinear models.; In the first part, the operations of a prototype refinery are described, modeled and solved, using GAMS, General Algebraic Modeling System. Two modeling formulations are proposed: the crude based model is the more traditional linear approach with extra side constraints, which ensure the same quality for all stream splits. The quality based model is smaller, because each stream is explicitly characterized by quality variables, but more dense and more "nonlinear".; The models range in size from 200 rows by 214 variables to 778 rows by 765 variables; the number of nonzero elements in the Jacobian matrix varies from 1311 to 4431 of which about 20% are nonlinear. The solutions are obtained using the optimization algorithms currently attached to GAMS that are able to solve nonlinear models, MINOS and CONOPT. The initial starting point, generated from the optimal solution of the linear relaxation of the crude based model, affects very positively the speed and reliability of the optimizers.; The second part describes solution alternatives using a modeling language--EMS--which is specialized for processing models. The implementation of a solution procedure--DWT--is described. The DWT algorithm employs reduced gradient techniques to eliminate a large percentage of variables, sometimes as much as 90%, by using the large number of equality constraints usually present in large chemical processing models.; The DWT implementation is compared with a SPARSE implementation, which presents the entire processing model to the optimizer. Tests were performed with the MINOS and Successive Quadratic Programming algorithms. The DWT algorithm did not outperform the SPARSE, based on the testing done on the available models.; The nonlinear equation solving procedure, which is used intensively by the DWT algorithm and also as the initial starting point generator for the SPARSE implementation, was improved by a bump by bump algorithm which takes advantage of the structure of the Jacobian matrix of the system of nonlinear equations.