Continuous global optimization of structured process systems models

Nonconvex models for the optimization of process systems in chemical engine ering give rise to multiple suboptimal solutions, and a number of complicat ions that often cause failure of standard local optimization techniques. A deterministic branch and bound algorithm is presented in this paper for the global optimization of structured process systems models that include non- convexities introduced by concave univariate, bilinear and linear fractiona l terms. The proposed branch and contract algorithm relies on a bounds cont raction operation, which consists of the solution of a finite sequence of c onvex bounds-contraction subproblems for the subset of nonconvex variables in a problem. The application of the proposed algorithm is illustrated with several numerical examples, which include heat exchanger networks, chemica l reactors, simplified process. flowsheets, and waste-water treatment syste ms. The results show that by executing the contraction operation at selecte d branch and bound nodes, large portions of the search region over which th e objective function takes only values above a known upper bound are elimin ated. It is shown that with the proposed approach the total number of nodes in the solution tree is kept relatively small, and for some problems, no b ranching is required at all. (C) 1998 Elsevier Science Ltd. All rights rese rved.