Computers & Chemical Engineering, Vol.22, No.12, 1749-1770, 1998
Continuous global optimization of structured process systems models
Nonconvex models for the optimization of process systems in chemical engineering give rise to multiple suboptimal solutions, and a number of complications 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 fractional terms. The proposed branch and contract algorithm relies on a bounds contraction operation, which consists of the solution of a finite sequence of convex 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, chemical reactors, simplified process. flowsheets, and waste-water treatment systems. The results show that by executing the contraction operation at selected branch and bound nodes, large portions of the search region over which the objective function takes only values above a known upper bound are eliminated. 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 branching is required at all.
Keywords:NONCONVEX NLPS;EQUILIBRIUM PROBLEM;BILINEAR PROGRAMS;MINLPPROBLEMS;ALGORITHM GOP;DESIGN;PHASE;EQUATIONS