Global optimization of a combinatorially complex generalized pooling problem



Global optimization strategies are described for a generalization of the pooling problem that is important to the petrochemical, chemical, and wastewater treatment industries. The problem involves both discrete variables, modeling the structure of a flow network, and continuous variables, modeling flow rates, and stream attributes. The continuous relaxation of this mixed integer nonlinear programming problem is nonconvex because of the presence of bilinear terms in the constraint functions. We propose an algorithm to find the global solution using the principles of the reformulation-linearization technique (RLT). A novel piecewise linear RLT formulation is proposed and applied to the class of generalized pooling problems. Using this approach we verify the global solution of a combinatorially complex industrial problem containing 156 bilinear terms and 55 binary variables, reducing the gap between upper and lower bounds to within 1.2%. © 2005 American Institute of Chemical Engineers AIChE J, 2006