Symbolic integration of logic in mixed-integer linear programming techniques for process synthesis

Abstract

This paper deals with the branch and bound solution of synthesis problems that are modeled as mixed-integer linear programming (MILP) problems. Logic relations between potential units in a superstructure are considered through symbolic integration within the numerical based branch and bound scheme. The objective of this integration is to reduce the number of nodes that must be enumerated by using the logic to decide on the branching of variables, and to determine by symbolic inference whether additional variables can be fixed at each node. Two different strategies for performing the integration are proposed that use the disjunctive and conductive normal form representations of the logic, respectively. The paper also addresses the question of how to systematically generate the logic for process flowsheet superstructures. Computational results are presented to compare the performance of the proposed methods and a variant that includes violated logic inequalities in the model with the cases when all logic inequalities are included in or excluded from the model.