Global optimization of large-scale MIQCQPs via cluster decomposition: Application to short-term planning of an integrated refinery-petrochemical complex

Integrated refinery-petrochemical facilities are complex systems that require advanced decision-support tools for optimal short-term planning of their operations. The problem can be formulated as a mixed-integer quadratically constrained quadratic program (MIQCQP), in which discrete decisions select operating modes for the process units, while the entire process network is represented by input-output relationships based on bilinear expressions describing yields and stream properties, pooling equations, fuels blending indices and cost indicators. We develop a novel decomposition-based algorithm for deterministic global optimization that divides the network into small clusters according to their functionality. Inside each cluster, we derive a mixed-integer linear programming (MILP) relaxation based on piecewise McCormick envelopes, dynamically partitioning the variables that belong to the cluster and reducing their domains through optimality-based bound tightening. Results for an industrial case study in Colombia show profit improvements above 10% and significantly reduced optimality gaps compared with the state-of-the-art global optimization solvers BARON and ANTIGONE.