(26b) Deterministic Global Optimization Approach to Midterm Planning of an Industrial Integrated Petroleum-Petrochemical Facility
Herein, we formulate a Mixed-Integer Quadratically-Constrained Quadratic Program (MIQCQP) to solve within a certain global optimality gap a midterm supply-chain problem for a full-scale integrated refinery â petrochemical complex in the context of the Colombian hydrocarbon market. Our approach clusters the refinery topology into subprocesses according to their functionality. For each cluster, a relaxed model (MILP) based on generalized11 and piecewise McCormick envelopes is formulated. The number of partitions (NP) for the discretized variables inside the cluster change dynamically, while variables that do not belong to the cluster are not discretized. The MILP solution provides a Lower Bound (LB) for the original problem. Then, fixing the binary variables obtained from the relaxed model solution, the original MIQCQP is transformed into a quadratic problem (QP) which provides an Upper Bound (UB). If the UB is improved, Optimality-Based Bound Tightening (OBBT)12 is applied to reduce the domain for the variables belonging to the cluster. This procedure is repeated until a stopping criteria is met, such us reaching maximum runtime, exploring all clusters or obtaining and optimality gap less than epsilon.
The methodology was tested through five cases studies that recreate typical planning scenarios for the Colombian hydrocarbon industry. The model has about 6975 equations, 35104 nonlinear terms derived from bilinear and trilinear expressions, 9592 and 279 continuous and discrete variables respectively. Results show that commercial solvers for deterministic global optimization13,14 get stuck at a local optimum solution with an optimality gap above 50%, on average. Furthermore, there is no improvement in the UB if the CPU time is increased from 2 to 6 hours. In contrast, we found a better UB for all the case studies with a maximum runtime of 1.3 hours on average. This demonstrates that clustering decomposition is a promising solution strategy for problems of that scale. Future work will incorporate the Reformulated Normalized Multiparametric Disaggregation Technique15 for comparison with the piecewise McCormick envelopes.
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