A Lagrangean Heuristic Approach for the Simultaneous Cyclic Scheduling and Optimal Control of Multi-Grade Polymerization Reactors

In this work we apply a decomposition technique to address the simultaneous scheduling and optimal control problem of multi-grade polymerization reactors. The simultaneous scheduling and control (SSC) problem is reformulated using Lagrangean Decomposition as presented by Guignard and Kim1. The resulting model is decomposed into scheduling and control subproblems, and solved using a heuristic approach used before by Van den Heever et.al.2 in a different kind of problem. The methodology is tested using a Methyl Methacrylate (MMA) polymerization system, and the High Impact Polystyrene (HIPS) polymerization system, with one continuous stirred-tank reactor (CSTR), and with a complete HIPS polymerization plant composed of a train of seven CSTRs. In these case studies, different polymer grades are produced using the same equipment in a cyclic schedule. The results of the heuristic decomposition technique are compared against those obtained by solving the problem without decomposition, whenever both solutions were available. The presence of a duality gap for the decomposed solution is observed, as expected, when integer variables and other nonconvexities are present. Computational times in the first two examples were lower for the decomposition heuristic than for the direct solution in full space, and the optimal solutions found were slightly better. The example related to the full scale HIPS plant was only solvable using the decomposition heuristic.