Lagrangean heuristic for the scheduling and control of polymerization reactors

Abstract

A decomposition technique is applied to address the simultaneous scheduling and optimal control problem of multigrade polymerization reactors. The simultaneous scheduling and control (SSC) problem is reformulated using Lagrangean decomposition as presented by Guignard and Kim. The resulting model is decomposed into scheduling and control subproblems, and solved using a heuristic approach used before by Van den Heever et al. 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. © 2007 American Institute of Chemical Engineers AIChE J, 2008

Combined Noncyclic Scheduling and Advanced Control for Continuous Chemical Processes

“…They also study simultaneous selection of closed-loop controllers and selection of controller parameters with the scheduling problem for polymerization processes [36,37]. Terrazas-Moreno and Flores-Tlacuahuac also investigate simultaneous cyclic scheduling and control of continuous chemical processes, and study a langrangean heuristic method for reduction of computational burden [15,18]. Baldea et al and Du et al demonstrate reduction of computational burden of the integrated problem by using reduced order, or scale-bridging models (SBM), in scheduling [8,21].…”

“…The majority of integrated scheduling and control formulations have used cyclic schedules [7][8][9][10][11][15][16][17][18][19][20][21][22]. However, it has been suggested that a dynamic cyclic schedule may improve process economics [23].…”

Sustainability and process control: A survey and perspective

“…Most of them attempt to introduce control considerations at the scheduling level, i.e. formulate the scheduling problem using detailed large-scale process models along with the corresponding control actions, possibly allowing for closedloop implementation [455][456][457][458][459]. The resulting problem, typically a mixed integer dynamic optimization problem, is computationally intensive, requiring specialized solution approaches [460,461].…”

A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries

“…In order to compare these algorithms, DICOPT works better for models within an important and difficult combinatorial part, while SBB performs better for models with fewer discrete variables but more difficult nonlinear programming problems. It important to quote that these solvers do no guarantee to get the global optimal solution; for the optimal solution of large scale MINLP problems, decomposition approaches are normally required (see Terrazas-Moreno et al, 2008).…”