Multi-objective Optimization of the Operation of an Industrial Low-Density Polyethylene Tubular Reactor Using Genetic Algorithm and Its Jumping Gene Adaptations

Abstract

In this study, a comprehensive model for an industrial low-density polyethylene (LDPE) tubular reactor is presented. The model parameters are tuned using industrial data on the temperature profile, the monomer conversion and the number-average molecular weight at the end of the reactor, and estimates of the several side products from the reactor. Complete details of the model are provided. Thereafter, a two-objective optimization of this LDPE reactor is performed; the monomer conversion is maximized while the sum of the normalized concentrations of the three important side products (methyl, vinyl, and vinylidene groups) is minimized. Three variants of the binary-coded non-dominated sorting genetic algorithmnamely, NSGA-II, NSGA-II-JG, and NSGA-II-aJGare used to solve the optimization problem. The decision variables used for optimization include the following: the feed flow rates of the three initiators and of the transfer agent, the inlet temperature, the inlet pressure, and the average temperatures of the fluids in the five jackets. Also, the temperature of the reaction mass is constrained to lie below a safe value. An equality constraint is used for the number-average molecular weight (M n,f) of the product, to ensure product quality. Pareto-optimal solutions are obtained. It is observed that the algorithms converge to erroneous local optimal solutions when hard equality constraints such as M n,f = desired number-average molecular weight (M n,d) are used. Correct global optimal Pareto sets are obtained by assembling appropriate solutions from several problems involving softer constraints of the type M n,f = M n,d ± an arbitrary number. Furthermore, the binary-coded NSGA-II-aJG and NSGA-II-JG perform better than NSGA-II near the hard end-point constraints. The solution of a four-objective problem (with each of the three normalized side product concentrations taken individually as objective functions) is comparable to that of the two-objective problem, and the former (more) computationally intensive problem does not need to be solved.

An interactive decision-support system for multi-objective optimization of nonlinear dynamic processes with uncertainty

“…In the last decade the multi-objective optimization aspects in the operation of dynamic processes (resulting in so-called multi-objective dynamic optimization or multi-objective optimal control problems (MOOCPs)) have gained 50 interest (see, e.g., Deb et al (2004); Sarkar & Modak (2004); Agrawal et al (2006); Logist et al (2010Logist et al ( , 2012). It has to be mentioned that these infinite dimensional optimal control problems are typically discretized resulting into finite dimensional large-scale nonlinear optimization problems (NLPs).…”

MMA bulk polymerization and its influence on in situ resin viscosity comparing several chemorheological models

“…Recent reviews have treated dynamic conversion in bulk radical polymerization, [1][2][3] and specific models have been developed for polypropylene, 4 polyphenylene oxide, 5 polymethyl methacrylate (PMMA), [6][7][8] other acrylates, 9 polyamides, 10 epoxies, 11 norbornenes, 12,13 and low density polyethylene, 14,15 with the focus on plant efficiency and safety. 16,17 Similar rheological assessments during chemical reaction have also been performed with reactive extrusion.…”

Selecting Model Parameter Sets from a Trade-off Surface Generated from the Non-Dominated Sorting Genetic Algorithm-II

“…The generation of Q o allows a check for global non-domination for both parent and offspring solutions (Deb 2001;Deb and Goel 2001;Deb et al 2000Deb et al , 2002. The NSGA-II has been applied widely in several different studies (Rakesh and Chandan 2005;Agrawal et al 2006;Atiquzzaman et al 2006;Jeong and Abraham 2006;Sarkar and Modak 2006;Shafii and Smedt 2009). Specifically in hydrological model calibration studies (Bekele and Nicklow 2007;Wöhling et al 2008;Confesor and Whittaker 2007;Gill et al 2006;Tang et al 2006;Khu and Madsen 2005;Madsen 2003) have used NSGA-II to generate a trade-off surface for different objectives.…”