Multi-objective Design Optimization of an Industrial Ldpe Tubular Reactor Using Jumping Gene Adaptations of Nsga and Constraint Handling Principle

Multi-objective optimization of an industrial low-density polyethylene (LDPE) tubular reactor is carried out at design stage with the following objectives: maximization of monomer conversion and minimization of normalized side products (methyl, vinyl, and vinylidene groups), both at the reactor end, with end-point constraint on number-average molecular weight (Mn,f) in the product. An inequality constraint is also imposed on reactor temperature to avoid run-away condition in the tubular reactor. The binary-coded elitist non-dominated sorting genetic algorithm (NSGA-II) and its jumping gene (JG) adaptations are used to solve the optimization problem. Both the equality and inequality constraints are handled by penalty functions. Only sub-optimal solutions are obtained when the equality end-point constraint on Mn,f is imposed. But, correct global optimal solutions can be assembled from among the Pareto-optimal sets of several problems involving a softer constraint on Mn,f. A systematic approach of constrained-dominance principle for handling constraints is applied for the first time in the binary-coded NSGA-II-aJG and NSGA-II-JG, and its performance is compared to the penalty function approach. Introduction Low-density polyethylene (LDPE) is one of the most widely used polymers in the world. Nearly one quarter of its annual production of 84 million tones worldwide, is produced by highpressure technology (Kondratiev and Ivanchev, 2005). Therefore, even small improvement in polymer production and/or properties can generate large revenue for the poly-olefins industry. The end properties of polymer, viz., tensile strength, stiffness, tenacity etc. are related to molecular parameters, which include average molecular weight, polydispersity index, shortand long-chain branching, and distribution of functional groups etc. The operating and design variables often influence the molecular parameters in non-commensurable ways. Therefore, these applications are perfect scenarios for multi-objective optimization (MOO). This article presents enhancement in the production, quality and strength of LDPE, simultaneously, by MOO of an industrial high-pressure tubular reactor for ethylene polymerization at design stage. The non-dominated sorting genetic algorithm (NSGA-II; Deb, 2001) and its jumping gene (JG) adaptations (Simoes et al., 1999; Kasat et al., 2003; Man et al., 2004; Shrikant et al., 2006) are used to optimize the reactor performance. Many studies on the modeling and simulation of high-pressure tubular reactor to produce LDPE have been reported in the literature, which were reviewed by Zabisky et al. (1992) and Kiparissides et al. (1993). In contrast, only some studies (Yoon and Rhee, 1985; Mavridis and Kiparissides, 1985; Brandolin et al., 1991; Kiparissides et al., 1994; Cervantes et al., 2000; Asteasuain et al., 2001; Yao et al., 2004) have appeared on the optimization of LDPE tubular reactor in the open literature. But, interestingly, all the studies on modeling used different kinetic parameters to simulate the reactor. Zabisky et al. (1992), Kalyon et al. (1994), and Brandolin et al. (1996) used