### 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,M-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,M-f = desired number-average molecular weight (M-n,M-d) are used. Correct
global optimal Pareto sets are obtained by assembling appropriate solutions from
several problems involving softer constraints of the type N-n,N-f = M-n,M-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.