Applications of Genetic Algorithm for Solving Multi-Objective Optimization Problems in Chemical Engineering

49 Any real-world optimization problem involves several objectives. Chemical engineering is no exception. Chemical processes, such as distillation (Figure 1), refinery operations, polymerization, etc., involve a number of process parameters which are to be set for achieving certain properties in the final product. Often such a process is modelled using a number of differential and/or algebraic equations describing the system. Optimization is also used for 'tuning' of first-principles models using experimental/industrial data. The main challenges in a chemical optimization problem are the existence of time-variant decision variables, multiple objectives and uncertainties in the model accuracy. In the early years, the several objectives were scalarized by using their weighted average as a single objective function and optimizing it. Unfortunately, the values of these weighting factors could not be assigned without controversy. The e-constraint method (see Chankong and Haimes, 1983) was probably the first approach used to solve multi-objective problems. In this technique, any one objective was selected for optimization, while the remaining objective functions were converted to equality constraints. This method was quite inefficient computationally, particularly since it involved the solution of several single-objective, highly-constrained problems. In the last decade, several multi-objective adaptations of the stochastic, population-based genetic algorithm (GA) have been developed for solving multiobjective problems efficiently. These could provide the entire Pareto set of optimal solutions in a single application, unlike the e-constraint method. This provided a big boost for solving real-life optimization problems. As discussed in previous articles, two popular adaptations of the simple GA (SGA; for single objective problems), are the non-dominated sorting genetic algorithms, NSGA-I and the elitist NSGA-II (Deb, 2001). Elitism improves the algorithm, but reduces the diversity of the population to some extent. A recent adaptation, NSGA-II-JG (Kasat and Gupta, 2003), inspired by the phenomenon of jumping genes (McKlintock, 1987) in natural biology, has been developed by our group and has been found to overcome the decrease in diversity caused by elitism, and combines the advantages of the elitism and the jumping gene operators. The JG operator is first described, followed by the use of these different adaptations of NSGA in chemical engineering over the years.