Methodology to Solve the Multi-Objective Optimization of Acrylic Acid Production Using Neural Networks as Meta-Models

It is paramount to optimize the performance of a chemical process in order to maximize its yield and productivity and to minimize the production cost and the environmental impact. The various objectives in optimization are often in conflict, and one must determine the best compromise solution usually using a representative model of the process. However, solving first-principle models can be a computationally intensive problem, thus making model-based multi-objective optimization (MOO) a time-consuming task. In this work, a methodology to perform the multi-objective optimization for a two-reactor system for the production of acrylic acid, using artificial neural networks (ANNs) as meta-models, is proposed in an effort to reduce the computational time required to circumscribe the Pareto domain. The performance of the meta-model confirmed good agreement between the experimental data and the model-predicted values of the existent relationships between the eight decision variables and the nine performance criteria of the process. Once the meta-model was built, the Pareto domain was circumscribed based on a genetic algorithm (GA) and ranked with the net flow method (NFM). Using the ANN surrogate model, the optimization time decreased by a factor of 15.5.

Pareto domain: an invaluable source of process information

Due to the highly competitive market and increasingly stringent environmental regulations, it is paramount to operate chemical processes at their optimal point. In a typical process, there are usually many process variables (decision variables) that need to be selected in order to achieve a set of optimal objectives for which the process will be considered to operate optimally. Because some of the objectives are often contradictory, Multi-objective optimization (MOO) can be used to find a suitable trade-off among all objectives that will satisfy the decision maker. The first step is to circumscribe a well-defined Pareto domain, corresponding to the portion of the solution domain comprised of a large number of non-dominated solutions. The second step is to rank all Pareto-optimal solutions based on some preferences of an expert of the process, this step being performed using visualization tools and/or a ranking algorithm. The last step is to implement the best solution to operate the process optimally. In this paper, after reviewing the main methods to solve MOO problems and to select the best Pareto-optimal solution, four simple MOO problems will be solved to clearly demonstrate the wealth of information on a given process that can be obtained from the MOO instead of a single aggregate objective. The four optimization case studies are the design of a PI controller, an SO2 to SO3 reactor, a distillation column and an acrolein reactor. Results of these optimization case studies show the benefit of generating and using the Pareto domain to gain a deeper understanding of the underlying relationships between the various process variables and performance objectives.

Multiobjective Optimization of an Industrial Styrene Reactor Using the Dual Population Evolutionary Algorithm (DPEA)

In the last few years, multiobjective evolutionary algorithms (MOEAs) have gained significant interest as a reliable option to optimize problems with conflicting objectives in science and engineering. These algorithms generate an optimal set of trade-off solutions referred to as the Pareto domain. In this investigation, a MOEA was used to optimize simultaneously conflicting design variables of an industrial styrene reactor. The dual population evolutionary algorithm (DPEA) was implemented to optimize the productivity, yield, and selectivity of styrene. To evaluate the robustness and versatility of the algorithm, two and three objective optimization case studies were conducted for three different configurations of the reactor: adiabatic, steam-injected, and isothermal.Results indicated that DPEA is a robust optimization strategy to generate a well-defined Pareto domain with a wide range of solutions. In addition, the Pareto-optimal solutions of the steam-injected configuration were superior to the adiabatic reactor and to a portion of the isothermal configuration. The optimal operating conditions corresponding to the Pareto domains were also slightly better in terms of profit when compared with previously published studies. The Pareto domains were then ranked using the Net Flow Method (NFM), a ranking algorithm that incorporates the knowledge and preferences of an expert into the optimization routine.

Multi-Objective Optimization of an Ethylene Oxide Reactor

In this study, multi-objective optimization is performed for a reactor producing ethylene oxide from ethylene. The optimization considered three objectives: the maximization of the ethylene oxide production and selectivity, and the maximization of a safety factor related to the presence of oxygen in the reactor. The Pareto domain for this optimization problem was first approximated using the Objective-Based Gradient Algorithm, and the Pareto-optimal solutions were ranked using the Net-Flow procedure to determine the best operating conditions. From the optimization results, it is recommended that the ethylene oxide reactor be operated at high inlet pressure and gas temperature, and low inlet volumetric gas flowrate and chemical reaction moderator concentration. These operating conditions led to the highest ranked compromise solution, balancing the trade-off between each of the three objectives. Finally, it was found that a decrease in the inlet pressure or variation in the volumetric gas flowrate could readily lead to operating conditions outside of the Pareto domain, and these input variables should therefore be carefully controlled throughout operation of the reactor.