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.