Chapter 7: Net Flow and Rough Sets: Two Methods for Ranking the Pareto Domain

This chapter presents a description of two multi-objective optimization (MOO) methods, Net Flow Method (NFM) and Rough Set Method (RSM), with a particular focus on engineering applications. Each of the methods provides its own algorithm for ranking the Pareto domain. NFM, which is a hybrid of the ELECTRE and PROMETHEE optimization schemes, employs the preferences of decision-makers in the form of three threshold values for each criterion and one set of relative weights that are used to classify the entire Pareto domain. RSM uses a set of decision rules that are based on the preferences of decision-makers that are established through the ranking of a small, diverse sample set extracted from the Pareto domain. These rules are then applied to the entire Pareto domain to determine the preferred zone of operation. Both methods require the intervention of experts to provide their knowledge and their preferences regarding the operation of the process.

The two methods are used to optimize the production of gluconic acid for multiple objectives. In this fermentation process, it is desired mainly to maximize the productivity and the final concentration of gluconic acid. Other objective functions, the final substrate concentration and the initial inoculum biomass concentration, can also be added to make a three- and four-objective optimization problem. It is shown that NFM and some variants of RSM performed similarly and possess good robustness.