The resolution of a Multi-Objective Optimization Problem (MOOP) does not end when the Pareto-optimal set is found. In real problems, a single solution must be selected. Ideally, this solution must belong to the non-dominated solutions set and must take into account the preferences of a Decision Maker (DM). Therefore, the searching for a single solution (or solutions) in MOOP is done in two steps. First, a Pareto optimal set is found. Multi-Objective Evolutionary Algorithms (MOEA), based on the principle of Pareto optimality, are designed to produce the complete set of non-dominated solutions. Second, a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), can be applied. In this work, a method, based on a weighted stress function, is proposed. It is able to integrate the user's preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importance of the criteria.

Given the global economic and societal importance of the polymer industry, the continuous search for improvements in the various processing techniques is of practical primordial importance. This review evaluates the application of optimization methodologies to the main polymer processing operations. The most important characteristics related to the usage of optimization techniques, such as the nature of the objective function, the type of optimization algorithm, the modelling approach used to evaluate the solutions, and the parameters to optimize, are discussed. The aim is to identify the most important features of an optimization system for polymer processing problems and define the best procedure for each particular practical situation. For this purpose, the state of the art of the optimization methodologies usually employed is first presented, followed by an extensive review of the literature dealing with the major processing techniques, the discussion being completed by considering both the characteristics identified and the available optimization methodologies. This first part of the review focuses on extrusion, namely single and twin-screw extruders, extrusion dies, and calibrators. It is concluded that there is a set of methodologies that can be confidently applied in polymer processing with a very good performance and without the need of demanding computation requirements.