Artificial intelligence in single screw polymer extrusion: Learning from computational data

Engineering Applications of Artificial Intelligence 116 (2022) 105397 Contents lists available at ScienceDirect Engineering Applications of Artificial Intelligence journal homepage: www.elsevier.com/locate/engappai Artificial intelligence in single screw polymer extrusion: Learning from computational data António Gaspar-Cunhaa,∗,Francisco Monacob,Janusz Sikorac,Alexandre Delbemb aInstitute for Polymers and Composites, University of Minho, Campus of Azurém, 4800-058 Guimarães, Portugal bInstitute of Mathematics and Computer Science, University of São Paulo, 400 Trabalhador São-Carlense Avenue, São Carlos, São Paulo 13566-590, Brazil cFaculty of Mechanical Engineering, Lublin University of Technology, 38 Nadbystrzyska Str., 20-618 Lublin, Poland ARTICLE INFO Keywords: Polymer extrusion Single screw Artificial intelligence Multi-objective optimization Data-mining ABSTRACT Single screw polymer extrusion can be seen as a multi-objective optimization problem where a set of design variables must be defined as a function of objectives and constraints that are to be satisfied simultaneously. The development of powerful modelling routines based on the use of numerical methods allows linking those objectives with the decision variables. In reality, only a single solution can be used in the problem under consideration. However, the computation times become prohibitive when effective optimization algorithms dealing with multi-objectives and decision-making are to be used, such as those based on populations of solutions. It is proposed here the use of Artificial Intelligence techniques to determine the interrelation between the design variables and the objectives. For that, a data analysis technique, named DAMICORE, was used to define these interrelations. Examples, involving the design of a screw extruder, a barrel grooves section, and a rotational barrel segment, were investigated using the proposed AI techniques. The results obtained show a good correspondence with the expected thermomechanical behaviour of the process. This constitutes an initial step in the application of AI techniques in different fields of engineering in the way of accomplishing, in the future, optimization based on the use of available data. 1. Introduction Single screw polymer extrusion is one of the most important plastics transformation technologies allowing to the production of a great variety of products, including pipes, profiles, film, and fibres. The process goes through several stages: plasticizing, shaping, and ancillary operations, which depend on the type of product to be produced. Plasticizing is the most important phase since it allows transport of the solid polymer, melting and mixing it, and creating the required pressure for the melted polymer to cross the die that gave the final shape to the product. This is a complex process in which the raw material, in pellets or powder form, is fed into the extruder where it melts by the action of heat conducted from the barrel and heat generated by friction and viscous dissipation. This involves the flow of the polymer in different physical states, solid, melt, and the coexistence of both. Also, the material has very specific properties, such as low thermal conduction and non-Newtonian behaviour, and the system is characterized by a complex geometry (Rauwendaal,1986;Agassant et al.,2017). Polymer engineering, like other fields of engineering and science, is faced frequently with the challenge to improve product properties while decreasing the costs and the quantity of material needed. ∗Corresponding author. E-mail addresses: [email protected] (A. Gaspar-Cunha), [email protected] (F. Monaco), [email protected] (J. Sikora), [email protected] (A. Delbem). Traditionally, to perform the required optimization, trial-and-error procedures based on experiments were adopted, involving a long and expensive effort. It is very frequent, even nowadays, the use of Taguchi methods to define the set of experiments to do, as a function of the decision variables, and, after the experimental results are obtained, some data analysis and/or regression techniques are applied to attain a simple equation or a response surface relating the decision variables with the objective (usually a single objective) (Taguchi,1990;Fei et al.,2013). Therefore, to have a good representation of reality, the number of experiments to do increases considerably with the number of decision variables needed and specific methodologies must be applied to take into account multiple objectives. With the development of numerical modelling software, experimentation was replaced by computer calculations allowing a fast and less expensive design/optimization process (Mehat and Kamaruddin, 2012). However, as with most real optimization problems, plasticizing extrusion is a hard problem to solve, involving discrete and continuous variables, convex and nonconvex search spaces, a huge number of decision variables and constraints, and multiple objectives. Also, the extruder machine is exposed to the environment, which implies https://doi.org/10.1016/j.engappai.2022.105397 Received 2 February 2022; Received in revised form 28 July 2022; Accepted 26 August 2022 Available online 22 September 2022 0952-1976/©2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 1. Single screw extrusion: system geometry, unrolled channel, and plasticizing phases. that it is subject to some significant uncertainties, such as the environmental temperature that influences barrel temperature and, as a consequence, the polymer melting. This implies that the solution obtained must be robust against changes in the environment (GasparCunha and Covas,2008;Denysiuk et al.,2018). An extensive and very recent revision of optimization of polymer processes was presented elsewhere (Gaspar-Cunha et al.,2022a,b). Taking into account the multi-objective nature of this problem, Multi-Objective Evolutionary Algorithms (MOEAs) or other populationbased algorithms, e.g., Multi-Objective Ant Colony Optimization (MOACO), Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Simulated Annealing (MOSA), and Multi-Objective Differential Evolution (MODE), can be applied (Deb,2001;Leguizamón and Coello,2011;Coello et al.,2004;Agrawal et al.,2008;Suman and Kumar,2006;Mezura-Montes et al.,2008). Nevertheless, the performance of an optimization procedure is strongly dependent on the modelling capacity to capture the characteristics of the process under study. Due to the complexity of the plasticizing extrusion, the differential equations that govern the process can be solved analytically or numerically. While in the former case the resulting equations are not able to take into account all the parameters and can be difficult to link the different stages of the process due to those simplifications, the second case involves high computation times to evaluate a single solution. Also, some complex engineering problems require the use of more than one numerical modelling software, such as, for example, if the aim is to analyse the mechanical behaviour of a plastic part and, simultaneously, it is necessary to analyse the flow of the polymer inside the tools used in its manufacture. Therefore, the application of AI techniques to deal with the eventual scarcity of data can be of primal importance. Simply, the application of data mining techniques can easily generate surrogates or metamodels linking directly the objectives with the decision variables, which can be incorporated in the evaluation phase of a Multi-Objective Optimization Algorithm (MOOA) to optimize the process (Pavelski et al., 2016). However, the nature of these complex problems requires some degree of interaction with a Decision Maker (DM), since it is necessary to define the relevant decision variables, constraints, and objectives. Simultaneously, in a multi-objective environment, the final solution of a Multi-Objective Optimization Problem (MOOP) is a set of Pareto points that requires the intervention of the DM to select the single solution to be used in the real world (Gaspar-Cunha et al.,2022b;Aittokoski et al., 2009). In this context, Machine Learning (ML) can play an important role in reducing these interactions by creating an intelligent system that can give a good answer, or at least a good approximation, concerning the solution to the problem under study (Jin et al.,2019;Ibañez et al., 2020). The main aim of this work is to apply a data mining framework named DAMICORE (Anon,2022) to capture the relations between the decision variables and the objectives regarding the data of the extrusion process taking into account new geometrical devices developed within the NEWEX project (Sanches et al.,2011a), namely: (i) special screws; (ii) active grooved feed sections and (iii) rotational barrel segments. The results were calculated using numerical modelling software. The decision variables are of two different categories, the ones that are directly involved in the calculations of the objectives and others that are not involved in the calculations. Therefore, the aim is not to optimize the process but only to capture these interrelations. The study will be performed using four different groups of data: a simple case, where only changes in the screw geometry and operating conditions of the machine were made; a case where the geometry of grooves was considered separately; a case where the geometry and operating conditions of the rotational barrel segment are considered; and, finally, a case where all the previous data is mixed together to infer about the influence of operating conditions and screw, grooves and rotational barrel segment geometry. This paper is organized as follows: in section two the polymer extrusion process, the modelling software, and the optimization problem are explained; in section three the state-of-the-art concerning data-driven 2 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 optimization and DAMICORE are presented; in section four the cases studied will be presented and the results obtained will be presented and discussed, and in section five the conclusions will be stated. 2. Polymer extrusion 2.1. Problem to solve In a single screw extruder, an Archimedes type screw rotates inside a heated barrel at a constant speed (N), as illustrated in Fig. 1. This figure also shows the transversal cuts in the different stages of the process, as indicated by the black arrows. The solid polymer, in pellets or powder form, is fed in the hopper and after melting and pressurized is forced to pass through the die. The mathematical modelling of plasticizing consists of solving the differential momentum and energy equations for each one of the stages identified taking into account the boundary conditions and a continuous link between the different stages, i.e., the results of one step are the starting point for the subsequent. For example, the following simplified momentum and energy equations must be solved for the melt flow zones of the process (Gaspar-Cunha,2009): 𝜕𝑃 𝜕𝑥 =𝜕 𝜕𝑦 (𝜂𝜕𝑉𝑥 𝜕𝑦 )(1) 𝜕𝑃 𝜕𝑧 =𝜕 𝜕𝑦 (𝜂𝜕𝑉𝑧 𝜕𝑥 )+𝜕 𝜕𝑦 (𝜂𝜕𝑉𝑧 𝜕𝑦 )(2) 𝜌𝑚𝐶𝑚𝑉𝑧(𝑦)𝜕𝑇 𝜕𝑧 =𝑘𝑚(𝜕2𝑇 𝜕𝑥2+𝜕2𝑇 𝜕𝑦2)+𝜂 𝛾2(3) where 𝑇is the melt temperature, P is the pressure, 𝑉xand 𝑉zare the melt velocities in the 𝑥and z directions, respectively, 𝜌m,𝐶mand 𝑘mare the specific mass, specific heat and thermal conductivity of the melt, respectively, 𝛾 is the shear rate and 𝜂is the viscosity. The pressure gradient in the 𝑦-direction is nil (Gaspar-Cunha,2009). For that purpose, the screw channel was unrolled (as illustrated in Fig. 1) and is considered a rectangular channel where all thermomechanical phenomena described occur and the calculations are performed in small increments along the channel using numerical methods. Therefore, the performance of the machine depends on the polymer properties (physical, thermal, and rheological), operating conditions (screw speed and barrel and die temperature profiles), and screw geometry, and can be measured by taking into account the purposes of the extruder, namely: output, average melt temperature, length of the screw required for melting the polymer, mechanical power consumption, mixing degree and viscous dissipation. Fig. 1 illustrates the use of a conventional screw, consisting of three zones: (i) feed zone, characterized by having a constant depth (𝐻i1); (ii) compression zone, where the depth decreases; and (iii) metering zone, with a constant depth, but smaller (𝐻i3). Within this work, the aim is to study the influence of the use of a Grooved Barrel Section (GBS) in the feed zone and a Rotational Barrel Segment (RBS) in the metering zone, to improve the pressure generated and the mixing induced, respectively. Improving the process consists in defining the value of the decision variables, operating conditions and system geometry, that optimize the objectives, i.e., maximization of output and mixing degree, and minimization of melt temperature at die exit, mechanical power consumption, and the length required for melting (Carrano et al., 2015). 2.2. Modelling of polymer extrusion The general characteristics of the program used in the calculations are related to the plasticizing phases, as illustrated in Fig. 1 (GasparCunha,2009): a) Solids conveying in the hopper (1D): analytical equations, where the pressure is determined by a mass balance and the force balance resulting from friction between the polymer and hopper walls (external friction) and between polymer and polymer (internal friction) and by gravity. b) Solids conveying (1D+): a non-isothermal flow of a solid plug with heat friction at all surfaces. Output is obtained by taking into account the geometry and the velocity profile in the barrel, pressure is obtained by a balance of forces and momentum and temperature by solving the energy equation in direction y, but with the calculations performed for small increments in the channel (z) direction (1D+). c) Delay (1D+): solid plug with a melt film near the inner barrel surface. The solids are modelled as in the solids conveying zone and the melt film is solved by taking into account the energy equation in the 𝑦-direction and the computations made for small increments in the 𝑧-direction. d) Melting I (1D+ and 2D+): using the 5-Zone Lindt model (Lindt and Elbirli,1985), where the melt pool increases its dimensions until total melting. The solid plug and the melt films are modelled as in the delay zone, while in the melt poll the equations of energy and momentum are solved simultaneously with mass balances and boundary conditions using finite differences in the 2D non-isothermal flow of a Non-Newtonian fluid. e) Melt conveying (2D+): 2D non-isothermal flow of a non-Newtonian fluid obtained through the simultaneous resolution of the energy and momentum equations, being the calculations performed in small increments along 𝑧-direction. f) Flow in the die (2D+): 2D non-isothermal flow of a NonNewtonian fluid, equal to the melt conveying zone. The details of the modelling, computer implementation, and experimental assessment can be found in Gaspar-Cunha (2009), except in what concerns the modelling of the barrel grooved section and rotational barrel segment, which is described next. In the last forty years, numerous theoretical and experimental studies have been performed using extruders with grooves in the barrel, from which it can be verified that there are two main methods of approaching the problem, the first considers that the coefficient of friction polymer-barrel with grooves can be replaced by an average friction coefficient, the second considers the existence of the flow of granules throughout the grooves (Potente,1985). The main objective of the grooves is to increase the coefficient of friction between the solid polymer granules and the inner wall of the cylinder, which is known to increase the throughput capacity of the extruder. The grooves can be longitudinal or helical (Fig. 2). Following the study presented in Gaspar-Cunha (2009), in this work the model of Potente (1985) was adopted to calculate the average friction coefficient. This method considers that the increase of friction caused by the grooves can be quantified by replacing the coefficient of friction polymer-cylinder with the average friction coefficient (𝑓ef ). The average effective friction coefficient results from the fact that when the solids bed moves along the screw channel, the barrel friction varies between the polymer-barrel friction (𝑓b) and the internal (polymer– polymer) friction (𝑓p−p), resulting in the following equation (Potente, 1985;Gaspar-Cunha et al.,2018): fef =𝑓𝑏+(𝑓𝑝−𝑝−𝑓𝑏)𝐵 𝜋𝐷𝑏{1 − exp [−𝛼(ℎ𝑁 𝐵𝑁𝑁)𝛽]} (4) where 𝛼and 𝛽are empirical constants, which for the conditions used should have the values of and 0.9, respectively, 𝐷bis the internal barrel diameter, 𝑁Nis the number of grooves, and B is the total with of grooves, given by: B=b𝑁N𝑁(5) Finally, the rotational barrel segment is located in the metering zone of the extruder, i.e., when the polymer is completely melted. It 3 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 2. Longitudinal and helical grooves in the barrel (𝑏𝑁is the grooves width and ℎ𝑁is the height of the grooves). Fig. 3. Definition of the relative barrel velocity (V’b). can rotate in the same or opposite direction as the screw and is in contact with the melted polymer. This is an innovative device that was described by Sikora and Sasimowski (Sikora and Sasimowski, 2006b,a;Sikora and Sikora,1998;Sasimowski,2008;Sasimowski et al., 2014) and modelled by Gaspar-Cunha (2019). The aim is to control the thermal, rheological, kinematic, and dynamic conditions in the plasticizing system, and, as a consequence, to improve the quality of the products because enhancing the above processes will result in the homogenization of the thermal and mechanical properties of materials and the structure of the products, without the need to use additional, expensive devices such as the gear pump and static mixer. Fig. 3 shows the three different situations that can occur when an RBS is implemented in an extruder: (a) the velocity of the RBS (𝑁b) is nil; (b) the velocity of the RBS has the same direction as that of the screw (𝑁s) and (c) the velocity of the RBS has a different direction than that of the screw. In the first case, the relative barrel velocity (𝑉b) results by transforming the rotational screw speed (𝑁s) in a linear velocity near the interior barrel velocity (see Ref. (Gaspar-Cunha, 2009)), this is: 𝑉b=𝜋 𝑁sD (where D is the external screw diameter). In the second case, the resulting (𝑉′b) velocity is reduced, while in the third the resulting velocity increases. All these three situations are implemented in the global plasticizing computer program. 3. Data-driven optimization 3.1. State-of-the-art Solving real-world optimization problems requires some interaction with the DM, usually the experts in the field. This is more pertinent when dealing with a MOOP. Thus, the aim is, based on data analysis, to reduce these interactions, creating an intelligent system able to give a good answer to the problem, or, at least, a good approximation to the (single) final solution. This is the role of (unsupervised and semi-supervised) machine learning, of being able to build a model with a low quantity of data. Also, there is a particular type of application that occurs when there is no direct link between decision variables and objectives, i.e., the absence of calculations, e.g., to link the operating conditions of the machine (decision variables) with its performance (objectives). This enables the use of AI techniques as a procedure for improving prediction by linking optimization procedures and facilitating decision-making (Chinesta et al.,2020). The application of data-driven algorithms can be seen (at least) in two ways: (i) use of surrogates or metamodels that replace the original method of calculating the objectives, making use of data analysis 4 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 previously made to determine the parameters of the model chosen, such as polynomial regression (Zhou et al.,2005), kriging (Chugh et al., 2018), Artificial Neural Networks (ANNs) (Jin and Sendhoff,2004), radial basis function networks (Regis,2014), swarm optimization (Sun et al.,2017); and (ii) use of data to help the computer system in deciding on the best solution to use in the specific problem (Dimiduk et al.,2018), i.e., automatic optimization, in the threshold of AI. A data-driven optimization structure is based on four main components: (i) data generation, experimental and/or computational; (ii) data pre-processing, such as sorting the data by one of the objectives to reduce the amount of data necessary; (iii) machine learning to estimate the surrogate model; and (iv) an optimization algorithm, making use of the surrogate model to find the solution. The aim is to extract models from the relation between inputs and outputs to predict the output from new inputs using numerical methods able to take into account the physical models present in the system. This is an alternative modelling approach for optimization. This constitutes a data-science field called Engineering AI, which involves multidimensional data visualization, data classification, modelling through surrogate models, extracting knowledge from data, and creating data-driven application systems (Ibañez et al.,2020). The quality and type of data play an important role in the entire process. First, machine learning can be based on direct or indirect data. In the first case, the data is obtained directly from the problem, by experiments, or by computation. In this case, the surrogate is obtained by training the data to fit in the model (Jin,2011;Chugh et al., 2019). Indirect data is the occasional data, and that is not possible to predict the type of data that can be generated, e.g., the environmental temperature that influences the extrusion process during the melting phase. Also, the data can be collected online or offline. Data collected offline means that no new data can be generated during the optimization. Thus, the quality of the surrogate model depends on the quality and quantity of data, namely in what concerns data pre-processing, data mining, and synthetic data generation, since it is difficult to validate the model before the solution is found to be applied in practice. When the data is collected online means that as the data is collected the model adapts to the results of the practical problem (Jin,2011;Jin et al., 2002;Hüsken et al.,2005). Finally, during the optimization process, at the beginning the data is generated randomly in the search space (in the case of Evolutionary Algorithms (EAs), for example), introducing some degree of uncertainty in the model. As a consequence, the optimal solution can be far from the initial solutions proposed by the algorithm and the model can generate wrong predictions when the solutions approach the optimum. However, if some data is obtained as the optimization evolves, the surrogate will be able to provide a better approximation around the optimum (Jin et al.,2002). This corresponds to a balance between exploitation, in the case of the initial data, and exploration, in the case of data obtained near the optimum. Anyway, kriging models can provide confident level information, while ensemble machine learning can provide uncertain information. Both are important to the optimization process. Different AI-based metamodels, i.e., modelling methods or machine learning techniques, were described in the literature, including linear and nonlinear regression, Support Vector Machines (SVM) (Cristianini and Taylor,2000), Incremental dynamic model decomposition (Schmid,2010;Williams et al.,2015), ANNs (Goodfellow et al., 2016), decision trees, and Code2Vect (Argerich et al.,2019). However, a limitation of machine learning is the possibility of the system being influenced by other variables not considered when the model is obtained. Kohonen networks, for example, are ANNs that can learn how to arrange data in an unsupervised way (Kohonen,2001;Seiffert and Jain, 2002), i.e., it requires no labelled samples. It places neurons from a bi-dimensional grid (neighbour neurons communicate) to find the best coverage of a set of n-dimensional vectors (samples) by the neurons. The assignment between neurons and samples naturally results in data clustering. The process of choosing the neuron’s displacements is self-organized and the resulting clustering is called a self-organized map. Cellular NN is another type of bi-dimensional grid (with local communication among neurons) that can learn from a set of unlabelled samples in a way that a stimulus (input) makes the outputs of the neurons oscillate until finding an equilibrium point (output). Both of those grid-based NN, as well as other unsupervised techniques, require inputs in a structure of n-dimensional vectors of features. They both apply reinforcement learning whose success usually requires data that possesses some locality to avoid many spurious feedbacks (which may become critical when modelling a system subject to exogenous factors — variables). Although the mapping of samples to feature vectors is a common practice, it may constrain the applicability of Artificial Intelligence in some fields since it may require experts on the problem domain, which is not easily available on the frontiers of knowledge. Kohonen and Cellular NN date from the 1980s and their applicability for several areas has been well mapped since then. Another perspective emerged in the first decade of the century that enabled the estimation of distances by compression algorithms (called NCD), which means that no feature vector or prior knowledge from data is required. It opened new opportunities to create ways to face the challenges of some realworld problems. The investigations of its potential for unsupervised and semi-supervised learning as well as optimization started in the last decade. DAMICORE (proposed in 2011) is a framework based on NCD aiming at facilitating investigations and developments of solutions in challenging scenarios, such as those where a small amount of raw data is available and the corresponding system is unshielded from exogenous effects. Most of the real optimization problems are characterized by a high number of decision variables, and high search space, but also by high dimensionality in the Pareto surface. In this way, data mining can be useful in clustering the Pareto front in such a way to enable the determination of the decision variables that influence a particular cluster, i.e., each cluster has its meaning – to the problem. The use of a single optimization methodology does not allow for the complete characterization of the region of optimality by (data mining) design rules (Deb and Srinivasan,2007;Deb et al.,2014). In the scenario of mining complex data (as those involving high dimensional search and objective spaces), DAMICORE can find useful information since it enables learning from raw data in a complete data agnostic way (it requires no priors). In other words, the mapping from decision space to objective space can be investigated independently from the dimensionality of them or the problem properties. Section 3.2 introduces the rationale of such a strategy based on DAMICORE and FS-OPA (Kharrat et al.,2020;Soares et al.,2017), a first DAMICOREbased method with practical results for feature sensitivity analysis to objectives of low-level (or one) expert knowledge. 3.2. Feature sensitivity analysis A Feature Sensitivity (FS) analysis aims at finding a set with the principal features of a problem, taking into account a real-world context (e.g., the database quality and its relevance for a purpose), its feature interactions, and their contribution to a target or objective. Such a scope differs from those that the standard feature selection algorithms have succeeded in. This is, an FS strategy is expected to benefit the learning of a problem from scratch. Such learning can induce a model for optimization algorithms (such as in Estimation of Distribution Algorithms — EDAs). We use phylogram-based models since they are adequate to work with small datasets and there is an optimization approach adequate to use such models: the Optimization based on Phylogram Analysis (OPA). Fig. 4 shows a diagram synthesizing OPA within the use of the FS analysis by it; that combination is called FS-OPA. The two principal FS steps involved are: (i) ‘‘Salienting Samples (SS) according to a criterion’’ 5 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 4. Diagram of the Optimization-based on Phylogram Analysis — OPA. Fig. 5. SS procedure that obtains the selected samples as shown in Fig. 4. and (ii) applying DAMICORE to construct a phylogram-based model. SS ranks the samples according to each of the Mcriteria (or nondominated fronts), producing the sets of selected samples (Fig. 5), denoted BC1 (the Best found samples according to Criterion 1), BC2, ..., BCM. DAMICORE (Section 3.3) constructs a phylogram (a model) for each BCi,i = 1, ..., M, generating Mmodels (BC1-based model, ..., BCM-based model). Then, a consensus strategy produces a unified phylogram-based model. Finally, OPA can generate new samples from such a model. This paper instantiates the procedures from Steps iand ii for modelling the polymer extrusion (Section 3.4). The learned model is expected to benefit, later, the optimization problem associated with polymer extrusion. However, the sampling from the unified model (the last OPA step) is not performed, thus, not a complete optimization cycle is run. Soares et al. (2017) and Martins et al. (2014) show some experimental results and proofs related to OPA’s performance for challenging combinatorial and multi-objective optimization problems. The main mechanisms of FS-OPA that are relevant for the scope of a datadriven design of an extruder concentrate on the DAMICORE method, introduced in Section 3.3. 3.3. Main concepts in DAMICORE DAMICORE, (DAta MIning of Code REpositories), first introduced by Sanches et al. (2011b), builds on concepts bored from Theory, Complex Networks, and Phylogenetic Inference, and is aimed at revealing hierarchical relationships between unstructured data objects. Its working principles are implemented through three steps: (𝑆1) given a metric of similarity, build a distance matrix comparing every two objects; (𝑆2) convert the matrix into a phylogenetic tree by connecting close objects according to hierarchical levels of similarity; (𝑆3) apply a community detection process to group close subtrees into clusters. In Fig. 6 the elements 𝑑𝑖𝑗 of the distance matrix correspond to a measure of dissimilarities between elements 𝑥𝑖and 𝑥𝑗,according to some given metric. The matrix is then broken down into a tree where the distance between any two items (leaf nodes) corresponds to the sum of the lengths of the branches connecting those two items. Finally, the third step identifies groups of items that are significantly connected into distinguishable similarity clusters. The original DAMICORE method selects three specific algorithms for this purpose, as shown in Fig. 7. As for the similarity measure, the Normalized Compression Distance, NCD, is a computable approximation of the Kolmogorov distance between two objects (Li and Vitányi,2019;Lui et al.,2015), which explores the fact that, for similar objects, it should be relatively easy to describe one in terms of the other. Formally, NCD is defined as 𝐷𝑧(𝑎𝑏) = 𝐶𝑧(𝑎𝑏) − 𝑚𝑖𝑛 {𝐶𝑧(𝑎), 𝐶𝑧(𝑏)} 𝑚𝑎𝑥 {𝐶𝑧(𝑎), 𝐶𝑧(𝑏)}(6) where aand bare the two data objects to be compared, ab is the concatenation of both objects, and 𝐶𝑧(x) is the size of the compressed version of object x, as obtained by applying a compression algorithm z. The rationale of NCD lies in the observation that the concatenation of two very similar objects is more efficient than if the two files were very dissimilar. Eq. (6) implies that for an ideal compressor and two identical files, 𝐶𝑧(ab) =C𝑧(a) =𝐶𝑧(b), thus yielding 𝐷𝑧(a,b) = 0; whereas for two files with no similarities at all, 𝐶𝑧(ab) = C𝑧(a)+C𝑧(b), yielding 𝐷𝑧(a,b) = 1. For non-ideal compressors, NCD ranges from 0 to 1. As for compressor Z, conventional data compression algorithms implemented by standard software utilities such as the popular ZIP (PKZIP: https://www.pkware.com/pkzip; WinZip: http://www.winzip. 6 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 6. Three steps of the DAMICORE method. Fig. 7. DAMICORE algorithm toolchain. com/win/bp) and the RAR (http://www.rarlab.com) file archivers may be employed. The second step of the toolchain relies on the Neighbour Joining (NJ) algorithm, widely employed in bioinformatics. From the distance matrix, NJ derives a tree with the minimum number of modifications needed to explain the differences among Taxon (a taxonomic unity in a classification system) — while non-optimal, the algorithm provides a computationally feasible alternative to other non-polynomial optimal methods. Basically, it works by joining, at each step, the two closest subtrees not already joined (Fig. 8), and making them descendent of a new ancestor node; the newly created ancestor node replaces the joined trees in the matrix, and so on recursively as far as the last join. The final step of DAMICORE is the detection of communities in the phylogenetic graph, i.e., groups of nodes distinguishably more connected among each other than with other nodes in the graph. Formal a community structure may be identified through the concept of modularity (Newman,2006), which is a measure of how much the density of edges in subgraphs is higher than what would be expected if all nodes were connected at random. It is computed by comparing the number of inner edges in a prospective community to the number of edges that would likely be found if the subgraph were rather completely random. The formulation of modularity Qcan be expressed as in the following equation: 𝑄=1 2𝑚 𝑛 ∑ 𝑖,𝑗 (𝐴𝑖𝑗 −𝑃𝑖𝑗 )𝛿(𝐶𝑖, 𝐶𝑗)(7) where Ais the adjacency matrix representing the graph, 𝑃𝑖𝑗 is the probability that the nodes 𝑣𝑖and 𝑣𝑗are connected in a purely random graph, nis the number of vertices, mis the number of edges, and 𝛿(𝐶i, 𝐶j) is 1if the nodes are in the same community, and 0otherwise. Based on modularity, Fast Newman (FN) (Newman,2004) is an efficient bottom-up constructive algorithm that works by performing a greedy search for a graph partition that maximizes the graph modularity. The combination of NCD, NJ and FN results in some relevant DAMICORE properties. NCD makes DAMICORE a data-type agnostic method capable of working with any kind of object: texts, images, audio, or other kinds of data files are all processed at the symbolic representation. NJ then builds a phylogeny exposing common aspects and how shared features are related hierarchically. Finally, FN then identifies communities in this phylogeny to cluster related objects into meaningful similarity groups. As result, DAMICORE can be used without any data pre-processing, such as filtering, outlier detection, and feature extraction, among other tasks that usually include configuration biases and require knowledge from experts in the field of the application. DAMICORE requires no parameter setup to run (although some execution options may improve its performance), which is adequate for non-experts in machine learning and data mining, and for developing cyber–physical solutions. 3.4. FS-OPA for the data-driven design of an extruder The data-driven design based on optimization uses candidate solutions in the decision space as samples. That data usually corresponds to dozens or hundreds of samples at each optimization iteration. Although such an amount is not a huge sampling (for such a complex problem), it may be enough to start to discover some aspects of the mechanisms that make an extruder efficient, for example. The first trick for applying FS-OPA to the extrusion problem is to save the data assigned to each variable (its values spread among the samples) in a file, composing an object of analysis. The corresponding phylograms provide information that can provide four levels of learning from raw data, named 4-Level FS based on OPA (4LFS-opa): 1. First-level learning. The proposed learning approach finds clades, where each of them is a cluster of variables that share information; while the sharing is relatively poor between clades. For optimization purposes, each cluster shows a set of variables with significant interactions. For example, they may correspond to correlated covariates in regression techniques. The output is a table with a list of variables (a cluster) per row. 2. Second-level learning. 4LFS-opa estimates the potential contribution of each clade (of the variables in it) to the objectives. It uses the clades of objectives (oclade) and measures the distances from those clades to each variable clade (vclade). The distance from a vclade to an oclade is the longest path (maximum of the number of edges from all the paths in the found phylogram) between the nodes in the union of vclade and oclade. Those distances (also called cophenetic distances) estimate the power of a clade to improve an objective, while each length of a path p from variable i in vclade to objective o in oclade that is normalized by the largest path found (from all clades and clades) is a rough estimate of the relative contribution of i to o. Note that a clade may have both variables and objectives together. The computation of those distances first requires the splitting of a mixed clade (mclade) into a pure vclade (the mclade without any objective) and a pure oclade (the mclade without variables). The output of the second level of learning possesses two matrices: one with the phylogram distances from vclades to oclades and another with the relative phylogram distances from each variable to each objective. 7 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 8. Neighbour Joining scheme. Fig. 9. Extruder geometry. 3. Third-level learning. The decomposition of a problem into subgroups (from clades) that has some equivalence, complementarity, a certain level of independence, and their relative power to improve an objective are useful components to compose a surrogate model, for example, a simple linear regression model for each objective. 4LFS-opa uses the results learned from levels one and two to construct M Bayesian Networks, one for each of the M objectives, used as a target variable. Thus, the output is M Bayesian Networks. 4. Fourth-level learning. A multivariate probabilistic model can be constructed from the list of information (in the last above item) together with the frequency distribution of variable values in each clade (or a variation of it). That is exactly the type of model required by Estimation of Distribution Algorithms (Soares et al.,2017) to work for relatively complex problems. Note that, EDAs compose a type of optimization method based on evolutionary theory. In other words, the data-driven learning enabled by DAMICORE can produce multivariate probabilistic models and, thus, an EDA, i.e., an entire optimization approach, that can learn from the raw and relatively-small amount of data at each iteration and decide how to walk in the decision space to improve each objective or a set of them. Thus, the output of the fourth level is a multiobjective EDA that can learn from raw data aiming at benefiting the optimization process. The case study with real data presented in Section 4illustrates the first and second learning levels described above. Other levels will be investigated in future work. 4. Case study Extruder geometry The extruder used has a square pitch screw with a diameter (D) of 2 mm and a L/D ratio equal to 2 (Fig. 9). It was fitted with a conventional screw with the lengths of the feed, compression, and metering zones equal to 8D, 8D, and 9D, respectively. The total length of the grooves zone (Lg) is 100 mm and the rotational barrel segment was located at turn 16D with a length (Lrbs) of 1D and 3D. Different screw geometries were tested, using three different internal diameters in the metering zone (𝐷3), i.e., Screw 1 with 22 mm, Screw 2 with 21 mm, and Screw 3 with 20 mm. The screw speed was fixed at 120 rpm. Screw 2 (22 mm) was also tested for three different pitches (Pitch) in all screw lengths, 20, 25, and 30 mm, respectively. Grooves geometry In the machine, a grooved barrel section was implemented allowing to change in the geometry of the grooves. Three different solutions (Model), patented in the framework of the NEWEX project, were studied (Gaspar-Cunha et al.,2018;Gaspar-Cunha,2019). In previous work, four models to compute the average coefficient of friction were studied to verify their suitability and their sensitivity to changes in the system geometry (Gaspar-Cunha,2019). From this study, it was concluded that the existence of grooves in the solids conveying zone is an effective way of improving the performance of the extruder, which depends on both the depth (hN) and the total width (B) of the grooves. Solution Model 1, as illustrated in Fig. 10. In this model the depth is decreasing from a maximum value at the beginning of the section (hN1), to zero at the end of the grooves zone, subsequently, the polymer will not accumulate in the grooves. Simultaneously, it is possible by simply moving the device shown to get changes in both the depth and total width of the grooves. Fig. 10-A represents the grooves device open, i.e., when the grooves have the maximum value for the initial depth (hN1), while Fig. 10-B is the case when this depth is nil. The changes in the total width can be implemented by moving only two or four of the existing grooves devices. In this case the possibility of including sections with different geometry of grooves with the length of 4D (100 mm) and where the depth varies linearly from a maximum value at the beginning of the grooves, until it cancels out. Solution Model 2 is shown in Fig. 11. The most important difference, when compared with Solution Model 1, concerns the variation of the depth along the length of the groove. In the present case, for example for Model 2b, along with the initial 25 mm (1D) the depth is constant (hN1) and equal to 1 mm, while in the remaining length (hN2), 75 mm (3D), is also constant, but equal to 6 mm. The different geometries tested in this case are described geometrically in Table A.2. Solution Model 3 is shown in Fig. 12. In this case, the grooved section is constituted by a sequence of interconnected rings that can be rotated independently to change the angle of the grooves existing in each one of the rings, as shown in Fig. 12. In this way, there is the possibility to study the influence of the grooves angle and compare the performance of longitudinal and helical grooves. The helical 8 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 10. Solution Model 1a: (A) totally open; (B) totally closed. Fig. 11. Solution Model 2: (A) totally open; (B) totally closed. grooves with a channel implemented in the direction of the screw channel enable the auto-cleaning of the grooves without deteriorating the performance. This is indicated in Table A.2 by variable Type: L — longitudinal; RH — right-helical; and LH — left-helical. Rotational barrel segment geometry In the present study the rotational barrel segment (shown in Fig. 13) was located at 16D. Two different lengths 1D (25 mm) and 3D (75 mm) and four different rotational barrel segment velocities (𝑁b=−80, −120, 80 and 100 rpm) were tested. Material properties Table 1 shows the relevant properties of the polymer used in the calculations, a Low-Density Polyethylene, Malen E FGAN 18-D003 from Basell. The viscosity was obtained experimentally using a capillary rheometer being the data fitted using the power-law model, as follows: 𝜂=𝜂0𝛾(𝑛−1)𝑒−𝑎(𝑇−𝑇0)(8) Operating conditions In all calculations, the barrel temperature (Tbarrel) was fixed at 170 ◦C, but in the solids zone (Tfeed) varies linearly between 30 ◦C and 70 ◦C. Screw speed only changes in the Screws dataset, in which the values of 40, 80, and 120 rpm were used. Datasets Two types of studies will be carried out: a partial and global analysis. In the first case, three different sets will be considered: (i) Screw Dataset — analysis of operating conditions and screw geometry; (ii) Grooves Dataset — analysis of grooves section; and (iii) RBS Dataset — analysis of rotational barrel segment. In the latter case, tree studies will be made: (i) global analysis with all data; (ii) global analysis with 50% of the best data for Output, and (iii) global analysis with 50% of the best data for WATS. For that purpose, Tables A1, A2, A3, and A4, in Appendix, present the data used, the decision variables values introduced in the modelling program, and the values of the objective resulting from the calculation. The decision variable’s values were defined as a function of the study made. In the Screws dataset (Table A.1) three different screws were used (Screw equal to 1, 2, and 3) corresponding to 𝐷3equal to 22, 21, and 20 mm, respectively. In this case, Grooves and RBS variables values were fixed as zero (0), since they were not present. Also, as referred, 9 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Fig. 18. Phylogram obtained by 4LFS-opa from the Global dataset, best 50% for Output. This analysis allows us to conclude that the results produced by the application of levels one and two of learning are following the knowledge about the extrusion process and that it constitutes an important step toward the application of the other learning levels. Future work includes the application of the same data at two additional learning levels: third-level learning where the aim will be to obtain a surrogate model relating to the data, which can be used together with an optimization algorithm; and fourth-level learning, which aims to obtain multivariate probabilistic models that can be used as an entire optimization approach. CRediT authorship contribution statement António Gaspar-Cunha: Conceptualization, Methodology, Writing – original draft, Supervision, Investigation, Formal analysis, Writing – review & editing. Francisco Monaco: Software, Data curation, Investigation, Formal analysis. Janusz Sikora: Supervision, Visualization, Investigation, Writing – review & editing. Alexandre Delbem: Supervision, Resources, Writing – review & editing, Investigation, Formal analysis. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements This research was partially funded by NAWA-Narodowa Agencja Wymiany Akademickiej, under grant PPN/ULM/2020/1/00125 and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 734205–H2020MSCA-RISE-2016. The authors also acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UID-B/05256/2020, and UID-P/05256/2020, the Center for Mathematical Sciences Applied to Industry (CeMEAI) and the support from the São Paulo Research Foundation, Brazil (FAPESP grant No 2013/07375-0, the Center for Artificial Intelligence (C4AI-USP), the support from the São Paulo Research Foundation, Brazil (FAPESP grant No 2019/07665-4) and the IBM Corporation. Appendix See Tables A.1–A.4 16 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Table A.1 Screw dataset. Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel NOutput 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 1.8 175.3 995 6.2 315.5 1.04 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 3.5 182.1 1594 12.4 295.9 1.36 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 5.2 188.6 2460 13.2 298.9 1.25 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 80 2.8 182.1 1953 10.6 334 1.38 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 3.5 182.1 1594 12.4 295.9 1.36 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 80 4.3 182.4 1314 14.7 279.1 1.07 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 40 1.716 175.1 1063 6.676 319.6 1.19 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 1.764 175.3 995 6.15 315.5 1.04 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 40 1.754 175.4 918 6.69 305.9 1.04 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 120 5.112 188.1 2404 13.996 329 1.39 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 5.229 188.6 2460 13.16 298.9 1.25 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 120 5.394 189.7 2224 14.71 292.4 1.12 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.3 176.3 946 8.7 263.3 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 80 4.6 183.2 1487 15.4 245 1.08 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.1 188.8 2201 17.1 219.2 1.11 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.099 176.1 1157 6.816 294.6 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.329 176.3 946 8.67 263.3 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.25 176.4 966 6.76 272.4 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 6.378 187.7 2425 15.66 266.2 1.14 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.143 188.8 2201 17.14 219.2 1.11 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.571 190.6 2116 17.55 204.5 1.12 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 2.8 176.8 724 14.2 209.7 1.04 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 80 5.9 182.9 1371 17.8 156.9 1.08 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 10.2 185.2 1727 21.6 70.3 1.09 0 3 0 0 25 16.6 20 100 200 200 225 20 70 170 40 2.458 177 1233 5.824 295.4 1.04 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 2.766 176.8 724 14.22 209.7 1.04 0 3 0 0 25 16.6 20 100 200 200 225 30 70 170 40 2.872 177.1 668 14.96 193 1.04 0 3 0 0 25 16.6 20 100 200 200 225 20 70 170 120 7.246 185.7 2518 16.604 195.5 1.09 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 10.176 185.2 1727 21.64 70.3 1.09 0 3 0 0 25 16.6 20 100 200 200 225 30 70 170 120 53.947 224.5 2432 25 2 1.32 1 Table A.2 Grooves dataset. Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel NModel bN hN1 hN2 NN Lg1 Lg2 B Type Output 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 4 100 0 24 L 5.43 188.5 2647 14.21 302.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 4 100 0 24 L 5.38 188.6 2597 14.17 303.1 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 4 100 0 24 L 5.38 188.6 2630 13.69 299.5 1.54 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 4 100 0 0 L 5.34 188.9 2278 14.64 308 1.46 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 5 100 0 30 L 5.47 188.3 2728 14.21 301.8 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 5 100 0 30 L 5.46 188.3 2669 13.83 299.2 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 5 100 0 30 L 5.35 188.3 2709 13.88 301.2 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 0 100 0 0 L 5.34 188.9 2278 14.64 308 1.46 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 5.48 189.2 2745 14.1 300.8 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 25 75 24 L 5.47 188.4 2741 14.23 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 50 50 24 L 5.47 188.4 2739 14.23 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 75 25 24 L 5.46 188.3 2737 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 4 100 0 24 L 5.46 188.3 2732 14.21 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 5 100 0 30 L 5.55 188.3 2768 13.97 298.8 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 25 75 30 L 5.48 188.2 2816 14.1 300.9 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 50 50 30 L 5.47 188.2 2745 14.21 300 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 75 25 30 L 5.47 188.3 2740 14.21 300 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 5 100 0 30 L 5.46 188.4 2739 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 L 5.43 188.5 2647 14.21 302.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 RH 5.39 188.5 2672 13.87 300.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 RH 5.37 188.5 2657 13.37 297.7 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 RH 5.36 188.5 2584 13.98 301.8 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 LH 5.35 188.3 2709 13.88 301.2 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 LH 5.36 188.4 2637 14.02 302.2 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 LH 5.38 188.6 2597 14.17 303.1 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 RH 5.47 188.3 2650 13.99 300.2 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 RH 5.45 188.3 2662 13.89 300.1 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 RH 5.44 188.3 2656 14.12 301.1 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 LH 5.46 188.4 2739 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 LH 5.47 188.2 2725 14.51 302.5 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 LH 5.47 188.1 2712 14.7 303.7 1.63 0 Table A.3 RBS dataset. Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel N Lrbs Lrbs/L Nb Output 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 05.3 188.9 2278 14.6 308 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −20 5.4 189 2295 14.8 334.2 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −40 5.5 189.2 2331 14.8 328.4 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −80 5.5 189.3 2383 14.8 317.3 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −120 5.7 189.8 2397 15.1 307.9 1.44 0 (continued on next page) 17 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Table A.3 (continued). Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel N Lrbs Lrbs/L Nb Output 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 20 5.3 188.8 2283 14.3 339.2 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 40 5.2 188.8 2238 14.4 347.5 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 80 4.9 188.8 2214 14.2 358 1.48 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 120 4.9 189 2185 14 366 1.48 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 0 5.3 188.9 2278 14.6 308 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −20 5.5 189.3 2358 14.8 383.3 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −40 5.8 190.1 2395 15.5 376.4 1.45 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −80 6.1 191.1 2583 15.6 339.9 1.44 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −120 6.4 192.2 2834 15.8 315.6 1.43 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 20 5.1 188.5 2241 14.1 405.1 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 40 4.8 188.2 2163 14 422.9 1.48 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 80 4 187.7 2195 12.8 451 1.5 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 120 3.7 187.8 2100 12.2 484.1 1.51 1 Table A.4 Global dataset.. Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel NModel bN hN1 hN2 NN Lg1 Lg2 B Type Lrbs Lrbs/L Nb Output 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 05.3 188.9 2278 14.6 308 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −20 5.4 189 2295 14.8 334.2 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −40 5.5 189.2 2331 14.8 328.4 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −80 5.5 189.3 2383 14.8 317.3 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −120 5.7 189.8 2397 15.1 307.9 1.44 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 20 5.3 188.8 2283 14.3 339.2 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 40 5.2 188.8 2238 14.4 347.5 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 80 4.9 188.8 2214 14.2 358 1.48 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 120 4.9 189 2185 14 366 1.48 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 0 5.3 188.9 2278 14.6 308 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −20 5.5 189.3 2358 14.8 383.3 1.46 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −40 5.8 190.1 2395 15.5 376.4 1.45 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −80 6.1 191.1 2583 15.6 339.9 1.44 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −120 6.4 192.2 2834 15.8 315.6 1.43 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 20 5.1 188.5 2241 14.1 405.1 1.47 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 40 4.8 188.2 2163 14 422.9 1.48 0 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 80 4 187.7 2195 12.8 451 1.5 1 1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 120 3.7 187.8 2100 12.2 484.1 1.51 1 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 0 5.3 188.9 2278 14.6 308 1.46 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −20 5.7 188.4 2975 14.4 372.1 1.13 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −40 5.8 188.9 3077 14.6 358 1.11 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −80 6.1 189.7 3306 15 330.2 1.12 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −120 6.4 191.1 3488 15 304.6 1.13 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 20 5.3 187.7 2798 14 398.4 1.1 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 40 5 187.6 2714 13.6 411.6 1.21 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 80 4.3 187.6 2767 11.7 430 1.3 0 1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 120 3.9 188 2771 6.1 482.4 1.28 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.8 175.3 995 6.2 315.5 1.04 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 3.5 182.1 1594 12.4 295.9 1.36 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.2 188.6 2460 13.2 298.9 1.25 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 2.8 182.1 1953 10.6 334 1.38 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 3.5 182.1 1594 12.4 295.9 1.36 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 4.3 182.4 1314 14.7 279.1 1.07 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.716 175.1 1063 6.676 319.6 1.19 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.764 175.3 995 6.15 315.5 1.04 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.754 175.4 918 6.69 305.9 1.04 0 1 0 0 25 16.6 22 100 200 200 225 20 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.112 188.1 2404 13.996 329 1.39 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.229 188.6 2460 13.16 298.9 1.25 0 1 0 0 25 16.6 22 100 200 200 225 30 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.394 189.7 2224 14.71 292.4 1.12 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.3 176.3 946 8.7 263.3 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 4.6 183.2 1487 15.4 245 1.08 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.1 188.8 2201 17.1 219.2 1.11 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.099 176.1 1157 6.816 294.6 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.329 176.3 946 8.67 263.3 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.25 176.4 966 6.76 272.4 1.04 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 6.378 187.7 2425 15.66 266.2 1.14 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.143 188.8 2201 17.14 219.2 1.11 0 2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.571 190.6 2116 17.55 204.5 1.12 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.8 176.8 724 14.2 209.7 1.04 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 5.9 182.9 1371 17.8 156.9 1.08 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 10.2 185.2 1727 21.6 70.3 1.09 0 3 0 0 25 16.6 20 100 200 200 225 20 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.458 177 1233 5.824 295.4 1.04 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.766 176.8 724 14.22 209.7 1.04 0 3 0 0 25 16.6 20 100 200 200 225 30 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.872 177.1 668 14.96 193 1.04 0 3 0 0 25 16.6 20 100 200 200 225 20 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.246 185.7 2518 16.604 195.5 1.09 0 3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 10.176 185.2 1727 21.64 70.3 1.09 0 3 0 0 25 16.6 20 100 200 200 225 30 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 53.947 224.5 2432 25 2 1.32 1 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 4 100 0 24 L 0 0 0 5.43 188.5 2647 14.21 302.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 4 100 0 24 L 0 0 0 5.38 188.6 2597 14.17 303.1 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 4 100 0 24 L 0 0 0 5.38 188.6 2630 13.69 299.5 1.54 0 1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 4 100 0 0 L 0 0 0 5.34 188.9 2278 14.64 308 1.46 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 5 100 0 30 L 0 0 0 5.47 188.3 2728 14.21 301.8 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 5 100 0 30 L 0 0 0 5.46 188.3 2669 13.83 299.2 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 5 100 0 30 L 0 0 0 5.35 188.3 2709 13.88 301.2 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 0 100 0 0 L 0 0 0 5.34 188.9 2278 14.64 308 1.46 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 0 0 0 5.48 189.2 2745 14.1 300.8 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 25 75 24 L 0 0 0 5.47 188.4 2741 14.23 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 50 50 24 L 0 0 0 5.47 188.4 2739 14.23 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 75 25 24 L 0 0 0 5.46 188.3 2737 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 4 100 0 24 L 0 0 0 5.46 188.3 2732 14.21 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 5 100 0 30 L 0 0 0 5.55 188.3 2768 13.97 298.8 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 25 75 30 L 0 0 0 5.48 188.2 2816 14.1 300.9 1.52 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 50 50 30 L 0 0 0 5.47 188.2 2745 14.21 300 1.52 0 (continued on next page) 18 A. Gaspar-Cunha, F. Monaco, J. Sikora et al. Engineering Applications of Artificial Intelligence 116 (2022) 105397 Table A.4 (continued). Decision variables Objectives ERROR Screw Grooves RBS Dext D1 D3 Lfeed L1 L2 L3 Pitch Tfeed Tbarrel NModel bN hN1 hN2 NN Lg1 Lg2 B Type Lrbs Lrbs/L Nb Output 𝑇𝑚𝑒𝑙𝑡 Power 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 75 25 30 L 0 0 0 5.47 188.3 2740 14.21 300 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 5 100 0 30 L 0 0 0 5.46 188.4 2739 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 L 0 0 0 5.43 188.5 2647 14.21 302.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 RH 0 0 0 5.39 188.5 2672 13.87 300.6 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 RH 0 0 0 5.37 188.5 2657 13.37 297.7 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 RH 0 0 0 5.36 188.5 2584 13.98 301.8 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 LH 0 0 0 5.35 188.3 2709 13.88 301.2 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 LH 0 0 0 5.36 188.4 2637 14.02 302.2 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 LH 0 0 0 5.38 188.6 2597 14.17 303.1 1.54 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 RH 0 0 0 5.47 188.3 2650 13.99 300.2 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 RH 0 0 0 5.45 188.3 2662 13.89 300.1 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 RH 0 0 0 5.44 188.3 2656 14.12 301.1 1.51 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 LH 0 0 0 5.46 188.4 2739 14.22 301.9 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 LH 0 0 0 5.47 188.2 2725 14.51 302.5 1.53 0 1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 LH 0 0 0 5.47 188.1 2712 14.7 303.7 1.63 0 References Agassant, J.F., Avenas, P., Carreau, P.J., Vergnes, B., Vincent, M., 2017. 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He is currently an Auxiliary Professor of Polymer Processing at the University of Minho. The main areas of scientific activity are the modelling of polymer extrusion-based processes and multiobjective optimization. He is the author or co-author of more than 170 works, including books edited, book chapters, papers published in international refereed journals, and more published in proceedings of international conferences. In 2015 was the general chair of the 8th International Conference on Evolutionary Multi-Criterion Optimization (EMO2015) and in 2019 was the general chair of the EUROGEN 2019 international conference. Francisco José Monaco holds a Ph.D. degree in Electrical Engineering from the University of São Paulo (USP) in 2002. He is currently an Assistant Professor at the Department of Computer Systems at USP, where he conducts research in computational modelling and Simulation, with emphasis on evolutionary multiobjective optimization and unsupervised machine learning. Dr. Monaco is the author of several scientific publications among journal papers, conference articles, and book chapters, serving also on conferences and journal technical committees, and in national and international research projects. Janusz Sikora - works at the Lublin University of Technology. He started working in 1990, in 1995 he obtained a doctoral degree, in 2000 the title of habilitated doctor, since 2009 he has been a full professor. His scientific interests mainly include technological issues of polymer processing. He is the creator or co-creator of over 100 patents and utility models. He is the author or co-author of over 270 publications. He was a coordinator of two international projects with FP7 and Horizon 2020. He is the author of opinions and expertise for industry, and he is involved in the process of evaluating investment and research projects for entities from all over Poland. He has received many medals and awards at international exhibitions of inventions. Alexandre Delbem is a Full Professor at the Department of Computer Systems of the Institute of Mathematical and Computer Sciences in the University of São Paulo (ICMCUSP) and Research Productivity Fellow 1C at CNPq (a Brazilian Research Foundation). He was chief of the Department from 2014 to 2018. Delbem investigates computerbased solutions to work with real-world problems that can be modelled as cyber–physical systems. Investigations focus on multidisciplinary applications in fields such as power restoration after blackouts in large-scale electrical networks, population dynamics and integrated projects of supply and attending networks involving agribusiness, healthcare, environment and social assistance. Software and hardware are developed to deal with some challenges inherent to complex systems: large-scale (computational complexity and estimation of distribution algorithms), multidimensionality (automatic construction of multivariate models for different data types), multicriteria decision making and optimization (multiobjective evolutionary algorithms) and real-time response (parallelization using FPGAs). 20