RPSGAe – A Multiobjective Genetic Algorithm with Elitism: Application to Polymer Extrusion A. Gaspar-Cunha, J. A. Covas Dept. of Polymer Engineering, University of Minho, Guimarães, PORTUGAL. gaspar,
[email protected] Abstract. The application of a Multiobjective Optimisation Genetic Algorithm to polymer extrusion is presented. The aim is to implement an automatic optimisation scheme of the process capable to define the values of important parameters, such as operating conditions and screw geometry, yielding the best performance in terms of prescribed attributes. This problem is solved using a multiobjective optimisation genetic algorithm with elitism, Reduced Pareto Set Genetic Algorithm (RPSGAe). The results obtained for specific case studies have physical meaning and correspond to a successful optimisation of the process. Keywords: Polymer extrusion, Screw design, Multiobjective optimisation, Genetic algorithms. 1- INTRODUCTION Extrusion is a major plastics production technology. It is used to produce widespread products such as tubing, pipes and profiles, film, sheet, filaments and fibres, electrical wires and cables. Plastics compounding, involving incorporation of additives in a polymer matrix in order to obtain materials with improved properties, is also carried out in extruders. The experimental and theoretical studies carried out during the last three decades allowed the understanding of the physical, thermal and mechanical phenomena occurring inside the extruder, and the development of mathematical models able to describe the entire process [1-4]. It is now possible to predict with good accuracy the values of important variables, such as mass output, power consumption, melt temperature, residence time distribution, pressure profiles and degree of mixing, for a given combination of polymer properties, operating conditions and screw configuration. However, process optimisation, i.e., the definition of the best screw configuration and/or operating conditions for a given application is still a trial and error procedure, where the above variables are changed, either experimentally or using the computer, until they meet the desirable performance. In this work, an automatic optimisation methodology of the polymer extrusion process, using a Multiobjective Optimisation Genetic Algorithms approach is proposed. For that purpose, the Reduced Pareto Set Genetic Algorithm (RPSGA) proposed earlier [5,6] was modified in order to incorporate elitism, avoiding in such a way the deterioration of the fitness during the successive generations [711]. In the RPSGA algorithm, the N individuals of the population, in each generation, are reduced to a pre-defined number of ranks (r=1,2,...,NRanks), then the value of the objective function is calculated using a ranking function. Elitism is introduced in the RPSGA by maintaining an external population of size 2*N (Figure 1). The algorithm starts by the random definition of an internal population of size N and the formation of an empty external population. Then, in each generation the best 2*N/Nranks individuals, obtained by reducing the internal population with the clustering algorithm [12], are copied to the external population. This process is repeated until the number of individuals of the external population reaches 2*N. At this point, the RPSGA is applied in order to sort the individuals of the external population. The best N/Nranks individuals of this population are incorporated in the internal population by replacing the individuals with lower fitness. Simultaneously, only the best N/Nranks are maintained in the external population. This algorithm was used to optimise the operating conditions and to design screws for a specific polymer extrusion problem.
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Pre-define the number of required ranks, Nranks; Pre-define the size of the Elitist population, Ne; Make Nelite=0; Make Rank[i]=0 for all the N individuals of the main population; First iteration, r =1; Do: 1. Calculate NR=r*(N/Nranks); 2. Reduce the population to NR individuals using a clustering algorithm; 3. Make i=1; 4. Do: - If (Rank[i]=0) Make Rank[i]=r; - Make i=i+1: 5. While (i
