Utilizing Multiple Objectives for the Optimization of the Pultrusion Process Based on a Thermo-Chemical Simulation

Cem C. Tutum, Ismet Baran, Jesper H. Hattel

Research output: Contribution to journalArticleAcademic

24 Citations (Scopus)
6 Downloads (Pure)


Pultrusion is one of the most effective manufacturing processes for producing composites with constant cross-sectional profiles. This obviously makes it more attractive for both researchers and practitioners to investigate the optimum process parameters, i.e. pulling speed, power and dimensions of the heating platens, length and width of the heating die, design of the resin injection chamber, etc., to provide better understanding of the process, consequently to improve the efficiency of the process as well the product quality. Numerous simulation approaches have been presented until now. However, optimization studies had been limited with either experimental cases or determining only one objective to improve one aspect of the performance of the process. This objective is either augmented by other process related criteria or subjected to constraints which might have had the same importance of being treated as objectives. In essence, these approaches convert a true multi-objective optimization problem (MOP) into a single-objective optimization problem (SOP). This transformation obviously results in only one optimum solution and it does not support the efforts to get more out of an optimization study, such as relations between variables and objectives or constraints. In this study, an MOP considering thermo-chemical aspects of the pultrusion process (e.g. cure degree, temperatures), in which the pulling speed is maximized and the heating power is minimized simultaneously (without defining any preference between them), has been formulated. An evolutionary multi-objective optimization (EMO) algorithm, non-dominated sorting genetic algorithm (NSGA-II [Deb et al., 2002]), has been used to solve this MOP in an ideal way where the outcome is the set of multiple solutions (i.e. Pareto-optimal solutions) and each solution is theoretically an optimal solution corresponding to a particular trade-off among objectives. Following the solution process, in other words obtaining the Pareto-optimal front, a further postprocessing study has been performed to unveil some common principles existing between the variables, the objectives and the constraints either along the whole front or in some portion of it. These relationships will reveal a design philosophy not only for the improvement of the process efficiency, but also a methodology to design a pultrusion die for different operating conditions
Original languageEnglish
Pages (from-to)2165-2174
JournalKey engineering materials
Publication statusPublished - 2013
Externally publishedYes


  • Multi-objective optimization
  • Evolutionary algorithm
  • Pultrusion process
  • Simulation
  • Thermo-chemical model
  • n/a OA procedure


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