Optimum design of pultrusion process via evolutionary multi-objective optimization

  • Cem C. TutumEmail author
  • Ismet Baran
  • Kalyanmoy Deb


Pultrusion is one of the most cost-effective manufacturing techniques for producing fiber-reinforced 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 as the product quality. Using validated computer simulations is “cheap” and therefore is an attractive and efficient tool for autonomous (numerical) optimization. Optimization problems in engineering in general comprise multiple objectives often having conflict with each other. Evolutionary multi-objective optimization (EMO) algorithms provide an ideal way of solving this type of problems without any biased treatment of objectives such as weighting constants serving as pre-assumed user preferences. In this paper, first, a thermochemical simulation of the pultrusion process has been presented considering the steady-state conditions. Following that, it is integrated with a well-known EMO algorithm, i.e., nondominated sorting genetic algorithm (NSGA-II), to simultaneously maximize the pulling speed and minimize “total energy consumption” (TEC) which is defined as a measure of total heating area(s) and associated temperature(s). Finally, the results of the evolutionary computation step is used as starting guesses for a serial application of a of gradient-based classical algorithm to improve the convergence. As a result, a set of optimal solutions are obtained for different trade-offs between the conflicting objectives. The trade-off solution, thus obtained, would remain as a valuable source for a multi-criterion decision-making task for eventually choosing a single preferred solution for the pultrusion process.


Multi-objective optimization Evolutionary algorithm Mathematical programming Pultrusion process Simulation Thermochemical model 


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMichigan State UniversityEast LansingUSA
  2. 2.Department of Mechanical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark

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