Multi-Objective Optimization for the Force System of Orthodontic Retraction Spring Using Genetic Algorithms

In this study, Castigliano’s second theorem is applied to predict the force and moment system produced by orthodontics T-spring. The developed analytical formulas include all spring design parameters (material, geometrical shape and wire cross section, type and position of spring end mounting system, and direction and magnitude of the activation forces). The analytical results are compared with those obtained by nonlinear finite element formulation with nonlinear capabilities as a large deflection and showed an acceptable agreement for the current application. The reliability of the proposed model is successfully tested to predict the effect of some design parameters on spring stiffness. The developed analytic force system formulas are used as an objective function for solving a multi-objective optimization problem to produce the required force and moment at spring ends. A new genetic algorithm scheme is developed to obtain optimal spring design parameters according to design objectives and constraints. The results show that depending on the above methodology we can make a good estimation of the required design parameters of the T-spring for a specific application.