Design of Curves and Surfaces Using Multi-Objective Optimization

Design by optimization of curves and surfaces is a powerful design technique. The mathematical modeling of the design problem often results in a multi-objective optimization (MOO) problem which cannot be handled as such by traditional single objective optimization algorithms. Hence an evolutionary MOO algorithm is used to handle this case. The use of MOO algorithm enhances the design process by enabling optimization of several design objectives at once. The algorithm is used for the optimization of NURBS curves and surfaces. The optimization variables are the knot vectors, the parametrizations and the NURBS weights; all of which are set automatically during the optimization process as those who define the optimal surface with respect to the design objectives.