In recent years, the aircraft design group at Stanford has successfully applied gradient-based optimizers to a variety of aeronautical design problems. Unfortunately, these methods cannot be applied to problems with discrete variables or discontinuous objective and constraint functions, because gradients are not defined in these domains. Furthermore, gradient-based optimizers must start with a specific parameterization of the design and are limited to finding optimal values of the chosen design variables.
Standard genetic algorithms are known to be effective in multi-modal and non-smooth domains, where calculus-based methods are ineffective. Modification of the basic algorithm, to allow variation of the parameter set during optimization, has produced a method that is very suitable for use in topological design studies. This approach allows the identification of successful features in simple designs described by few variables, which can then be included in designs of greater complexity. This capability is particularly attractive for synthesis studies, because it is similar to the process used by designers. In wing design, for example, parameters such as wing area and span are generally determined before the airfoil sections are chosen. A number of design tasks that are not easily solved by gradient-based optimization have been successfully handled by the new genetic method.
Although this work culminated in the thesis of Dr. Peter Gage, we continue to work with GA's for a number of problems. The figure below shows the performance of a new GA on a 4-D Wood's Problem.
firstname.lastname@example.org (Peter Gage)