An Improved Genetic Algorithm Using a Directional Search

The genetic algorithm (GA), a very powerful tool used in optimization, has been applied in various fields including statistics. However, the general GA is usually computationally intensive, often having to perform a large number of evaluations of an objective function. This paper presents four different versions of computationally efficient genetic algorithms by incorporating several different local directional searches into the GA process. These local searches are based on using the method of steepest descent (SD), the Newton-Raphson method (NR), a derivative-free directional search method (denoted by “DFDS”), and a method that combines SD with DFDS. Some benchmark functions, such as a low-dimensional function versus a high-dimensional function, and a relatively bumpy function versus a very bumpy function, are employed to illustrate the improvement of these proposed methods through a Monte Carlo simulation study using a split-plot design. A real problem related to the multi-response optimization problem is also used to illustrate the improvement of these proposed methods over the traditional GA and over the method implemented in the Design-Expert statistical software package. Our results show that the GA can be improved both in accuracy and in computational efficiency in most cases by incorporating a local directional search into the GA process.