Dr. Abdelkhalik conducts research in the area of dynamics, control, and global optimization with applications to spacecraft trajectory planning, wave energy converter control, data assimilation in oil reservoirs, systems design, and traffic engineering. In some applications, the design space has numerous local minima, with mixed variables (integer and real), and the number of optimization variables can be varied among different solutions to explore new regions in the design space. Global optimization methods can handle problems with mixed variables and numerous local minima, but variable-size design space optimization is yet to be explored. The research focus is on the study of global optimization methods that can handle variable-size design space problems. Other research efforts include the recursive implementation of evolutionary optimization algorithms for the sake of improving the computational efficiency in data assimilation problems.