A combined genetic algorithms-shooting method approach to solving optimal control problems

Abstract

In this paper, an alternative method for solving optimal control problems is presented. By applying calculus of variations, the optimal control problem can be reduced to solving a two-point boundary value problem. Here, the solution is generated with a combination of two methods - genetic algorithms (GA) and the shooting method. An estimate of the optimal solution is first obtained using GA. This solution is in turn used as the initial guess for the shooting method. This combined method is applied to an optimal missile guidance problem. The performances of the combined method and GA are evaluated by simulation and compared. The results clearly show that the proposed combined method is able to locate the optimal solution more efficently than GA. The results also show that the combined method never fails to correctly determine the optimal solution. Therefore, it proves to be more robust than the shooting method whose convergence is not always guaranteed.