A hybrid backtracking search optimization algorithm for nonlinear optimal control problems with complex dynamic constraints

• The improved BSA (IBSA) is proposed to enhance the convergent speed and the global search ability, by adopting the harmony search strategy and an adaptive amplitude control factor with individual optimum fitness feedback.
• The hp-adaptive gauss pseudospectral method (hpGPM) is adopted to overcome the drawbacks of the fixed discrete points generated during the conventional controls parameterization.
• A novel hybrid two-stage optimization algorithm integrating the IBSA with the hpGPM is proposed to find a global optimum more quickly and accurately.

Nonlinear optimal control (NOC) problem with complex dynamic constraints (CDC) is difficult to compute even with direct method. In this paper, a hybrid two-stage approach integrating an improved backtracking search optimization algorithm (IBSA) with the hp-adaptive Gauss pseudo-spectral methods (hpGPM) is proposed. Firstly, BSA is improved to enhance its convergent speed and the global search ability, by adopting the harmony search strategy and an adaptive amplitude control factor with individual optimum fitness feedback. Then, at the beginning stage of the hybrid search process, an initialization generator is constructed using IBSA to find a near optimum solution. When the change in fitness function approaches to a predefined value which is small enough, the search process is replaced by hpGPM to accelerate the search process and find an accurate solution. By this way, the hybrid algorithm is able to find a global optimum more quickly and accurately. Two NOC problems with CDC are examined using the proposed algorithm, and the corresponding Monte Carlo simulations are conducted. The comparison results show the hybrid algorithm achieves better performance in convergent speed, accuracy and robustness.