A penalty function-based greedy diffusion search algorithm for the optimization of constrained nonlinear dynamical processes with discrete-valued input
Xiang Wu, Kanjian Zhang · Journal of Industrial and Management Optimization · 2022
This paper considers an optimization problem of nonlinear dynamical processes with discrete-valued input and continuous-time inequality constraints. This problem requires to determine an order and some instants. Since the order is a discrete variable and the constraints are complex, classical optimal control approaches cannot be used directly to solve this problem. To tackle this issue, a penalty function-based greedy diffusion search algorithm is proposed based on a novel transformation for each discrete value, a novel second-order smoothing technique, a $ l_1 $ penalty function, and a novel greedy rule. In the novel greedy rule, there exist only two parameters, which can be set in advance. Thus, unlike existing hybrid approaches, no parameters is required adjusted in the penalty function-based greedy diffusion search algorithm. Following that, the global convergence results of the proposed algorithm are established. Finally, an energy management problem in an electrical vehicle is used to illustrate the effectiveness of the proposed algorithm. The numerical simulation results show that the algorithm proposed by this paper can obtain a better solution with less time-consuming, fewer iterations, and fewer errors compared with existing methods.