Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm

This paper presents a hybrid scheme for solving optimal control problems‎. ‎Discretizing the time interval and assuming a constant control value on each sub-interval transforms the optimal control problem into an assignment problem‎. ‎To cluster feasible solutions, a novel method is proposed in this paper, which applies metaheuristic algorithms—specifically, genetic algorithms and particle swarm optimization—to generate a large number of solutions. ‎Subsequently‎, ‎the K-means clustering method is employed to classify these solutions into clusters‎. ‎Enhancing the median of each cluster‎, ‎using metaheuristic techniques, ultimately results in improved medians‎. ‎The best median from the final iteration of the algorithm serves as an acceptable solution for the optimal control problem‎. ‎In some cases‎, ‎it even succeeds in discovering a new best solution‎.

Keywords:

Clustering‎ , ‎K-Means algorithm‎ , ‎Optimal control problem , ‎Genetic algorithm‎ , ‎ ‎Particle swarm optimization