The hub location’s method for solving optimal control problems

Abstract

In this paper, the p-hub median’s algorithm is modified to find an approximate solution of bounded continuous-time nonlinear optimal control problems (NOCP). For this purpose, after presenting the similarities between uncapacitated single allocation p-Hub median problem (USApHMP) which is a special case of the well-studied hub location problem and a discretized form of NOCP, an improvement on sequential general variable neighborhood search algorithm (SGVNS) is proposed. This algorithm that denoted as new-sequential general variable neighborhood search (N-SGVNS) is based on three local searches that use efficient neighborhood interchange. In addition, comparing the NOCP with the USApHMP has led us to introduce a suitable method to find an approximate solution for NOCP. Our results of the implementation of the N-SGVNS on the real-world data set for the USApHMP show the high accuracy of the obtained solutions. Because of the proposed algorithm is able to solve the USApHMP successfully, we hoped that this method would also be successful for NOCP. Solving of benchmark NOCP and then comparing the results of the N-SGVNS with recently developed algorithms suggest that the presented strategy may provide an outstanding framework for designing cost-effective control functions.