Numerical Computation of a Mixed-Integer Optimal Control Problem Based on Quantum Annealing

Abstract

It is extremely challenging to solve the mixed-integer optimal control problems (MIOCPs) due to the complex computation in solving the integer decision variables. This paper presents a new method based on quantum annealing (QA) to solve MIOCP. The QA is a metaheuristic which applies quantum tunneling in the annealing process. It has a faster convergence speed in optimal-searching and is less likely to run into local minima. Hence, QA is applied to deal with this kind of optimization problems. First, MIOCP is transformed into a mixed-integer nonlinear programming (MINLP). Then, a method based on QA is adopted to solve the MINLP and acquire the optimal solution. At last, two benchmark examples including Lotka-Volterra type fishing problem and distillation column are presented and solved. The effectiveness of the methodology is verified by the acquired optimal schemes.