Numerical Computation of a Mixed-Integer Optimal Control Problem Based on Quantum Annealing
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Numerical Computation of a Mixed-Integer Optimal Control Problem Based on Quantum Annealing LIU Zhe 1 (
),
LI Shurong 1∗ (
),
GE Yulei 2 (
)
(1. Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2. Qingdao Topscomm Communication Co., Ltd., Qingdao 266024, Shandong, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 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. Key words: mixed-integer, optimal control, quantum annealing, distillation column CLC number: TP 301 Document code: A
0 Introduction The solution of mixed-integer optimal control problem (MIOCP) or dynamic optimization usually plays important roles in lots of industrial processes. Therefore, it is of great importance to study the MIOCP and the corresponding optimization algorithm. Researches with respect to this field have made great progress and a number of scholars have presented different kinds of theories. Kocis and Grossmann[1] studied a global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems. Allgor and Barton[2] formulated a general form of mixed-integer optimization in their researches. They also proposed outer approximation algorithms for the separable nonconvex mixed-integer nonlinear programs[3]. Floudas[4] described the fundamentals and several applications of mixed-integer optimization in his paper. Berger et al.[5] proposed a new mixed-integer optimization model for the rescue path planning in an uncertain adversarial environment. There are also some other notable applications of dynamic optimization to chemical engineering processes. Biegler and Sentoni[6] studied a kind of effiReceived date: 2019-12-20 Foundation item: the National Natural Science Foundation of China (No. 61573378), and the BUPT Excellent Ph.D. Students Foundation (No. CX2019113) ∗E-mail: [email protected]
cient formulation and solution of predictive control dynamic optimization model. Ge et al.[7] studied an optimization of alkali-surfactant-polymer (ASP) flooding to increase the oil recovery based on a dynamic scale iterative dynamic programming (IDP) with mixed-integer. In this paper, an MIOCP of distillation column i
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