A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm

Zhe Liu () and Shurong Li ()
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Zhe Liu: Beijing University of Posts and Telecommunications
Shurong Li: Beijing University of Posts and Telecommunications

Annals of Operations Research, 2022, vol. 311, issue 2, No 13, 853-898

Abstract: Abstract This article is concerned with the numerical solution for a class of interval multi-objective mixed-integer optimal control problems (IMOMIOCPs). The IMOMIOCPs under investigation are typical NP-hard problems involve unknown-but-bounded interval parameters, multiple objectives, and mixed-integer dynamic controls. Accordingly, a new numerical method based on quantum heuristic algorithm is designed, which has the following modules: (i) Control vector parameterization and the fourth order Runge–Kutta method for model discretization, (ii) interval programming based on interval credibility for addressing interval parameters, (iii) coevolution of Quantum Annealing and Quantum Krill Herd for searching the optimal mixed-integer decisions, and (iv) the multiple populations for multi-objective technology for establishing the Pareto optimal front. The analyses on convergence and computational complexity of the proposed optimization mechanism are given. Moreover, simulation results on benchmark functions and a practical engineering IMOMIOCP verify that the proposed numerical method is more excel at achieving promising results than some classic algorithms and state-of-the-art algorithms.

Keywords: Interval multi-objective optimization; Mixed-integer optimal control problems; Quantum annealing; Quantum krill herd; Polymer flooding (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-03998-1

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