UDC 004.021
APPLICATION OF MULTILEVEL QUANTUM SYSTEMS FOR PARALLEL EVALUATION OF SOLUTIONS IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS
L. A. Demidova, Dr. in technical sciences, full professor, professor of the Department of ERP Systems, RTU MIREA, Moscow, Russia;
orcid.org/0000-0003-4516-3746, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
V. V. Maslennikov, lecturer at the Department of ERP Systems, RTU MIREA, Moscow, Russia;
orcid.org/0000-0003-3201-2228, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The article discusses a universal method for implementing quantum-inspired multiobjective optimization algorithms based on the usage of multilevel quantum systems for parallel evaluation of solutions. This meth od uses key principles of quantum mechanics, such as superposition, probabilistic representation of quantum states, and quantum interference. Special attention is paid to the concept of quantum superposition, which allows analyzing many potential solutions simultaneously, thereby increasing the speed of search for optimal solutions on the Pareto front. The mathematical principles of describing multilevel quantum systems using density matrix based on Heisenberg-Weyl operators are described, which makes it possible to interact with a multilevel quantum system in terms of its physical characteristics, as well as analyze the coherence and dy namics of the system. In addition, a mathematical description of the mechanisms for choosing promising so lutions using the analogy of quantum interference is presented. Based on the proposed method, quantum inspired version of NSGA-III multiobjective optimization genetic algorithm is implemented. The quality of the algorithm is evaluated on test tasks of multiparty multiobjective optimization. Test results show that the developed quantum-inspired algorithm surpasses classical multiobjective optimization algorithms in accura cy of approximation of the Pareto front and the ability to find uniformly distributed solutions.
Key words: : optimization, multiobjective optimization, quantum-inspired algorithm, qudit, density matrix, Heisenberg-Weyl operators, quantum superposition, quantum interference, Pareto front, evaluation of solu tions.