Quantum Dynamics Framework with Quantum Tunneling Effect for Numerical Optimization

In recent years, optimization algorithms have developed rapidly, especially those which introduce quantum ideas, which perform excellently. Inspired by quantum thought, this paper proposes a quantum dynamics framework (QDF) which converts optimization problems into the problem of the constrained ground state of the quantum system and analyzes optimization algorithms by simulating the dynamic evolution process of physical optimization systems in the ground state. Potential energy equivalence and Taylor expansion are performed on the objective function to obtain the basic iterative operations of optimization algorithms. Furthermore, a quantum dynamics framework based on the quantum tunneling effect (QDF-TE) is proposed which adopts dynamic multiple group collaborative sampling to improve the quantum tunneling effect of the QDF, thereby increasing the population diversity and improving algorithm performance. The probability distribution of solutions can be visually observed through the evolution of the wave function, which also indicates that the QDF-TE can strengthen the tunneling effect. The QDF-TE was evaluated on the CEC 2017 test suite and shown to be competitive with other heuristic optimization algorithms. The experimental results reveal the effectiveness of introducing a quantum mechanism to analyze and improve optimization algorithms.