Multiscale Quantum Gradual Approximation Algorithm: An Optimization Algorithm With a Step-by-Step Approximation Strategy

Abstract

In quantum swarm intelligence algorithms, the tunneling effect of the particles is determined by the potential energy acting on the particles. The tunneling effect of the particles affects the global search ability and convergence speed of the algorithm. Quantum algorithms with a single potential energy are prone to premature convergence under certain complex test functions. In this paper, we propose a multiscale quantum gradual approximation algorithm (MQGAA), which simply uses different approximation strategies to obtain different potential energy functions, to solve the premature problem of the optimization algorithm. In the MQGAA, particles undergo a transition from an unconstrained state to a constrained state at each scale. To demonstrate the effectiveness of the proposed algorithm, experiments are carried out with several common and effective stochastic algorithms on N-dimensional double-well potential functions and classical benchmark functions. We also use the Wilcoxon rank test to detect the performance of MQGAA. The experimental results show that the algorithm using a step-by-step approximation strategy achieves a better optimization performance on some complex test functions.

Keywords

• Taylor approximation
• unconstrained state
• constrained state
• multiscale
• multiscale quantum harmonic oscillator algorithm