The energy level stabilization process of the multi-scale quantum harmonic oscillator algorithm (MQHOA) is the core part of the algorithm

which plays an important role in avoiding the algorithm falling into local optimum and improving the accuracy of the algorithm.In the studying of the energy level stabilization process of the algorithm

it is found that different energy level stabilization criteria will result in different performance of the algorithm at the same energy level.The relatively loose criterion makes the iteration of the algorithm inadequate in the process of energy level stabilization and easy to fall into premature.The more stringent criterion can make the wave function reach a stable state at the same energy level

improve the global search ability of the algorithm

but meanwhile the computing cost will also rise.Experiments show that loose energy level stability criterion of the algorithm has good effect on solving unimodal simple functions

and strict energy level stability criterion of it is suitable for solving multimodal complex functions.The algorithm has been effectively applied in resource optimization

adaptive control and energy consumption optimization management.