Quantization-based Optimization with Perspective of Quantum Mechanics

Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a new researching framework for global optimization algorithms. In this paper, we provide the analysis for quantization-based optimization based on the Schr"odinger equation to reveal what property in quantum mechanics enables global optimization. We present that the tunneling effect derived by the Schr"odinger equation in quantization-based optimization enables to escape of a local minimum. Additionally, we confirm that this tunneling effect is the same property included in quantum mechanics-based global optimization. Experiments with standard multi-modal benchmark functions represent that the proposed analysis is valid.