从量子与热力学视角解析量化优化，揭示其全局寻优机制。
Intuitive Analysis of the Quantization-based Optimization: From Stochastic and Quantum Mechanical Perspective
- 通过迭代量化降低目标函数等值集测度，逼近最优解。
- 基于随机微分方程的模拟验证其在基准函数上优于非线性优化。
- 融合热力学与量子力学分析，适用于复杂优化问题研究者。
本文对基于目标函数量化的优化技术进行了直观分析。该方法通过量化降低包含多个鞍点和局部极小值的等值集测度，最终在极限等值集处找到最优解。为研究其动态行为，我们从直观分析推导出一个过阻尼Langevin动力学模型，以实现等值集的迭代最小化。我们认为，量化优化本质上融合了热力学与量子力学优化的核心思想，是全局优化的重要方法。基于所提出的随机微分方程（SDE），我们利用Witten-Laplacian开展了热力学与量子力学分析。在基准函数上的仿真结果表明，该量化优化方法在非线性优化性能上具有显著优势。
原文摘要 · Abstract (English)
In this paper, we present an intuitive analysis of the optimization technique based on the quantization of an objective function. Quantization of an objective function is an effective optimization methodology that decreases the measure of a level set containing several saddle points and local minima and finds the optimal point at the limit level set. To investigate the dynamics of quantization-based optimization, we derive an overdamped Langevin dynamics model from an intuitive analysis to minimize the level set by iterative quantization. We claim that quantization-based optimization involves the quantities of thermodynamical and quantum mechanical optimization as the core methodologies of global optimization. Furthermore, on the basis of the proposed SDE, we provide thermodynamic and quantum mechanical analysis with Witten-Laplacian. The simulation results with the benchmark functions, which compare the performance of the nonlinear optimization, demonstrate the validity of the quantization-based optimization.
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