论文标题
优化问题的量子动力学
Quantum Dynamics of Optimization Problems
论文作者
论文摘要
在这封信中，通过建立优化问题的schrödinger方程，优化问题将其转变为一个势能作为势能的约束状态量子问题。建立了目标函数与波浪函数之间的数学关系，并实现了优化问题的量子解释。在黑匣子模型下，优化问题的schrödinger方程用于建立动力学方程，即优化算法的时间演变的fokker-planck方程，以及根据Fokker-planck Equalation的解释给出优化算法的基本迭代结构。 Fokker-Planck方程的建立允许使用动态方法研究优化算法，并有望成为算法动力学的重要理论基础。
In this letter, by establishing the Schrödinger equation of the optimization problem, the optimization problem is transformed into a constrained state quantum problem with the objective function as the potential energy. The mathematical relationship between the objective function and the wave function is established, and the quantum interpretation of the optimization problem is realized. Under the black box model, the Schrödinger equation of the optimization problem is used to establish the kinetic equation, i.e., the Fokker-Planck equation of the time evolution of the optimization algorithm, and the basic iterative structure of the optimization algorithm is given according to the interpretation of the Fokker-Planck equation. The establishment of the Fokker-Planck equation allows optimization algorithms to be studied using dynamic methods and is expected to become an important theoretical basis for algorithm dynamics.
