论文标题
关于改进和自适应动力学模拟退火的收敛性
On the convergence of an improved and adaptive kinetic simulated annealing
论文作者
论文摘要
受[Fang等人的工作的启发。一种改进的退火方法及其大型行为。随机过程。应用。 (1997), Volume 71 Issue 1 Page 55-74.], who propose an improved simulated annealing algorithm based on a variant of overdamped Langevin diffusion with state-dependent diffusion coefficient, we cast this idea in the kinetic setting and develop an improved kinetic simulated annealing (IKSA) method for minimizing a target function $U$.为了分析其融合，我们利用了[Monmarché最近引入的框架。亚稳定设置和动力学模拟退火中的低碳率。概率。理论相关领域（2018年），第172页第1215-1248页。]对于动力学模拟退火（KSA）的情况。 IKSA的核心思想在于引入一个参数$ c> \ inf U $，事实上，该参数修改了优化景观，并以最大$ c - \ inf u $的最大限制了IKSA的关键高度。因此，与KSA相比，IKSA的收敛性更高。为了调整参数$ c $，我们提出了一种自适应方法，我们称之为iaksa，该方法利用了算法生成的运行最小值，因此避免了需要手动调整$ c $以提高性能的需求。我们对某些标准的全局优化基准函数提出了积极的数值结果，这些函数验证了与其他基于langevin的退火方法相比，Iaksa的收敛性改善。
Inspired by the work of [Fang et al.. An improved annealing method and its large-time behaviour. Stochastic Process. Appl. (1997), Volume 71 Issue 1 Page 55-74.], who propose an improved simulated annealing algorithm based on a variant of overdamped Langevin diffusion with state-dependent diffusion coefficient, we cast this idea in the kinetic setting and develop an improved kinetic simulated annealing (IKSA) method for minimizing a target function $U$. To analyze its convergence, we utilize the framework recently introduced by [Monmarché. Hypocoercivity in metastable settings and kinetic simulated annealing. Probab. Theory Related Fields (2018), Volume 172 Page 1215-1248.] for the case of kinetic simulated annealing (KSA). The core idea of IKSA rests on introducing a parameter $c > \inf U$, which de facto modifies the optimization landscape and clips the critical height in IKSA at a maximum of $c - \inf U$. Consequently IKSA enjoys improved convergence with faster logarithmic cooling than KSA. To tune the parameter $c$, we propose an adaptive method that we call IAKSA which utilizes the running minimum generated by the algorithm on the fly, thus avoiding the need to manually adjust $c$ for better performance. We present positive numerical results on some standard global optimization benchmark functions that verify the improved convergence of IAKSA over other Langevin-based annealing methods.
