Mathematical Aspects of the Digital Annealer's Simulated Annealing Algorithm

被引：2

作者：

Fukushima-Kimura, Bruno Hideki ^{[1
]}

Kawamoto, Noe ^{[2
]}

Noda, Eitaro ^{[2
]}

Sakai, Akira ^{[1
]}

机构：

[1] Hokkaido Univ, Fac Sci, Kita 10,Nishi 8,Kita Ku, Sapporo, Hokkaido 0600810, Japan

[2] Hokkaido Univ, Grad Sch Sci, Kita 10,Nishi 8,Kita Ku, Sapporo, Hokkaido 0600810, Japan

来源：

JOURNAL OF STATISTICAL PHYSICS | 2023年 / 190卷 / 12期

关键词：

Simulated annealing; Digital Annealer; Stochastic optimization; Combinatorial optimization; QUBO; Ising model; Ground states; COOLING SCHEDULES; OPTIMIZATION;

D O I：

10.1007/s10955-023-03179-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Digital Annealer is a CMOS hardware designed by Fujitsu Laboratories for high-speed solving of Quadratic Unconstrained Binary Optimization (QUBO) problems that could be difficult to solve by means of existing general-purpose computers. In this paper, we present a mathematical description of the first-generation Digital Annealer's Algorithm from the Markov chain theory perspective, establish a relationship between its stationary distribution with the Gibbs-Boltzmann distribution, and provide a necessary and sufficient condition on its cooling schedule that ensures asymptotic convergence to the ground states.

引用

页数：13

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