Fast Solving Complete 2000-Node Optimization Using Stochastic-Computing Simulated Annealing

Abstract

In this paper, we evaluate stochastic-computing simulated annealing (SC-SA) for solving large-scale combinatorial optimization problems. SC-SA is designed using stochastic computing, where the computatoin is reazlied using random bitstream, resulting in fast converging to the global minimum energy of the problems. The proposed SC-SA is compared with a typical SA and existing simulated-annealing (SA) processors on the maximum cut (MAX-CUT) problems, such as Gset that is a benchmark for SA. The simulation results show that SC-SA realizes a few orders of magnitude faster than a typical SA. In addition, SC-SA achieves better MAX-CUT scores than other existing methods on K2000 that is a complete 2000-node optimization problem.

Figures (8)

• Figure 1: Example of an Ising model with three spins. The Ising model is used to represent combinatorial optimization problems solved by SA or SC-SA with reaching the global minimum energy of the model.
• Figure 2: Spin-gate circuit that calculates \ref{['eqn:I']}, \ref{['eqn:updown']}, and \ref{['eqn:m']} based on stochastic computing and integral stochastic computing.
• Figure 3: (a) Example of a MAX-CUT problem with five veritces and (b) the solution of MAX-CUT problem. A cut value of the solution is maximized with two separated groups of Group A (veritces 1,5) and Group B (veritces 2,3,4).
• Figure 4: $h$ and $J$ for the MAX-CUT problem shown in in Fig.3 (a).
• Figure 5: Simulation conditions: (a) $I_0$ control as $I_0(t+\tau) = (1/\beta)\cdot I_0(t)$ for reaching the global minimum energy and (b) an example of an energy transition.