Enhanced Convergence in p-bit Based Simulated Annealing with Partial Deactivation for Large-Scale Combinatorial Optimization Problems

TL;DR

This paper introduces two novel algorithms, TApSA and SpSA, that enhance the convergence of p-bit based simulated annealing by partially deactivating p-bits, significantly improving solutions for large-scale combinatorial optimization problems.

Contribution

The paper proposes two new algorithms, TApSA and SpSA, which mitigate oscillations in p-bit based simulated annealing, enabling better performance on large-scale problems.

Findings

Improved normalized cut values from 0.8% to 98.4% on benchmarks.

Identified feedback mechanism as cause of oscillations.

Demonstrated effectiveness on maximum cut problems with up to 5,000 nodes.

Abstract

This article critically investigates the limitations of the simulated annealing algorithm using probabilistic bits (pSA) in solving large-scale combinatorial optimization problems. The study begins with an in-depth analysis of the pSA process, focusing on the issues resulting from unexpected oscillations among p-bits. These oscillations hinder the energy reduction of the Ising model and thus obstruct the successful execution of pSA in complex tasks. Through detailed simulations, we unravel the root cause of this energy stagnation, identifying the feedback mechanism inherent to the pSA operation as the primary contributor to these disruptive oscillations. To address this challenge, we propose two novel algorithms, time average pSA (TApSA) and stalled pSA (SpSA). These algorithms are designed based on partial deactivation of p-bits and are thoroughly tested using Python simulations on maximum cut benchmarks that are typical combinatorial optimization problems. On the 16 benchmarks from 800 to 5,000 nodes, the proposed methods improve the normalized cut value from 0.8% to 98.4% on average in comparison with the conventional pSA.