🤖 AI Summary
This work addresses the challenge of energy stagnation and poor convergence in probabilistic-bit simulated annealing (pSA) when solving large-scale combinatorial optimization problems, which arises from oscillatory dynamics inherent to p-bits. The study is the first to identify these oscillations as stemming from the system’s feedback mechanism and proposes an innovative strategy that suppresses them by selectively deactivating a subset of p-bits. Building on this insight, two novel algorithms—time-averaged pSA (TApSA) and stagnation-aware pSA (SpSA)—are developed. Evaluated through p-bit hardware modeling, Ising formulation, and Python-based simulations on 16 Max-Cut benchmark instances with 800 to 5,000 nodes, the proposed methods achieve an average improvement of 0.8%–98.4% in normalized cut values over conventional pSA, demonstrating substantially enhanced convergence performance.
📝 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 5000 nodes, the proposed methods improve the normalized cut value from 0.8 to 98.4% on average in comparison with the conventional pSA.