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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Enhanced convergence in p-bit based simulated annealing with partial deactivation for large-scale combinatorial

Naoya Onizawa1, Takahiro Hanyu2

  • 1Research Institute of Electrical Communication, Tohoku University, Sendai, 980-8577, Japan. naoya.onizawa.a7@tohoku.ac.jp.

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This study addresses limitations in simulated annealing with probabilistic bits (pSA) for optimization. Novel TApSA and SpSA algorithms improve performance by managing p-bit oscillations, enhancing solutions for complex problems.

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Area of Science:

  • Computational Science
  • Optimization Algorithms
  • Statistical Physics

Background:

  • Simulated annealing with probabilistic bits (pSA) is used for combinatorial optimization.
  • pSA faces limitations due to oscillations among probabilistic bits (p-bits).
  • These oscillations impede energy reduction in the Ising model, hindering complex problem-solving.

Purpose of the Study:

  • To critically investigate the limitations of pSA in large-scale combinatorial optimization.
  • To identify the root cause of energy stagnation in pSA.
  • To propose novel algorithms for improving pSA performance.

Main Methods:

  • In-depth analysis of the pSA process and p-bit oscillations.
  • Detailed simulations to understand energy stagnation and feedback mechanisms.
  • Development and testing of two new algorithms: time average pSA (TApSA) and stalled pSA (SpSA).
  • Implementation using Python simulations on maximum cut benchmarks.

Main Results:

  • Identified inherent feedback mechanisms in pSA as the cause of disruptive oscillations.
  • TApSA and SpSA algorithms were designed based on partial deactivation of p-bits.
  • On 16 benchmarks (800-5000 nodes), proposed methods improved normalized cut values by 0.8% to 98.4% on average compared to conventional pSA.

Conclusions:

  • The proposed TApSA and SpSA algorithms effectively mitigate pSA limitations caused by p-bit oscillations.
  • These novel methods offer significant performance improvements for large-scale combinatorial optimization problems.
  • Partial deactivation of p-bits is a viable strategy for enhancing simulated annealing algorithms.