Scale Invariance Properties in the Simulated Annealing Algorithm

Abstract

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2002
Accession Number
ADA442644

Entities

People

  • Mark Fleischer
  • Sheldon H. Jacobson

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Ground and Sea Platforms
  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Annealing
  • Computer Science
  • Equations
  • Estimators
  • Information Theory
  • Invariance
  • Markov Chains
  • Mathematics
  • Monte Carlo Method
  • New York
  • Parallel Processing
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Inference
  • Statistics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms