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A piecewise Markovian model for simulated annealing with stochastic cooling schedules

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. Kolonko
M. Kolonko*
Affiliation:
Universität Hildesheim
*
∗Postal address: Institut für Mathematik, Universität Hildesheim, Marienburger Platz 22, D-31141 Hildesheim, Germany
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Abstract

We introduce a stochastic process with discrete time and countable state space that is governed by a sequence of Markov matrices . Each Pm is used for a random number of steps Tm and is then replaced by Pm+1. Tm is a randomized stopping time that may depend on the most recent part of the state history. Thus the global character of the process is non-Markovian.

This process can be used to model the well-known simulated annealing optimization algorithm with randomized, partly state depending cooling schedules. Generalizing the concept of strong stationary times (Aldous and Diaconis [1]) we are able to show the existence of optimal schedules and to prove some desirable properties. This result is mainly of theoretical interest as the proofs do not yield an explicit algorithm to construct the optimal schedules.

Keywords

INHOMOGENEOUS MARKOV CHAINSSEMI-REGENERATIVE PROCESSESSTRONG STATIONARY TIMES

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 649 - 658
Copyright
Copyright © Applied Probability Trust 1995 

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