Convergence Results for a Class of Time-Varying Simulated Annealing Algorithms

TL;DR

This paper establishes almost sure convergence conditions for a broad class of time-varying simulated annealing algorithms, including derandomized versions, with practical assumptions on kernels and cooling schedules.

Contribution

It provides the first known convergence results for simulated annealing algorithms using time-varying kernels, expanding theoretical understanding.

Findings

First convergence results for time-varying kernel simulated annealing

Conditions on kernels and schedules are easy to verify

Includes derandomized algorithms in the analysis

Abstract

We provide a set of conditions which ensure the almost sure convergence of a class of simulated annealing algorithms on a bounded set $\mathcal{X}\subset\mathbb{R}^d$ based on a time-varying Markov kernel. The class of algorithms considered in this work encompasses the one studied in Belisle (1992) and Yang (2000) as well as its derandomized version recently proposed by Gerber and Bornn (2016). To the best of our knowledge, the results we derive are the first examples of almost sure convergence results for simulated annealing based on a time-varying kernel. In addition, the assumptions on the Markov kernel and on the cooling schedule have the advantage of being trivial to verify in practice.