Non-Stationary Stochastic Global Optimization Algorithms

TL;DR

This paper extends a formal framework for stochastic global optimization algorithms to include non-stationary processes, covering various algorithms like genetic algorithms and simulated annealing, with new convergence conditions and formalizations.

Contribution

It generalizes convergence conditions to non-stationary Markov processes and formalizes additional algorithms within the systematic framework.

Findings

Generalized convergence lemma for non-stationary Markov processes

Developed Markov kernels for selection schemes

Formalized simulated-annealing and evolutionary strategies

Abstract

Gomez proposes a formal and systematic approach for characterizing stochastic global optimization algorithms. Using it, Gomez formalizes algorithms with a fixed next-population stochastic method, i.e., algorithms defined as stationary Markov processes. These are the cases of standard versions of hill-climbing, parallel hill-climbing, generational genetic, steady-state genetic, and differential evolution algorithms. This paper continues such a systematic formal approach. First, we generalize the sufficient conditions convergence lemma from stationary to non-stationary Markov processes. Second, we develop Markov kernels for some selection schemes. Finally, we formalize both simulated-annealing and evolutionary-strategies using the systematic formal approach.