# A theory of the phenomenology of multipopulation genetic algorithm with an application to the Ising model

## TL;DR

This paper develops a theoretical framework for understanding multipopulation genetic algorithms using statistical mechanics, and demonstrates its application as an efficient alternative to traditional methods in the Ising model.

## Contribution

It introduces a dynamic model for MPGA based on network connectivity and applies it to improve the efficiency of the Ising model simulation.

## Key findings

- The model predicts solution quality evolution in MPGA.
- MPGA can effectively replace thermalization in Ising model simulations.
- Connectivity influences the dynamics and efficiency of MPGA.

## Abstract

Genetic algorithm (GA) is a stochastic metaheuristic process consisting on the evolution of a population of candidate solutions for a given optimization problem. By extension, multipopulation genetic algorithm (MPGA) aims for efficiency by evolving many populations, or islands, in parallel and performing migrations between them periodically. The connectivity between islands constrains the directions of migration and characterizes MPGA as a dynamic process over a network. As such, predicting the evolution of the quality of the solutions is a difficult challenge, implying in the waste of computer resources and energy when the parameters are inadequate. By using models derived from statistical mechanics, this work aims to estimate equations for the study of dynamics in relation to the connectivity in MPGA. To illustrate the importance of understanding MPGA, we show its application as an efficient alternative to the thermalization phase of Metropolis-Hastings algorithm applied to the Ising model.