Genetic algorithm demystified for cosmological parameter estimation

TL;DR

This work investigates genetic algorithms (GA) as a supplementary tool to Markov chain Monte Carlo (MCMC) for cosmological parameter estimation in a curved ΛCDM framework. By using cosmic chronometers (CC) and Pantheon+ Type Ia supernovae (SNe) data, the authors study how GA hyperparameters—particularly the fitness function and mutation rate—shape the evolved parameter distributions and how GA results compare with MCMC posteriors. They show that a carefully chosen fitness function (FF$_3$) yields highly localized, non-Gaussian parameter sets that align with MCMC estimates when SNe data are included, and demonstrate that GA–Fisher uncertainty estimates can reproduce MCMC-like constraints under informative data. The study concludes that GA can provide valuable, complementary insights to MCMC for cosmological analysis, with practical guidance on hyperparameter tuning, and suggests extensions to more complex cosmologies and alternative sampling/optimization strategies.

Abstract

Genetic algorithm (GA) belongs to a class of nature-inspired evolutionary algorithms that leverage concepts from natural selection to perform optimization tasks. In cosmology, the standard method for estimating parameters is the Markov chain Monte Carlo (MCMC) approach, renowned for its reliability in determining cosmological parameters. This paper presents a pedagogical examination of GA as a potential corroborative tool to MCMC for cosmological parameter estimation. Utilizing data sets from cosmic chronometers and supernovae with a curved $Λ$CDM model, we explore the impact of GA's key hyperparameters -- such as the fitness function, crossover rate, and mutation rate -- on the population of cosmological parameters determined by the evolutionary process. We compare the results obtained with GA to those by MCMC, analyzing their effectiveness and viability for cosmological application.

Figures (6)

• Figure 1: [Top] Anatomy of a population in GA and [Bottom] GA's flowchart.
• Figure 2: [Left] Expansion rate from CC Moresco:2020fbm and [right] distance moduli from SNe Brout:2021mpjBrout:2022vxfScolnic:2021amr with curved $\Lambda$CDM predictions \ref{['eq:normalized_expansion_rate_lcdm']} and \ref{['eq:distance_modulus_lcdm']}. Note that $h=H_0/100$ km s$^{-1}$Mpc$^{-1}$ and $\Omega_{de0}=1-\Omega_{m0}-\Omega_{k0}$.
• Figure 3: Changing fitness---GA final population distribution for different fitness functions; FF=$-\chi^2/2, 100/\chi^2, \exp(-\chi^2/2)$ with fixed mutation (0.5,0.3) and crossover (50%) rates. (Left column) results obtained with only CC data; (right column) results with CC and SNe. In the right column, the Gaussian (GA-Fisher) corresponds to the GA best solution compounded with a Fisher matrix uncertainty estimate based on the likelihood.
• Figure 4: Changing mutation---GA final population distribution for different mutation rates; mutation=$(0.5, 0.3), (0.8, 0.2)$ with fixed fitness function $\exp(-\chi^2/2)$ and crossover rate (50%). (Left column) results obtained with only CC data; (right column) results with CC and SNe. In the right column, the Gaussian (GA-Fisher) corresponds to the GA best solution compounded with a Fisher matrix uncertainty estimate based on the likelihood.
• Figure 5: Changing crossover---GA final population distribution for different crossover rates; crossover=$50\%, 80\%, 30\%$ with fixed fitness function $\exp(-\chi^2/2)$ and mutation rate $(0.5, 0.3)$. (Left column) results obtained with only CC data; (right column) results with CC and SNe. In the right column, the Gaussian (GA-Fisher) corresponds to the GA best solution compounded with a Fisher matrix uncertainty estimate based on the likelihood.