Parameter Tuning of the Firefly Algorithm by Three Tuning Methods: Standard Monte Carlo, Quasi-Monte Carlo and Latin Hypercube Sampling Methods

TL;DR

This study tackles parameter tuning for the Firefly Algorithm (FA) by comparing standard Monte Carlo (MC), quasi-Monte Carlo (QMC), and Latin Hypercube Sampling (LHS) as tuning methods across six benchmarks. Through rigorous statistical tests (t-tests, F-tests, Friedman, ANOVA), it finds no meaningful differences in solution quality or tuned parameter values among the three tuning approaches, indicating FA parameters are largely independent of the tuning method. The results suggest FA is robust and flexible to tuning choices, making any of the three methods suitable for parameter tuning in diverse optimization problems. The work also highlights nuanced variance differences on certain benchmarks and points to future work in extending tuning to more parameters and applying Bayesian optimization for hyper-parameter tuning.

Abstract

There are many different nature-inspired algorithms in the literature, and almost all such algorithms have algorithm-dependent parameters that need to be tuned. The proper setting and parameter tuning should be carried out to maximize the performance of the algorithm under consideration. This work is the extension of the recent work on parameter tuning by Joy et al. (2024) presented at the International Conference on Computational Science (ICCS 2024), and the Firefly Algorithm (FA) is tuned using three different methods: the Monte Carlo method, the Quasi-Monte Carlo method and the Latin Hypercube Sampling. The FA with the tuned parameters is then used to solve a set of six different optimization problems, and the possible effect of parameter setting on the quality of the optimal solutions is analyzed. Rigorous statistical hypothesis tests have been carried out, including Student's t-tests, F-tests, non-parametric Friedman tests and ANOVA. Results show that the performance of the FA is not influenced by the tuning methods used. In addition, the tuned parameter values are largely independent of the tuning methods used. This indicates that the FA can be flexible and equally effective in solving optimization problems, and any of the three tuning methods can be used to tune its parameters effectively.

Figures (4)

• Figure 1: Main methods for parameter tuning.
• Figure 2: Main steps of parameter tuning for a given algorithm.
• Figure 3: Three different tuning methods.
• Figure 4: Boxplots of parameter values by MC, QMC, and LHS.