An Analysis of Physical, Pseudo-Random and Chaotic Randomness Sources in Nature-Inspired Optimisation

Many studies replace the pseudo-random generator of a nature-inspired optimiser with chaotic or physical sequences and report improvements, but rarely control for the statistical properties through which a sequence acts. We decompose the effect of a randomness source into distribution, dependence and origin with surrogate data. From a physical entropy source, a wood fire on video, we derived conditions differing in one measured property and compared them with the PCG64 generator, logistic and tent maps in particle swarm optimisation (PSO), differential evolution (DE), the grey wolf optimiser (GWO), a genetic algorithm (GA) and artificial bee colony (ABC) on the 2022 Congress on Evolutionary Computation benchmarks. Conditioned physical randomness was equivalent to PCG64 at the pooled level (Cliff’s delta = −0.02). The degradation was traced to two measured properties: a skewed marginal harmed all algorithms, most severely those with index-scaling selection, and serial dependence harmed GWO when weak and all algorithms when strong. The tent map collapsed at a = 2 but was usable for a ∈ [1.99, 2); the logistic map’s advantage for DE was a crossover-rate effect, and the tent map’s advantage for GA was traced to clustered mutation. In the tested settings, optimisers need randomness whose statistics match their operators, not a particular origin.