Uniform and non-uniform pseudorandom number generators in a genetic algorithm applied to an order picking problem

Abstract

In recent years, a trend towards alternative random or more precisely pseudorandom number generators could have been observed, viz. non-uniform generators that are based on chaotic maps (e.g. Ikeda Map) and uniform generators that are based on linear recurrence (e.g. Xorshift). Especially, chaotic maps have shown their superiority over canonical pseudorandom number generators in different heuristics solving both single- and multi-objective problems. However, the reasons for this superiority have not been completely unveiled and are probably based on the non-uniform distribution of the generated pseudorandom numbers. The aim of this research is therefore to investigate the influence of both uniform and non-uniform pseudorandom number generators on the convergence behaviour and computing time of a Genetic Algorithm (GA) applied to an order picking problem. A GA is a heuristics that imitates the natural selection process using stochastic methods for both the initial creation as well as the further evolution of the population. The influence of different non-uniform pseudorandom generators is therefore compared against uniform pseudorandom number generators by optimising the picking order of a discrete warehouse. As a result, Xorshift-based pseudorandom number generators are often better — though not significantly — with respect to the convergence for less complex test cases. On the other hand, the Ikeda Map is often significantly better for more complex test cases. However, uniform Xorshift-based pseudorandom number generators are often superior with respect to computation time.