On the use of single non-uniform mutation in lightweight metaheuristics

This paper introduces two novel lightweight algorithms based on a single non-uniform mutation (SNUM) operator: a single solution algorithm and a SNUM-based compact Genetic Algorithm. The first algorithm, called also SNUM with reference to the operator, performs the search by an iterative process that perturbs one design variable selected randomly from a single solution. The latter, called compact SNUM (cSNUM), incorporates the SNUM mechanism into the compact Genetic Algorithm scheme, that replaces a population of solutions with a probabilistic model. Both approaches are characterised by a purposely simple and highly generic algorithmic structure. These two attractive features make it possible to readily employ the core part of each algorithm and combine it with other techniques for extended complexity. The results obtained from applying the two proposed algorithms on the BBOB and CEC-2017 benchmarks reveal that the use of SNUM is largely beneficial. Not only the two algorithms (in particular cSNUM) are able to deal with separable functions, especially when the problem dimensionality increases, but they also prove to be competitive on other classes of functions, displaying very good performances compared to other methods from the literature, also on non-separable functions