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

This research paper proposes a memetic algorithm based on a hybridization of two metaheuristic approaches, a single-solution method and a compact optimization algorithm. The hybrid algorithm is thus a bi-module framework, where each module encapsulates a different search logic. Both modules use the Non-Uniform Mutation, although with different flavors: the first one acting on a single variable at a time, the second one acting on multiple variables. Hence, the algorithm is dubbed "compact Single/Multi Non-Uniform Mutation" (in short, cSM). It is designed for being suitable for tackling optimization problems on memory-constrained devices, i.e., devices for which the available memory may be not enough to run population-based metaheuristics. The performance of cSM is evaluated by an extensive comparative analysis including 12 state-of-the-art memory-saving (also called "lightweight") algorithms on three well-known testbeds, namely the BBOB, the CEC-2014, and CEC-2017 benchmarks, as well as seven real-world optimization problems included in the CEC-2011 benchmark. In the case of the CEC benchmarks, our method is also compared against the top (population-based) algorithms that participated in respective competitions. The numerical results indicate that, compared to all the other lightweight algorithms under study, the proposed algorithm is better at handling most functions at different dimensionalities, especially in the case of non-separable problems.

No abstract