Application of α-stable mutation in a hierarchic evolutionary inverse solver

The multi-deme Hierarchic Genetic Strategy (HGS) developed at the end of the 20th century already proved its capabilities of solving ill-conditioned multi-modal continuous global optimization problems, both benchmarks and real-world engineering inversions. As a standard it uses the mutation operator based on the normal probability distribution. It is a common choice in the continuous evolutionary optimization, but in practice it exhibits some properties that significantly reduce its exploratory abilities, which are crucial in the search for multiple solutions. Those drawbacks can be largely overcome if we replace the normal distribution with a special α-stable distribution for α < 2. In this paper, we study the application of such distribution in the HGS mutation operator. First, we execute standard multi-modal benchmarks to show the impact of particular values of the stable distribution parameters. Then, using selected values of those parameters we employ the HGS with the α-stable mutation in solving an advanced ill-conditioned inverse parametric problem connected to the oil and gas resource investigation. The obtained results show that the α-stable mutation delivers more solutions than the classical normal mutation within a slightly better time budget. Another important conclusion is that the number of solutions is significantly more predictable in the case of α-stable mutation, which is a very advantageous feature from the point of view of the application of a stochastic strategy in the inverse problem solution.