In this paper, we propose the use of a hybrid algorithm for the inversion of 3D Alternate Current (AC) resistivity logging measurements. The forward problem is solved using a goal-oriented self-adaptive hp-Finite Element Method (hp-FEM) that provides exponential convergence of the numerical error with respect to the mesh size. The inverse problem is solved using a Hierarchical Genetic Search (HGS) coupled with a Broyden–Fletcher–Goldfar–Shanno (BFGS) method. Individuals from the genetic populations represent the resistivity of the formation layers. The fitness function is estimated based on hp-FEM results. The hybrid method controls the accuracy of evaluation of particular individuals, as well as the accuracy of the genetic coding. After finding those regions where the fitness function has small values, the local search method by means of BFGS algorithm is executed. The paper is concluded with numerical results for the hybrid algorithm. magnetic field (magnetizing field) electric field electric current density electric free charge distribution permittivity, permeability, conductivity, resistivity and angular frequency domain in ℝ 3 and its boundary ∂Ω=Γ main space of forward solutions (see (3) and (4)) and its conjugate and biconjugate spaces sesquilinear form of Maxwell's equation (see (10)) quantity of interest functional (see (23)) primal and dual forward solutions approximate hp-FEM forward solutions primal and dual relative hp-FEM errors admissible set of inverse solutions (see (43)) and fitness function domain (see Section 5) 
A hybrid method for inversion of 3D AC resistivity logging measurements