The new hp-HGS multi-deme, genetic strategy (hp-adaptive finite element method combined with hierarchic genetic strategy) for economic solving parametric inverse problems is presented in this paper. Inverse problems under consideration are formulated as the global optimization ones, where the objective is to express the discrepancy between the computed and measured energy. The efficiency of the proposed strategy results from coupling an adaptative accuracy of solving optimization problems with the accuracy of hp-FEM problem solver. The paper briefly reports the results of the asymptotic analysis that ensures the global search possibility and allows to compare the efficiency with the single population algorithm as well as with the instance of HGS without adaptation of the direct solver accuracy. A computational example shows the course of tuning the hp-FEM strategy for the simple L-shape domain benchmark.