Multi-deme, twin adaptive strategy hp-HGS

作者：Barabasz Barbara^*; Migorski Stanislaw; Schaefer Robert; Paszynski Maciej

来源：Inverse Problems in Science and Engineering, 2011, 19(1): 3-16.

DOI：10.1080/17415977.2010.531477

• finite element method
• hp-adaptivity
• hierarchical genetic search
• multi-modal problems
• heat transfer

The article presents a twin adaptive, effective stochastic strategy for solving difficult inverse problems formulated as global optimization ones. It is especially dedicated to multimodal, noisy problems. The hp-hierarchic genetic strategy (hp-HGS) strategy offers two ways to decrease computational and memory costs. Firstly, it decreases the number of objective evaluations by using an adaptation of the inverse problem accuracy (HGS strategy). Secondly, the cost of the direct problem solution, necessary for objective evaluation, is decreased by the proper scaling of the finite element method error using the hp adaptation technique. The theory of hp-HGS mentioned in this article can guarantee its asymptotic correctness in the probabilistic sense i.e. the possibility of finding all solutions from a specified set. The theoretical results make the comparison of the expected computational cost of a single genetic epoch at a particular level of the hp-HGS tree possible. Moreover, Theorem 3.1 verifies the hp-HGS applicability condition (the Lipschitz continuity of the energy functional) for heat conduction problems. A simple computational test for the heat conduction inverse problem in an L-shape domain shows the hp-HGS behaviour in the case of objective bimodality.

• 出版日期2011