Improved harmony search methods to replace variational principle in geotechnical problems

Variational principle is an important principle in engineering discipline. This principle is suitable for simple problems where an analytical expression can be determined, but there are many practical problems where the classical variational principle is practically impossible to be applied. In this paper, the authors will try to demonstrate that the variational principle can be replaced by the use of modern artificial intelligence based optimization method (harmony search method) which can be applied to much more complicated problems. Two different improved harmony search algorithms are proposed in this paper. The new algorithms differ from the original algorithm in that: (1) The harmonies are rearranged into several pairs and the better pairs are used to develop several new harmonies; (2) Different probabilities are assigned to different harmonies. The robustness of the proposed methods is demonstrated by using three difficult examples, and the sensitivities of the related optimization parameters are investigated through statistical orthogonal analysis.