Two-stepped evolutionary algorithm and its application to stability analysis of slopes

Based on genetic algorithm and genetic programming, a new evolutionary algorithm is developed to evolve mathematical models for predicting the behavior of complex systems. The input variables of the models are the property parameters of the systems, which include the geometry, the deformation, the strength parameters, etc. On the other hand, the output variables are the system responses, such as displacement, stress, factor of safety, etc. To improve the efficiency of the evolution process, a two-stepped approach is adopted; the two steps are the structure evolution and parameter optimization steps. In the structure evolution step, a family of model structures is generated by genetic programming. Each model structure is a polynomial function of the input variables. An interpreter is then used to construct the mathematical expression for the model through simplification, regularization, and rationalization. Furthermore, necessary internal model parameters are added to the model structures automatically. For each model structure, a genetic algorithm is then used to search for the best values of the internal model parameters in the parameter optimization step. The two steps are repeated until the best model is evolved. The slope stability problem is used to demonstrate that the present method can efficiently generate mathematical models for predicting the behavior of complex engineering systems.