Application of Multi-Objective Optimization Techniques to Geotechnical Engineering Problems

Abstract

This research work has its motivation in the ever-increasing use of computational methods in the areas of Civil Engineering. Parameter estimation has assumed a critical importance in predicting failure curves more accurately. Error-in-variables approach gives us a chance to predict simultaneously dependent and independent variables. A method like least square can take into account the error in only ‘x’ values and does not consider the error in values of ‘y’. The vector of unknown parameters (𝜎𝑐 , 𝜎𝑡 , ∅) can also be estimated by the EIV approach along with the variable data points. The failure criterion used is the MSDPu rock failure criterion which deals with failure of low porosity rocks and represents a multi-axial surface in stress space. The objective functions are modelled as a multi-objective optimization problem with the first function accounting for the error due to variables and the second function accounting for the error due to the model. Although, the optimization problem has increased dimension in case of EIV approach, it provides an efficient tool to predict the set of reconciled data and unknown parameters. NSGA-II is an efficient MOEAs developed by Deb et al. (2001) for multi-objective optimization which follows the principle of a fast elitist non-dominated sorting procedure. The two error functions hence formulated by the EIV method is efficiently minimized by the evolutionary algorithm with a little bit of parametric tuning. Estimating pile length for piles is quite difficult, and requires a good knowledge of the subsoil conditions. If the required conditions are formulated into objective functions along with constraint handling then optimized function of (d/L) against load bearing capacity can be found out by NSGA-II.