For designing of pavements, California Bearing Ratio (CBR) value is an important parameter which is used to determine the strength of the subgrade soils. However, it is to be mentioned that, CBR test is tedious and laborious. Thus, in the present paper an attempt has been made to develop relationships between CBR and various soil index properties such as specific gravity (G), coefficient of uniformity (Cu), coefficient of curvature (Cc), liquid limit (LL), plastic limit (PL), plasticity index (PI), optimum moisture content (OMC) and maximum dry density (MDD) for alluvial soil in West Bengal, India. Empirical relationships have been proposed for both soaked and un-soaked CBR values as a function of these soil index properties by Genetic Expression Programing (GEP). Further, the same index properties have been used to predict CBR values by artificial neural network (ANN) and krigging method. The results clearly reveals that the GEP and ANN and krigging methods can be successfully used for predicting both the soaked and un-soaked CBR values by using the index properties of soil. Moreover, the developed relationships have been compared with the past available relationships. Furthermore, a multi objective optimization has been carried out for getting maximum CBR values.