### Empirical Models and Soft Computing Techniques  
[PERSON] et al. [11] provided a preliminary relation of measuring horizontal ground displacement in meter's relying on 60 case histories, majority of them are obtained in Niigata and Noshiro, Japan. It can be seen from Table 1 that the equations are very common and easy to apply that contains only two parameters of site geometry and not considered seismic and geotechnical parameters but it has been suggested for limited dataset making it insufficiently broad to be extended to additional lateral displacement sites. [PERSON] and [PERSON] [25] suggested \"liquefaction severity index\" (\(LSI\)) to estimate maximum horizontal ground displacement generated by an earthquake. The \(LSI\) (inches) was calculated using distance to seismic energy source (\(R\)) (km); and moment magnitude (\(M_{w}\)) with maximum range of horizontal ground displacement as 2.5 m. This model assumes that the value of \(LSI\) depends on only seismic parameters (\(R\), \(M_{w}\)). At the time, the proposed equation drew the attention of engineers. Although this method may have been useful for assessing lateral spreads inside the western United States, but lacks applicability and hence didn't receive widespread use. [PERSON] et al. [21] used multiple linear regression (MLR) for developing relation to estimate lateral ground deformation for free face and sloping ground situations, respectively, utilizing data gathered by [PERSON] and [PERSON] [26; 27], including three kinds of input variables:  
1. Seismic parameters--seismic source distance (\(R\), km) and earthquake magnitude, (\(M\)). 2. Topographic characteristics (in percent)--gradient of ground surface (\(S\)) and free face ratio. Geotechnical parameters (in percent)--average mean particle size within \(T_{15}\) (\(D50_{15}\), mm) and averaged fines contents in \(T_{15}\) (\(F_{15}\))  
The MLR approach was used to create the [PERSON] et al. [12] model, presented in 1992, was built on upgraded results of [PERSON] and [PERSON] [26; 27] for estimating lateral ground displacement, \(D_{H}\left(\text{m}\right)\). As indicated in Table 1 the models include free face and sloping ground conditions equations. This model gained attraction amongst geotechnical engineers due to its utilization of a huge dataset from various earthquakes, as well as geometry of site, geotechnical data, and seismic characteristics. Although, it does have some limits in terms of applications. For example, the free face equation was used when \(5\leq W\leq 20\%\), [PERSON] and [PERSON] [28] gathered the latest dataset of liquefaction-induced lateral ground deformation based on uncertainties of different boreholes, which outperformed [PERSON] et al. [11] [PERSON] [29], [PERSON] [30], [PERSON] et al. [31], [PERSON] et al. [12], and [PERSON] and [PERSON] [32] models. Soft computing is made up of a variety of techniques that function together, such as: artificial neural network, genetic algorithm, neuro-computing etc. [PERSON] and [PERSON] [13] reported that new area of machine learning has arisen for handling decisions, modeling, and control issues. [PERSON] and [PERSON] [33] and [PERSON] and [PERSON] [13] both used artificial neural networks (ANN) to estimate horizontal ground displacement. [PERSON] et al. [31] computed lateral displacement for free face and sloping ground using genetic programming (GP) using upgraded case data from [PERSON] et al. [12]. In comparison to the MLR approach, the proposed GP approach has some advantages. Table 1 shows the proposed equations for free