## 1 Introduction  
Investigation of the retaining walls (RWs) behavior under dynamic conditions was originally done in the studies of [PERSON] and [PERSON] [1], and [PERSON] [2]. Afterwards, several cases of numerical and experimental research have been conducted to introduce a method/approach for rational design of RWs under dynamic condition. All relevant studies of active earth pressures can be grouped into three categories i.e., experimental, numerical and analytical. One of the important techniques in field of lateral earth pressure under seismic loading is the Mononobe-Okabe (M-O) method, which has been carried out by [PERSON] et al. [3]. In their studies, a closed-form stress plasticity solution was suggested for gravitational and earthquake-induced earth pressures on RWs. Results of the conducted shake table tests using centrifuge by [PERSON] [4] and [PERSON] and [PERSON] [5] showed that the obtained earth pressure values during shaking are lower than those obtained by the M-O suggested method. Several walls with backfills situations of liquefiable, saturated, cohesion less were considered and used as material for centrifuge dynamic excitation tests in the study conducted by [PERSON] et al. [6]. They found that in the walls with saturated backfill, excess pore pressure generation is the most influential factor on the seismic lateral earth pressure. In another study, a series of RWs constructed by dry medium dense sand under dynamic situation were modeled using finite difference code FLAC in the study carried out by [PERSON] and [PERSON] [7]. They found that the seismic earth pressure results are in agreement with M-O technique, nevertheless, accelerations increased and seismic earth pressures were larger than the values estimated by the M-O approach. In order to approve the assumptions of [PERSON] and [PERSON]'s analytical solution and to describe its range values, a research study was done by [PERSON] et al. [8] using the numerical approach i.e., the commercial finite-element package ABAQUS. The versatility of the numerical methods, finite-element and finite-difference, permitted the treatment of more realistic situations that are not amenable to the analytical solution, including the heterogeneity of the retained soil, and translational flexibility of the wall foundation. In another study, [PERSON] [9] tried to identify the characteristics of the lateral seismic soil pressure on RWs considering various analyses of soil-structure-interaction. Based on the conducted analyses, [PERSON] [9] developed a technique to estimate the maximum seismic soil pressures in order to construct walls resting on firm foundation material and mentioned that the obtained results are better than those suggested in the study conducted by [PERSON] [10]. It seems that most of the previous related research is based on empirical and numerical techniques for the design of RWs. Since there are some other new available techniques such as artificial intelligence (AI), the authors of this study decided to design the safety factor (SF) of the RW developing new hybrid AI methods. Artificial neural network (ANN) is considered to be an AI technique that is able to forecast almost all problems in science and engineering fields [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. However, they have several limitations which discussed and introduced in previous research [22; 23; 24]. As stated in several references [25; 26; 27], the use of efficient optimization algorithms (OAs) can overcome these limitations. Various optimization algorithms such as the genetic algorithm (GA), particle swarm optimization (PSO), artificial bee colony (ABC), and imperialist competitive algorithm (ICA) can be used to solve continuous and non-continuous problems. Due to the high ability of the global search for these OAs, weights and deviations of an ANN can be determined to improve its performance forecast. The above-mentioned hybrid models have been widely-used to solve nonlinear and complex engineering problems [28; 29; 30; 31; 32; 33].