## 1 Introduction
Overall, the modeling accuracy of the genetic programming approach has significantly surpassed those of other neural computing approaches [36; 37]. Among various artificial intelligence algorithms, neural computing still stands out as an auspicious tool for modeling complex geotechnical engineering problems including the CC prediction. This is because neural computing, with a flexible learning paradigm, has high ability to adapt to nonlinear modeling problems, noise in data, and multivariate datasets [38; 39; 40]. Herein, the flexible structure of the neural computing model is a key that can approximate any targeted function with arbitrary accuracy. Thus, neural computing can possess the capability of universal learning [41]. Notably, the learning phase of a neural computing model is formulated as the minimization of a loss function. The standard method of backpropagation algorithms is often employed due to good convergence speed and high prediction performance. Nonetheless, the loss function is generally complex and contains many local minima. Hence, building a neural computing model with the backpropagation algorithms for the CC prediction is still tricky, which often gets trapped in a locally optimal solution [32]. This issue prevents neural computing from predicting the CC at higher accuracy. To address this, hybrid and ensemble systems that integrate metaheuristic optimization and neural computing should be developed for predicting soil CC in order to enhance accuracy. A literature review showed that various metaheuristic algorithms have been successfully employed for optimizing the neural computing models, i.e., genetic algorithm [42], particle swarm optimization [43], differential evolution [44], artificial bee colony (ABC) [45], cuckoo search [46], differential flower pollination [47], and ant-lion optimizer [48]. Herein, the weights of the neural computing models were searched and optimized. Although the performance of these models has been improved, it is still not easy to train the model, because these metaheuristic algorithms are stochastic processes which may cause stagnation in many situations [49]. This study addresses the above-mentioned issue by proposing a new hybrid neural computing approach for predicting soil CC. Thus, a new hybrid algorithm, which is based on ABC [50] and the Levenberg-Marquardt (LM) backpropagation [51], was developed and proposed to optimize the neural computing model. Herein, the ABC acts as a global search method used to optimize the model's weights. During the searching process of ABC, the LM algorithm is randomly activated to play the role of a local search used to enhance the convergence speed of the overall optimization process. The ABC is selected because this is a swarm intelligence that has demonstrated better performance as compared with other benchmark algorithms [50]. In addition, ABC has been successfully employed to solve various real-world problems [52; 53]. For the case of the LM, this algorithm stands out as one of the most robust methods for training neural computing models. This fact is demonstrated by its successful applications in various research domains [54; 55]. The proposed hybrid neural computing model was verified at a large-scale real-life urban project at Hai Phong city (Vietnam). For this task, a dataset of the project with 441 samples, which recorded results of the soil CC and their twelve physical parameters, were used. The subsequent part of this paper is organized as follows: Section 2 reviews the employed computational approaches of multilayer perceptron artificial neural network (MLP ANN) and ABC; Section 3 provides general information regarding the study site and the collected dataset; Section 4 presents the proposed ANN model using the combination of ABC and LM in detail; Section 5 reports the experimental results; followed by concluding remarks on the study stated in Section 6.