## 1 Introduction  
The artificial neural network (ANN), a soft computing technique, has been successfully applied to many manufacturing and engineering areas [1]. Neural networks, which originated in mathematical neurobiology, are being used as an alternative to traditional statistical models. Neural networks have the notable ability to derive meaning from complicated or imprecise data and can be used to extract patterns and detect trends that are too complicated to be recognized by either humans or traditional computing techniques. This means that neural networks have the ability to identify and respond to patterns that are similar but not identical to the ones with which they have been trained [2]. ANN has become one of the most important data mining techniques, and can be used for both supervised and unsupervised learning. In fact, feedforward neural networks (FNNs) are the most popular neural networks in practical applications. For a given set of data, a multi-layered FNN can provide a good non-linear relationship. Studies have shown that an FNN, even with only one hidden layer, can approximate any continuous function [3]. Therefore, it is the most commonly used technique for classifying nonlinearly separable patterns [4, 5] and approximating functions [6, 7]. The training process is an important aspect of an ANN model when performance of ANNs is mostly dependent on the success of the training process, and therefore the training algorithm. The aim of the training phase is to minimize a cost function defined as a mean squared error (MSE), or a sum of squared error (SSE), between its actual and target outputs by adjusting weights and biases. Presenting a satisfactory and efficient training algorithm has always been a challenging task. A popular approach used in the training phase is the back-propagation (BP) algorithm, which includes the standard BP [8] and the improved BP [9, 10, 11]. However, researchers have pointed out that the BP algorithm--a gradient-based algorithm--has disadvantages [12, 13]. These drawbacks include the tendency to become trapped in local minima [14] and slow convergence rates [15]. Heuristic algorithms are known for their ability to produce optimal or near optimal solutions for optimization problems. In recent years, several heuristic algorithms--including genetic algorithm (GA) [16], particle swarm optimization (PSO) [17], and ant colony optimization (ACO) [18]--have been proposed for the purpose of training neural networks to enhance the problems of BP-based algorithms. Some algorithms could reduce the probability of being trapped in local minima; however, they still suffer from slow convergence rates. Among heuristic algorithms, PSO is one of the most efficient optimization algorithms in terms of reducing the aforementioned drawbacks of back propagation [19]. However, conventional PSO suffers from the premature convergence problem, especially in complex problems. Cuckoo Search (CS) is a recent heuristic algorithm that has been proposed and developed in recent years by [PERSON] and [PERSON] [20, 21]. This algorithm was inspired by the lifestyle of the cuckoo bird. The particular egg laying and breeding characteristics of the cuckoo bird, in that it lays its eggs in another bird's nest, was the basis for the development of this optimization algorithm. The CS and improved CS algorithms have been used in solving various problems, and are considered to outperform other algorithms [22, 23, 24]. Though PSO converges quickly, it may have premature convergence. CS may converge slightly slower, but it has better explorative ability. In this paper, a hybrid algorithm of PSO and CS (PSOCS) is proposed for training FNNs. In particular, this hybrid algorithm is used to train FNN weights and biases for function approximation and classification problems. The performance of PSOCS, PSO, and CS in training FNNs is also investigated to show the efficiency of the proposed algorithm.