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Recently, an explosive growth in the potential use of natural metaphors in modelling and solving large-scale non-linear optimization problems. Artificial neural network (ANN) is a potent gadget broadly utilized in many data classification tasks. Fundamentally, nature-inspired algorithms have demonstrated their effectiveness and ability over traditional algorithms for generating the optimal ANN parameters, rules and topology that provide the best classification performance with regarding to the quality of the solution, computational cost and avoiding local minima. The literature is vast and growing. This study provides a review on the basic theories and main recent algorithms for optimizing the ANN. Different types of nature-inspired meta-heuristic algorithms are presented; outlining the concepts and components that are used in order to give a summary and ease of the state-of-the-arts to find suitable methods in real world applications for the readers. Additionally, this survey covers the most used type of neural networks, feed-forward neural network (FFNN) in several optimized applications. The performances of FFNNs designed by nature-inspired algorithms have been explored in single and multi-dimensional optimization space; highlighting their models, features, objectives, constraints, etc. to analyse their differences and similarities. A comprehensive survey of the earliest works and recent modified in the last decade in addition to expect approaches has been investigated in details.