Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era.

Machine learning algorithms are inherently multiobjective in nature, where approximation error minimization and model's complexity simplification are two conflicting objectives. We proposed a multiobjective genetic programming (MOGP) for creating a heterogeneous flexible neural tree (HFNT), tree-like flexible feedforward neural network model. The functional heterogeneity in neural tree nodes was introduced to capture a better insight of data during learning because each input in a dataset possess different features.MOGP guided an initial HFNT population towards Pareto-optimal solutions, where the final population was used for making an ensemble system. A diversity index measure along with approximation error and complexity was introduced to maintain diversity among the candidates in the population. Hence, the ensemble was created by using accurate, structurally simple, and diverse candidates from MOGP final population. Differential evolution algorithm was applied to fine-tune the underlying parameters of the selected candidates. A comprehensive test over classification, regression, and time-series datasets proved the efficiency of the proposed algorithm over other available prediction methods. Moreover, the heterogeneous creation of HFNT proved to be efficient in making ensemble system from the final population.

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