Evolutionary algorithms (EAs) are very popular tools to design and evolve artificial neural networks (ANNs), especially to train them. These methods have advantages over the conventional backpropagation (BP) method because of their low computational requirement when searching in a large solution space. In this paper, we employ Chemical Reaction Optimization (CRO), a newly developed global optimization method, to replace BP in training neural networks. CRO is a population-based metaheuristics mimicking the transition of molecules and their interactions in a chemical reaction. Simulation results show that CRO outperforms many EA strategies commonly used to train neural networks.
Using EA to train ANNs has become an active research topic. Many EAs, e.g. genetic algorithm (GA) @cite_13 , simulated annealing (SA) @cite_27 , and particle swarm optimization (PSO) @cite_25 have been used. Yet relatively few invasive" methods have been studied to achieve the best performance of EA-based neural networks. Sexton used Tabu Search (TS) for neural network training @cite_5 , where TS was used to train a fixed neural network with six hidden layer neurons. The TS solution is given in the form of vectors representing all the weights of the network. The testing data set was a collection of randomly generated two-dimensional points @math where @math and @math . The output data set was generated by simple mathematical functions. The result demonstrated that TS-based networks could outperform conventional BP-derived networks. SA and GA were also implemented for the same data set @cite_22 .
@cite_22 @cite_27 @cite_5 @cite_13 @cite_25
2083651719 2112061072 2021309800 2809090039
This paper aims at verifying the accuracy of Artificial Neural Networks (ANN) in assessing the transient stability of a single machine infinite bus system. The fault critical clearing time obtained through ANN is compared to the results of the conventional equal area criterion method. The multilayer feedforward artificial neural network concept is applied to the system. The training of the ANN is achieved through the supervised learning; and the back propagation technique is used as a learning method in order to minimize the training error. The training data set is generated using two steps process. First, the equal area criterion is used to determine the critical angle. After that the swing equation is solved using the point-to-point method up to the critical angle to determine the critical clearing time. Then the stability of the system is verified. As a result we find that the critical clearing time is predicted with slightly less accuracy using ANN compared to the conventional methods for the same input data sets unless the ANN is well trained. Evolving gradient-learning artificial neural networks (ANNs) using an evolutionary algorithm (EA) is a popular approach to address the local optima and design problems of ANN. The typical approach is to combine the strength of backpropagation (BP) in weight learning and EA's capability of searching the architecture space. However, the BP's "gradient descent" approach requires a highly computer-intensive operation that relatively restricts the search coverage of EA by compelling it to use a small population size. To address this problem, we utilized mutation-based genetic neural network (MGNN) to replace BP by using the mutation strategy of local adaptation of evolutionary programming (EP) to effect weight learning. The MGNN's mutation enables the network to dynamically evolve its structure and adapt its weights at the same time. Moreover, MGNN's EP-based encoding scheme allows for a flexible and less restricted formulation of the fitness function and makes fitness computation fast and efficient. This makes it feasible to use larger population sizes and allows MGNN to have a relatively wide search coverage of the architecture space. MGNN implements a stopping criterion where overfitness occurrences are monitored through "sliding-windows" to avoid premature learning and overlearning. Statistical analysis of its performance to some well-known classification problems demonstrate its good generalization capability. It also reveals that locally adapting or scheduling the strategy parameters embedded in each individual network may provide a proper balance between the local and global searching capabilities of MGNN. This paper presents an improved particle swarm optimization (PSO) and discrete PSO (DPSO) with an enhancement operation by using a self-adaptive evolution strategies (ES). This improved PSO DPSO is proposed for joint optimization of three-layer feedforward artificial neural network (ANN) structure and parameters (weights and bias), which is named ESPNet. The experimental results on two real-world problems show that ESPNet can produce compact ANNs with good generalization ability. At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function (which maps input vectors to output vectors) follows the so-called kernel gradient associated with a new object, which we call the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.