# A Gradient-Based Particle-Bat Algorithm for Stochastic Configuration Network
## 1 Introduction
In the discussion of the input weights, some scholars indicate that the method based on the inequality supervision mechanism to search weights leads to a certain rejection rate, therefore, the conditions of inequality constraints should be relaxed, so as to improve the acceptance rate of the random value and reduce the number of iterations for the searching of input weights [19]. However, the accuracy of the network will be reduced once the inequality constraints are relaxed, which has a certain cost. Some scholars also focus on regularization parameters and scale factors of weights and bias that affect the network performance, and optimize them using a chaotic sparrow search algorithm, which makes the network achieve better performance [20]. Meanwhile, some scholars also applied various feedback learning mechanisms to optimize SCN [21; 22]. There are few studies on how to optimize the input side parameters directly. SCN searches the input side parameters randomly until the parameters could satisfy the inequality constraints. The specific method is to expand the search interval gradually linearly, and randomly generate a large number of weights and biases in the interval to judge whether the inequality constraints are satisfied, then select the best one. The method will affect the efficiency of SCN. Therefore, an efficient optimization algorithm needs to be designed. The gradient descent method is often used to solve optimization problems in practical engineering, that is, to solve for a minimum in the direction of gradient descent or to solve for a maximum in the direction of gradient ascent. However, this method is easy to fall into the local minimum for non-convex optimization problems, so it needs to be combined with an intelligent optimization algorithm to achieve better performance [23; 24]. The bat algorithm [25; 26] and Particle Swarm Optimization (PSO) algorithm [27] are population-based stochastic optimization technical algorithms, which seek the optimal solution by imitating the group behavior of the biological world. The bat algorithm is a search algorithm to simulate the predation behaviors of bats,which has been successfully applied to microgrid scheduling [28], harmful plants classification [29], text categorization [30], and the categorization salesman problem [31]. These algorithms could search more regions in the solution space of the objective function simultaneously,which is flexible and easy to implement, and requires fewer parameters to be adjusted. In addition, the gradient information could be used to determine the search direction because of the randomness of intelligent optimization algorithms. Therefore, using the hybrid optimization algorithm to search the input parameters of SCN could optimize the network structure and improve the convergence speed. This paper focuses on improving the search algorithm for the input weights and biases. In order to accelerate the convergence speed, an optimization model was established based on the inequality constraint mechanism by analyzing the convergence principle of SCN. Then, an improved optimization algorithm (G-BAPSO) is proposed, which combines the gradient information of the objective function and searches for the optimal weights and biases using the hybrid PSO and bat algorithm. Finally, an optimized stochastic configuration network based on the G-BAPSO algorithm is established. The structure of this paper is as follows: The theory of SCN is introduced in Section 2; G-BAPSO-SCN is proposed in Section 3, including the optimization model and algorithm. In Section 4, the G-BAPSO algorithm is verified on some benchmark functions, and the performance of G-BAPSO-SCN and other models is compared in some regression and classification problems. The experimental results are analyzed in Section 5, and Section 6 gives the conclusion of this paper.