## 1 Introduction
### Contributions and Organization  
According to the no free lunch theorem (NFL) [28], no metaheuristic algorithm can efficiently solve all optimization problems. An algorithm that gives excellent results for one optimization problem may perform poorly when applied to another optimization problem. This inequality was the motivation for this research. The main work of this paper was based on the refinement of the biologically inspired reptile search algorithm (RSA) [29]. In an extensive application, we applied this algorithm to solving various regression and classification problems. RSA is a newly developed optimization technique that can efficiently solve various optimization problems. However, when applied to highly multidimensional nonconvex optimization problems like neural network training, the algorithm shows prominent shortcomings, such as stagnation at local minima, slow convergence speed, and high computational complexity. Therefore, in this paper, some improvements are proposed to make up for the above-mentioned drawbacks. The reason for local minima stagnation is the lack of exploration in the high-walking stage of the RSA algorithm. Local minima trapping can be avoided if the solution candidates explore the search space as widely as possible. Therefore, to enhance exploration, a sine operator was included in the high walking stage of the RSA algorithm. The modified sine operator with enhanced global search capabilities avoids local minima trapping by conducting a full-scale search of the solution space. The second innovation was designed to enhance the convergence capabilities in the hunting phase of the RSA algorithm. The Levy flight operator with jump size control factor \(\zeta\) was used to increase the exploitation capabilities of the search agents. The lower value of \(\zeta\) results in small random steps in the hunting phase of IRSA. This enables the solution candidates to search the area nearest to the obtained solution, which greatly improves the convergence capabilities of the algorithm. As compared to the other state-of-the-art optimization algorithms, the computational complexity of RSA is very high. This time complexity limits the application of the algorithm in solving high-dimensional complex optimization algorithms. In the original RSA, the major causes of the complexity are the hunting operator \(\mu_{(j,k)}\) and the reduce function \(R_{(j,k)}\). Especially while computing \(R_{(j,k)}\), division by a small value, \(\epsilon\), greatly increases the computational time of the algorithm. However, in the proposed algorithm with the above-mentioned improvisation, there was no need to calculate these complex operators, and they were excluded from the algorithm. This results in an almost 3-to-4-fold reduction in time complexity. Thus, the proposed novel IRSA algorithm gives two benefits. First, there was a 10 to 15% improved performance as compared to the original RSA (experimentally verified in Section 3.2). Second, there was a 3-to-4-fold reduction in time complexity as compared to the original RSA (experimentally verified in Section 3.3). The major contributions of the research are:  
* An improved reptile search algorithm (IRSA) based on a sine operator and Levy flight was proposed to enhance the performance of the original RSA. * The proposed IRSA was evaluated using 23 benchmark test functions. Various qualitative, quantitative, comparative, statistical, and complexity analyses were performed to validate the positive effects of the improvisations. * This research also proposed a hybrid methodology that integrates Multi-Layer Perceptron Neural Network with the improvised RSA for solving various classification problems. * Finally, the IRSA was applied to train a radial basis function neural network (RBFNN) for short-term wind and solar power predictions. The remaining article is assembled into seven sections. The proposed methodology is explained in Section 3.