## 1 Introduction
### Motivation and Contribution  
The rapidly evolving landscape of cyber threats demands equally adaptive and sophisticated defense mechanisms. While traditional optimization methods have proven effective in more structured environments, they often struggle with the complex, high-dimensional, and non-linear optimization challenges inherent in training neural networks for cybersecurity applications. Enhancing the training efficiency of Multi-Layer Perceptrons (MLPs) for attack detection has become increasingly crucial, as these neural networks are pivotal in identifying subtle patterns and anomalies indicative of potential security breaches. Given the shortcomings of conventional optimization techniques, there is a growing need for innovative approaches capable of navigating intricate optimization landscapes more effectively, delivering robust solutions that are both highly accurate and computationally efficient. This paper introduces a novel Cybersecurity Optimizer (CSO), specifically designed to address the challenges associated with training Multi-Layer Perceptrons (MLPs) for cybersecurity threat detection. The key contributions of this work are outlined as follows:  
* Introduction to a Novel Optimization Algorithm: This paper presents the Cybersecurity Optimizer (CSO), an innovative algorithm that integrates principles from evolutionary computation and adapts them with modern AI techniques. This combination results in a powerful tool designed to converge rapidly to optimal solutions, thereby reducing training time and enhancing the overall performance of MLPs. * Enhanced MLP Training: By applying the CSO to the MLP training process, we demonstrate significant improvements in the network's ability to detect and classify cybersecurity threats with greater accuracy compared to MLPs trained with traditional optimization methods. * Benchmarking Against Standard Optimizers: The CSO is comprehensively compared with other well-established optimization algorithms across a range of standard benchmark functions. This comparison highlights the superior performance of the CSO in terms of both convergence speed and solution quality. * Real-World Application and Validation: The practical effectiveness of the CSO is validated in a real-world cybersecurity scenario, where it is used to train an MLP for network intrusion detection. The results confirm the optimizer's capabilities in a practical context, demonstrating its potential for broader applications in cybersecurity technologies. The remainder of this paper is structured as follows: Section 2 provides a literature review, covering an overview of Multi-Layer Perceptron (MLP) neural networks, their training methodologies, and an introduction to cybersecurity challenges. Section 3 describes the proposed methodology, focusing on the CYO and its mathematical model, which encompasses stages such as initialization, adaptive learning, mutation, crossover, selection, archiving, as well as exploration and exploitation mechanisms. Section 4.2 elaborates on the application of the CYO for training MLPs in attack detection, offering a detailed mathematical model of the cybersecurity-based MLP trainer, including problem representation, the objective function, and the various phases of the algorithm. Section 5 provides an experimental analysis of the CYO, featuring the CEC2022 benchmark functions (F1-F12), and a comparison of the results with other optimization algorithms. This section also presents an analysis of convergence curves, search history curves, trajectory curves, fitness curves, sensitivity analysis, and visualizations using heatmaps, box plots, and histograms. Section 5.2 investigates the application of the CYO for MLP training in attack detection, presenting experimental results on datasets such as NSL-KDD, CICIDS2017, UNSW-NB15, Bot-IoT, and CSE-CIC-IDS2018. This section also discusses real-world applications and validation, the anomaly detection algorithm and architecture, justification for using a supervised approach, and considerations for long-term training.