Abstract
One of the key challenges in cyber-physical systems (CPS) is the dynamic fitting of data sources under multivariate or mixture distribution models to determine abnormalities. Equations of the models have been statistically characterized as nonlinear and non-Gaussian ones, where data have high variations between normal and suspicious data distributions. To address nonlinear equations of these distributions, a cuckoo search algorithm is employed. In this paper, the cuckoo search algorithm is effectively improved with a novel strategy, known as a convergence speed strategy, to accelerate the convergence speed in the direction of the optimal solution for achieving better outcomes in a small number of iterations when solving systems of nonlinear equations. The proposed algorithm is named an improved cuckoo search algorithm (ICSA), which accelerates the convergence speed by improving the fitness values of function evaluations compared to the existing algorithms. To assess the efficacy of ICSA, 34 common nonlinear equations that fit the nature of cybersecurity models are adopted to show if ICSA can reach better outcomes with high convergence speed or not. ICSA has been compared with several well-known, well-established optimization algorithms, such as the slime mould optimizer, salp swarm, cuckoo search, marine predators, bat, and flower pollination algorithms. Experimental outcomes have revealed that ICSA is superior to the other in terms of the convergence speed and final accuracy, and this makes a promising alternative to the existing algorithm.
Highlights
With the norm of cyber-physical systems (CPS), cyber defense systems such as intrusion detection and threat intelligence, which deal with data sources under the constraints of nonnormality and nonlinearity, should be designed to handle these constraints and produce accurate outcomes [1,2]
A new strategy, called convergence improvement strategy, is proposed for improving the performance of the meta-heuristic algorithm to achieve better convergence, in addition to improving final accuracy, and enhancing the ability to select the most significant attributes for CPS problems. This strategy is two-fold: the first aspect is based on searching the best-so-far solutions for a better solution using Equation (6) to save time in the optimization process if the near-optimal solution is found around this best-so-far case, but this best-so-far solution may be a trap to drift the algorithm into local minima, reducing the possibility of reaching better outcomes
This section validates the performance of the proposed algorithm, improved cuckoo search algorithm (ICSA), to examine its efficacy, in addition to witnessing its superiority compared to some well-established optimization algorithms under various statistical analyses
Summary
With the norm of cyber-physical systems (CPS), cyber defense systems such as intrusion detection and threat intelligence, which deal with data sources under the constraints of nonnormality and nonlinearity, should be designed to handle these constraints and produce accurate outcomes [1,2] These models have been developed using nonlinear equation systems (NESs) [3], which need to be accurately solved in reasonable time [4]. The evolutionary algorithms (EAs) and swarm algorithms (SAs) have achieved significant achievements in real-world optimization problems [7–18], the convex, discontinuous nonlinear optimization problem [11,19,20] They have been widely used in the literature for solving the NESs. the existing algorithms still suffer from local minima and convergence speed to the optimal root.
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