# Somersault Foraging and Elite Opposition-Based Learning Dung Beetle Optimization Algorithm
###### Abstract
The reference [20] has proven that DBO significantly outperforms classical optimization algorithms such as the HHO [21], the GWO [18], the WOA [15], the SSA [22], and PSO [14] in optimization capability. Since the DBO was proposed, it or its variants have found applications in diverse domains, including air quality prediction [23], engineering design problems [24], fault diagnosis [25], etc. When contrasted with other algorithms, the DBO algorithm similarly reveals shortcomings, which encompass a sluggish convergence rate, a proclivity for being trapped in local optima, as well as an imbalance between exploration and exploitation capabilities. Many scholars have made improvements to DBO to enhance its performance by addressing these issues. To address the issue of inadequate diversity within the DBO population, reference [26] integrated the idea of quantum state update into quasi-oppositional learning to generate the initial population. Experimental results demonstrated that the initial population generated by this method significantly enhanced both the algorithm's capacity for global exploration and its rate of convergence. To boost the algorithm's capacity to avoid local optima, reference [27] introduced a Cauchy-Gaussian mutation strategy during algorithm stagnation, substantially mitigating the likelihood of the population being trapped in local optima, and further augmenting the algorithm's solution precision. In order to tackle the disparity between the exploratory and exploitative capabilities within the DBO algorithm, reference [28] incorporated the search methodology of the Improved Sine Algorithm (MSA) [29] into the DBO population, ultimately fostering equilibrium between exploration and exploitation. This paper is aimed at addressing the challenges posed by delayed convergence rate and vulnerability to entrapment in local optima, and imbalanced exploration and exploitation in DBO by proposing a Somersault Foraging and Elite Opposition-BasedLearning Dung Beetle Optimization (SFEDBO) Algorithm. An elite opposition-based learning strategy is employed as the method for population initialization, generating an initial population with greater diversity. An adaptive strategy is employed to dynamically adjust the number of rolling dung beetles and hatching balls, ensuring a balance between exploration and exploitation. The somersault foraging strategy is incorporated to boost the algorithm's capability of evading local optima. In addition, the SFEDBO algorithm has been utilized in the design of pressure vessels [30], tension/extension spring design problems [31], and 3D unmanned aerial vehicle (UAV) path planning problems [32], all of which have achieved good results, further demonstrating the great potential of this algorithm for practical applications. The key contributions presented in this paper are as follows:  
* We are the first to apply the EOBL strategy to the DBO algorithm, generating an initial population with higher diversity through this strategy. This innovation accelerates the early convergence speed of the algorithm, and it also enhances its global search capability. * We design a novel adaptive strategy that dynamically adjusts the ratio of ball-rolling dung beetles to brood balls according to the algorithm's running phase. This strategy enhances exploration capability in the early stages and strengthens exploitation efficiency in the later stages, ultimately fostering a harmonious integration of exploration and development. * We innovatively introduce the somersault foraging strategy. This strategy simulates the somersault movements of manta rays during foraging, enabling the algorithm to effectively escape from local optima when trapped and explore a broader solution space. * We evaluated the SFEDBO algorithm using benchmark test functions and compared the results with those of other algorithms, proving that the performance of the SFEDBO algorithm is highly superior compared to other algorithms.