A modified RIME algorithm with covariance learning and diversity enhancement for numerical optimization

Metaheuristics are widely applied for their ability to provide more efficient solutions. The RIME algorithm is a recently proposed physical-based metaheuristic algorithm with certain advantages. However, it suffers from rapid loss of population diversity during optimization and is prone to fall into local optima, leading to unbalanced exploitation and exploration. To address the shortcomings of RIME, this paper proposes a modified RIME with covariance learning and diversity enhancement (MRIME-CD). The algorithm applies three strategies to improve the optimization capability. First, a covariance learning strategy is introduced in the soft-rime search stage to increase the population diversity and balance the over-exploitation ability of RIME through the bootstrapping effect of dominant populations. Second, in order to moderate the tendency of RIME population to approach the optimal individual in the early search stage, an average bootstrapping strategy is introduced into the hard-rime puncture mechanism, which guides the population search through the weighted position of the dominant populations, thus enhancing the global search ability of RIME in the early stage. Finally, a new stagnation indicator is proposed, and a stochastic covariance learning strategy is used to update the stagnant individuals in the population when the algorithm gets stagnant, thus enhancing the ability to jump out of the local optimal solution. The proposed MRIME-CD algorithm is subjected to a series of validations on the CEC2017 test set, the CEC2022 test set, and the experimental results are analyzed using the Friedman test, the Wilcoxon rank sum test, and the Kruskal Wallis test. The results show that MRIME-CD can effectively improve the performance of basic RIME and has obvious superiorities in terms of solution accuracy, convergence speed and stability.

A multi-strategy improved gazelle optimization algorithm for solving numerical optimization and engineering applications

Aiming at the shortcomings of the gazelle optimization algorithm, such as the imbalance between exploration and exploitation and the insufficient information exchange within the population, this paper proposes a multi-strategy improved gazelle optimization algorithm (MSIGOA). To address these issues, MSIGOA proposes an iteration-based updating framework that switches between exploitation and exploration according to the optimization process, which effectively enhances the balance between local exploitation and global exploration in the optimization process and improves the convergence speed. Two adaptive parameter tuning strategies improve the applicability of the algorithm and promote a smoother optimization process. The dominant population-based restart strategy enhances the algorithms ability to escape from local optima and avoid its premature convergence. These enhancements significantly improve the exploration and exploitation capabilities of MSIGOA, bringing superior convergence and efficiency in dealing with complex problems. In this paper, the parameter sensitivity, strategy effectiveness, convergence and stability of the proposed method are evaluated on two benchmark test sets including CEC2017 and CEC2022. Test results and statistical tests show that MSIGOA outperforms basic GOA and other advanced algorithms. On the CEC2017 and CEC2022 test sets, the proportion of functions where MSIGOA is not worse than GOA is 92.2% and 83.3%, respectively, and the proportion of functions where MSIGOA is not worse than other algorithms is 88.57% and 87.5%, respectively. Finally, the extensibility of MSIGAO is further verified by several engineering design optimization problems.