TLDR: The research paper introduces MRIME-CD, a modified RIME algorithm that addresses the original RIME’s issues with population diversity and local optima. It integrates three strategies: Gaussian-based Covariance Learning (GCLS) for diversity and balanced exploitation, Average Bootstrapping (ABS) for enhanced global search, and Stochastic Covariance Learning (SPDM) to escape stagnation. Extensive testing on benchmark functions and engineering problems demonstrates MRIME-CD’s superior accuracy, convergence speed, and stability.
Metaheuristic algorithms are powerful tools in artificial intelligence, offering efficient solutions to complex optimization problems across various fields like natural sciences, medicine, and engineering. These algorithms, inspired by natural phenomena, are favored for their simple structure, ability to avoid local optima, and lack of need for gradient information. They are broadly categorized into evolutionary-based, swarm-based, human-based, mathematical-based, and physical-based algorithms.
Among the newer physical-based metaheuristic algorithms is the RIME algorithm, introduced in 2023. Inspired by the growth process of ice fog, RIME models two distinct freezing fog growth mechanisms. While it boasts advantages such as few control parameters and fast convergence, the basic RIME algorithm faces significant challenges. It often suffers from a rapid loss of population diversity during optimization, making it prone to getting stuck in local optima. This leads to an imbalance between exploration (searching new areas) and exploitation (refining existing solutions), especially when tackling more complex optimization problems.
Enhancing RIME for Better Performance
To overcome these limitations, researchers have proposed a modified version called MRIME-CD, which stands for Modified RIME with Covariance Learning and Diversity Enhancement. This new algorithm integrates three key strategies to significantly boost its optimization capabilities:
First, a Gaussian-based Covariance Learning Strategy (GCLS) is introduced during the soft-rime search phase. This strategy aims to increase population diversity and balance RIME’s tendency for over-exploitation. It achieves this by using a bootstrapping effect from dominant populations, essentially learning from the most promising solutions to guide the search more effectively. The GCLS models a Gaussian distribution based on dominant groups, ensuring that better individuals have a greater impact on population evolution while still retaining valuable information from a wider range of individuals. A roulette domain selection mechanism is used to construct these dominant groups, selecting optimal individuals and those close to them to enrich diversity.
Second, an Average Bootstrapping Strategy (ABS) is incorporated into the hard-rime puncture mechanism. The original hard-rime mechanism, while speeding up convergence, could drastically reduce population diversity by directing individuals too quickly towards the optimal solution. The ABS moderates this by allowing RIME particles to consider the weighted average position of both the optimal agent and the dominant population in the early stages. This encourages individuals to explore more diverse directions, enhancing the algorithm’s global search ability without sacrificing convergence efficiency.
Finally, a Stochastic Covariance Learning-based Population Diversity Mechanism (SPDM) is proposed to address algorithm stagnation. As optimization progresses, populations can cluster around local optima, leading to insufficient diversity and a halt in the search for better solutions. The SPDM introduces a new stagnation indicator that considers population distribution and fitness changes. When the algorithm detects stagnation, the stochastic covariance learning strategy is activated to update stagnant individuals, helping the algorithm jump out of local optimal solutions and continue its search for the global optimum.
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Rigorous Validation and Promising Results
The effectiveness of the proposed MRIME-CD algorithm was rigorously tested on a series of benchmark functions, including the CEC2017 and CEC2022 test sets. These test suites comprise a variety of complex, non-linear, non-derivable, and non-convex functions, providing a comprehensive evaluation environment. The experimental results were analyzed using statistical tests such as the Friedman test, Wilcoxon rank sum test, and Kruskal Wallis test.
The findings consistently demonstrated that MRIME-CD significantly outperforms the basic RIME algorithm and several other advanced metaheuristic algorithms in terms of solution accuracy, convergence speed, and stability. The algorithm showed stable performance across different dimensions and test sets, highlighting its robustness. Furthermore, the individual analysis of the three improvement strategies confirmed that each contributes positively to RIME’s performance, and they work synergistically to enhance the overall optimization capability of MRIME-CD.
Beyond benchmark functions, MRIME-CD was also applied to ten real-world engineering constrained problems. In these applications, MRIME-CD ranked first in eight out of ten problems, consistently providing better design solutions compared to its competitors. This indicates its strong potential for solving practical engineering challenges where design variables and constraints are complex.
While MRIME-CD shows superior performance, the computation of the covariance matrix can be time-consuming, making it currently more suitable for optimization problems that do not require extremely high computational speed. Future research aims to explore parallel computing to accelerate the program and further investigate the algorithm’s parameter sensitivity. The development of multi-objective and binary versions of MRIME-CD is also planned to address an even wider range of practical problems.
For more detailed information, you can refer to the full research paper: A modified RIME algorithm with covariance learning and diversity enhancement for numerical optimization.
