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

2025-09-11

AI Summary

RIME suffers from rapid population diversity loss, premature convergence to local optima, and imbalance between exploration and exploitation. To address these issues, this paper proposes CD-RIME—an improved RIME algorithm integrating covariance learning and diversity enhancement. Key innovations include a covariance learning mechanism, a stochastic covariance update strategy, weighted dominant population guidance, a novel stagnation detection metric, and average bootstrapping to sustain population vitality. Comprehensive evaluations on the CEC2017 and CEC2022 benchmark suites demonstrate that CD-RIME significantly outperforms the original RIME and several state-of-the-art metaheuristics in solution accuracy, convergence speed, and robustness, as validated by Friedman, Wilcoxon, and Kruskal–Wallis statistical tests. The proposed method substantially strengthens global search capability and enhances escape performance from local optima.

Technology Category

Search and Optimization: Metareasoning and MetaheuristicsReasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: Learning & Optimization for ROB

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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.

Problem

• Enhances RIME algorithm to prevent premature convergence
• Addresses population diversity loss in numerical optimization
• Improves global search ability and local optimum escape

Innovation

• Covariance learning strategy enhances population diversity
• Average bootstrapping strategy improves global search ability
• Stochastic covariance learning updates stagnant individuals