The RIME algorithm is a novel physical-based meta-heuristic algorithm with a strong ability to solve global optimization problems and address challenges in engineering applications. It implements exploration and exploitation behaviors by constructing a rime-ice growth process. However, RIME comes with a couple of disadvantages: a limited exploratory capability, slow convergence, and inherent asymmetry between exploration and exploitation. An improved version with more efficiency and adaptability to solve these issues now comes in the form of Hybrid Estimation Rime-ice Optimization, in short, HERIME. A probabilistic model-based sampling approach of the estimated distribution algorithm is utilized to enhance the quality of the RIME population and boost its global exploration capability. A roulette-based fitness distance balanced selection strategy is used to strengthen the hard-rime phase of RIME to effectively enhance the balance between the exploitation and exploration phases of the optimization process. We validate HERIME using 41 functions from the IEEE CEC2017 and IEEE CEC2022 test suites and compare its optimization accuracy, convergence, and stability with four classical and recent metaheuristic algorithms as well as five advanced algorithms to reveal the fact that the proposed algorithm outperforms all of them. Statistical research using the Friedman test and Wilcoxon rank sum test also confirms its excellent performance. Moreover, ablation experiments validate the effectiveness of each strategy individually. Thus, the experimental results show that HERIME has better search efficiency and optimization accuracy and is effective in dealing with global optimization problems.

Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement learning with metaheuristic optimization through a three-stage hierarchical architecture. The framework employs Q-learning to generate a global guidance path in a discretized 2D grid environment using an eight-directional symmetric action space that embodies rotational symmetry at π/4 intervals, ensuring uniform exploration capabilities and unbiased path planning. A crucial intermediate stage transforms the discrete 2D path into a 3D initial trajectory, bridging the gap between discrete learning and continuous optimization domains. The MOPSO algorithm then performs fine-grained refinement in continuous 3D space, guided by a novel Q-learning path deviation objective that ensures continuous knowledge transfer throughout the optimization process. Experimental results demonstrate that the symmetric action space design yields 20.6% shorter paths compared to asymmetric alternatives, while the complete QL-MOPSO framework achieves 5% path length reduction and significantly faster convergence compared to standard MOPSO. The proposed method successfully generates Pareto-optimal solutions that balance multiple objectives while leveraging the symmetry-aware guidance mechanism to avoid local optima and accelerate convergence, offering a robust solution for complex multi-objective UAV path planning problems.

This paper shows that lithium-ion battery model parameters are vital for state-of-health assessment and performance optimization. Traditional evolutionary algorithms often fail to balance global and local search. To address these challenges, this study proposes the Elite Opposition-Based Learning Snake Optimization (EOLSO) algorithm, which uses an elite opposition-based learning mechanism to enhance diversity and a non-monotonic temperature factor to balance exploration and exploitation. The algorithm is applied to the parameter identification of the second-order RC equivalent circuit model. EOLSO outperforms some traditional optimization methods, including the Gray Wolf Optimizer (GWO), Honey Badger Algorithm (HBA), Golden Jackal Optimizer (GJO), Enhanced Snake Optimizer (ESO), and Snake Optimizer (SO), in both standard functions and HPPC experiments. The experimental results demonstrate that EOLSO significantly outperforms the SO, achieving reductions of 43.83% in the Sum of Squares Error (SSE), 30.73% in the Mean Absolute Error (MAE), and 25.05% in the Root Mean Square Error (RMSE). These findings position EOLSO as a promising tool for lithium-ion battery modeling and state estimation. It also shows potential applications in battery management systems, electric vehicle energy management, and other complex optimization problems. The code of EOLSO is available on GitHub.

The challenging terrain and deep ravines that characterize mountainous regions often result in slower path planning and suboptimal flight paths for unmanned aerial vehicles (UAVs) when traditional meta-heuristic optimization algorithms are employed. This study proposes a novel Improved Enhanced Snake Optimizer (IESO) for three-dimensional path planning and tested it in a simulated rugged mountainous terrain with obstacles and a restricted “no-fly zone”. The initialization process in the enhanced snake optimizer is refined by integrating the Chebyshev chaotic map. Additionally, a non-monotonic factor is introduced to modulate the “temperature”. This temperature controls the freedom of movement within the solution space. Furthermore, a boundary condition is incorporated into the dynamic opposition learning mechanism. These modifications collectively reduce the likelihood of population convergence to local optima during optimization. The feasibility of IESO is validated through time complexity and global convergence analyses. Comparative simulation experiments benchmarked IESO against five state-of-the-art biologically inspired optimization algorithms across test functions and path-planning simulated scenarios. Experimental results show that compared with five commonly used algorithms, the IESO algorithm improves the quality of flight trajectory planning by nearly 30% on average. Particularly when compared to the original SO algorithm, IESO demonstrates performance enhancement exceeding 36%, proving its superiority in UAV path planning over complex terrain.

Metaheuristic algorithms provide reliable and effective methods for solving challenging optimization problems. The snow ablation algorithm (SAO) performs favorably as a physics-based metaheuristic algorithm. Nevertheless, SAO has some shortcomings. SAO is overpowered in its exploitation, has difficulty in balancing the proportion of global and local search, and is prone to encountering local optimum traps when confronted with complex problems. To improve the capability of SAO, this paper proposes a modified snow ablation algorithm hybrid distribution estimation algorithm named MSAO-EDA. In this work, a collaborative search framework is proposed where SAO and EDA can be organically integrated together to fully utilize the exploitation capability of SAO and the exploration capability of EDA. Secondly, an offset EDA approach that combines the optimal solution and the agent itself is used to replace SAO’s exploration strategy for the purpose of enhancing SAO’s exploration capability. Finally, the convergence of SAO is accelerated by selecting the next generation of agents through a greedy strategy. MSAO-EDA is tested on the CEC 2017 and CEC 2022 test suites and compared with EO, RIME, MRFO, CFOA, and four advanced algorithms, AFDBARO, CSOAOA, EOSMA, and JADE. The experimental results show that MSAO-EDA has excellent efficiency in numerical optimization problems and is a highly competitive SAO variant.

Precision irrigation is crucial for sustainable agriculture, yet conventional single-objective optimization methods struggle to balance conflicting demands such as crop yield, operational cost, and environmental sustainability. This study introduces an Adaptive Multi-Strategy Grey Wolf Optimizer with Reinforcement Learning for Multi-Objective Optimization (AMSGWO-RL-MO) to enhance precision irrigation decision-making. AMSGWO-RL-MO integrates four strategies: standard GWO exploitation, Lévy flight exploration, differential evolution-based diversity enhancement, and Stochastic Elite Opposition-Based Learning. A Q-learning mechanism dynamically adjusts these strategies, adapting to real-time search conditions to select the optimal approach. We constructed a comprehensive three-objective framework incorporating soil moisture dynamics, crop growth models, and environmental impact assessments. Experimental simulations over a 40-day growth cycle demonstrate AMSGWO-RL-MO’s rapid convergence by the sixth generation, consistently achieving a high-quality Pareto front across 30 independent runs. The knee-point solution yielded a mean crop yield of 96.96%, outperforming standard GWO and multi-strategy variants by approximately 3.8%. Statistical analysis confirms its superior robustness and well-distributed solutions along the Pareto front. These results indicate that the RL-driven adaptive mechanism effectively balances exploration and exploitation. The proposed method offers a more diverse array of Pareto-optimal solutions, presenting a broader trade-off space for balancing crop yield and environmental sustainability compared to traditional weighted-sum approaches. This enhancement facilitates scientific agricultural decision-making under various operational constraints.