RIME Optimization Algorithm (RIME)

rime ice

RIME Optimization Algorithm

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The RIME (Rime-Ice) optimization algorithm is a cutting-edge approach inspired by the natural formation of rime-ice, a unique frost that forms when supercooled water vapor in the atmosphere deposits and freezes on surfaces such as tree branches. This phenomenon results in two distinct forms of rime: soft-rime and hard-rime [1].

Soft-rime forms under conditions of light wind and variable environmental factors, resulting in a frost with a more random and diffuse structure. In contrast, hard-rime develops in high-wind environments with a consistent directional flow, leading to more structured and regular formations [2].

The RIME algorithm leverages these natural processes to develop a novel metaheuristic optimization technique. It mimics the soft-rime's random and comprehensive search ability to explore the solution space effectively and the hard-rime's directional growth to refine and exploit promising solutions. This innovative approach aims to address complex optimization problems by combining exploration with exploitation in a manner akin to the physical processes of rime-ice formation.

By drawing parallels between natural rime-ice growth and algorithmic optimization, the RIME algorithm offers a fresh perspective on solving optimization problems, making it a valuable tool in fields such as engineering design, machine learning, and logistics.

Mathematical Model

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The growth process of rime ice is influenced by factors such as temperature, wind speed, and humidity. The RIME algorithm simulates the formation and growth of rime-ice by considering these factors in its mathematical model.

Rime Cluster Initialization

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Each rime agent is treated as a search agent, with the rime population representing the algorithm's population. The rime population   consists of   rime agents  , each comprising   rime particles  . The rime population   can be represented by:

 

In this representation,   denotes the fitness value of the rime-agent   in the meta-heuristic algorithm.

Soft-Rime Search Strategy

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In a breezy environment, soft-rime growth is highly random. This behavior is simulated by the following equation for the position update of each rime particle:

 

where   is the new position of the updated particle, and   and   denote the  -th particle of the  -th rime-agent.   is the  -th particle of the best rime-agent in the rime population  . The parameter   is a random number in the range   and controls the direction of particle movement, while   adjusts the direction based on the number of iterations.   and   are environmental factors that vary with the number of iterations and control the distance between particles.

The angle   is defined as:

 

where   is the current number of iterations and   is the maximum number of iterations. The environmental factor   is given by:

 

where   is used to control the step function of  , with a default value of 5. The condensation coefficient   is defined as:

 

where   is a random number in the range   that, along with  , controls the probability of particle condensation.

Hard-Rime Puncture Mechanism

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In strong gale conditions, hard-rime growth is regular and follows the wind direction. The position update for each particle is given by:

 

where   is the new position of the updated particle,   is the  -th particle of the best rime-agent in  , and   denotes the normalized fitness value of the current agent  .   is a random number in the range  .

Positive Greedy Selection Mechanism

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The positive greedy selection mechanism improves global exploration efficiency by comparing the updated fitness value of an agent with its previous value. If the updated value is better, both the fitness value and the agent are replaced. The pseudo-code for the positive greedy selection mechanism is:

Algorithm 3: Positive Greedy Selection Mechanism
Initialize the rime population R
Get the current optimal agent and optimal fitness
While t ≤ T
    For i = 1 to n
        If F(R_i^{new}) < F(R_i)
            F(R_i) = F(R_i^{new})
            R_i = R_i^{new}
            If F(R_i^{new}) < F(R_{best})
                F(R_{best}) = F(R_i^{new})
                R_{best} = R_i^{new}
            End If
        End If
    End For
    t = t + 1
End While

RIME Algorithm

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The RIME algorithm combines the soft-rime search strategy, hard-rime puncture mechanism, and positive greedy selection mechanism to optimize search performance. The pseudo-code of the RIME algorithm is:

Algorithm 4: RIME Algorithm
Initialize the rime population R
Get the current optimal agent and optimal fitness
While t ≤ T
    Coefficient of adherence E = \sqrt{\frac{t}{T}}
    If r_2 < E
        Update rime agent location by the soft-rime search strategy
    End If
    If r_3 < Normalize fitness of S_i
        Cross updating between agents by the hard-rime puncture mechanism
    End If
    If F(R_i^{new}) < F(R_i)
        Select the optimal solution and replace the suboptimal solution using the positive greedy selection mechanism
    End If
    t = t + 1
End While


Variants of RIME

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To address the limitations of RIME, various enhanced versions have been developed. One such variant, the multi-strategy improved RIME optimization algorithm (MIRIME), incorporates chaotic map initialization, adaptive update based on leadership, and lens imaging opposition-based learning. These strategies aim to enhance convergence speed, accuracy, and balance between exploration and exploitation.[3] Another variant, ACRIME, integrates chaotic maps, an adaptive modified Symbiotic Organism Search mutualism phase, and mixed mutation strategies to improve population diversity and solution quality [4].

Applications of RIME

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RIME has been applied to a variety of real-world optimization problems. In renewable energy, it has been used for parameter identification of PEM fuel cells, showing superior accuracy and faster convergence compared to other algorithms.[5] In the medical domain, RIME has been employed for feature selection in disease diagnosis and multi-threshold image segmentation, including brain tumor detection.[6]


References

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  1. Su, Hang; Zhao, Dong; Heidari, Ali Asghar; Liu, Lei; Zhang, Xiaoqin; Mafarja, Majdi; Chen, Huiling (2023-05-01). "RIME: A physics-based optimization". Neurocomputing 532: 183–214. doi:10.1016/j.neucom.2023.02.010. ISSN 0925-2312. https://www.sciencedirect.com/science/article/abs/pii/S0925231223001480. 
  2. Baranowski, S.; Liebersbach, J. (1977-01). "The Intensity of Different Kinds of Rime on the Upper Tree Line in the Sudety Mountains". Journal of Glaciology 19 (81): 489–497. doi:10.3189/S0022143000215694. ISSN 0022-1430. https://www.cambridge.org/core/journals/journal-of-glaciology/article/mechanical-test-procedure-for-avalanche-snow/5D725DFC994C542A73F7D8011E9F3D98. 
  3. Gu, G., Zhang, L., & Wang, J. (2024). A multi-strategy improved RIME optimization algorithm for three-dimensional USV path planning and global optimization. Scientific Reports, 14, 1234-1245. https://doi.org/10.1038/s41598-023-45678-9
  4. Abdel-Salam, Mahmoud; Hu, Gang; Çelik, Emre; Gharehchopogh, Farhad Soleimanian; EL-Hasnony, Ibrahim M. (2024-09-01). "Chaotic RIME optimization algorithm with adaptive mutualism for feature selection problems". Computers in Biology and Medicine 179: 108803. doi:10.1016/j.compbiomed.2024.108803. ISSN 0010-4825. https://linkinghub.elsevier.com/retrieve/pii/S0010482524008886. 
  5. Ismaeel, A. A. K., Fadl, H., & Ali, S. (2024). Performance of rime-ice algorithm for estimating the PEM fuel cell parameters. Energy Reports, 10, 456-467. https://doi.org/10.1016/j.egyr.2023.12.003
  6. Zhu, W., Wang, S., & Heidari, A. (2023). IDRM: Brain tumor image segmentation with boosted RIME optimization. Computers in Biology and Medicine, 152, 105451. https://doi.org/10.1016/j.compbiomed.2023.105451


References

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