Polar Lights Optimizer

Aurora borealis over Eielson Air Force Base

Introduction

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Polar Lights Optimization (PLO) is a metaheuristic algorithm inspired by the aurora phenomenon, also known as polar lights [1]. This optimization technique is designed to mimic the natural behavior of high-energy particles in the Earth's magnetic field [2]. The aurora phenomenon, observed at high latitudes, results from the interaction between solar wind particles and the Earth's magnetic field, creating luminous patterns in the sky [3]. PLO leverages concepts from this natural process, including gyration motion and aurora oval walk strategies, to optimize solutions in various problem domains.

Algorithm Description

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PLO is based on the motion of energetic particles in a magnetic field, which is modeled through the following key components:

Initialization

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The algorithm starts with an initial population of candidate solutions. Each candidate solution is a vector in a  -dimensional space. The initial population is generated randomly within predefined bounds:   where:

  •   – Population size
  •   – Dimension of the problem
  •   – Lower bounds of the solution space
  •   – Upper bounds of the solution space
  •   – Random values between  

Gyration Motion

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Particles exhibit gyration motion, which is modeled by the following update formula for velocity:   where:

  •   – Initial velocity
  •   – Particle charge
  •   – Magnetic field intensity
  •   – Particle mass
  •   – Damping factor

This motion helps explore local regions of the search space.

Aurora Oval Walk

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The aurora oval walk is modeled by the following update formula:   where:

  •   – Step size distribution
  •   – Average position of the particle population
  •   – Random number

This component facilitates global exploration of the search space.

 
Chaotic collisions between particles.

Combination

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By combining the Gyration Motion and the Aurora Oval Walk, a new formula is modeled to achieve a better balance:   where:

  •   - The weight of v(t)
  •   - The weight of Ao
  •   – Random number

The particle motion in the PLO encompasses both global exploration and local exploitation.

Particle Collision

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The particle collision strategy helps avoid premature convergence and enhances global exploration:   where:

  •   – Position of the collided particle
  •   – Random number
  •   – Collision probability

Pseudo-code

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The PLO algorithm can be summarized in the following pseudo-code:

Initialize population X(N, D)
For each iteration t = 1 to T do
    For each particle i in X do
        Compute particle velocity v(t)
        Update particle position using gyration motion
        Update particle position using aurora oval walk
        Apply particle collision strategy
        Update the best solution found
    End For
End For
Output the best solution found

Time Complexity

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The time complexity of the PLO algorithm is:   where:

  •   – Number of particles
  •   – Dimension of the problem
  •   – Number of evaluations


Applications

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PLO has been successfully applied to various real-world problems, including:

Multi-Threshold Image Segmentation

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PLO is used to optimize threshold values for effective image segmentation, enabling accurate differentiation between regions in an image.

Feature Selection

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In medical data analysis, PLO is utilized to select relevant features, improving the performance of classification and prediction models. The binary PLO-based feature selection method has been tested on multiple datasets.

References

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  1. Lemström, Selim (1883-05-01). "The Aurora Borealis". Nature 28 (707): 60–63. doi:10.1038/028060a0. ISSN 1476-4687. https://www.nature.com/articles/028060a0. 
  2. Yuan, Chong; Zhao, Dong; Heidari, Ali Asghar; Liu, Lei; Chen, Yi; Chen, Huiling (2024-08-22). "Polar Lights Optimizer: Algorithm and Applications in Image Segmentation and Feature Selection". Neurocomputing: 128427. doi:10.1016/j.neucom.2024.128427. ISSN 0925-2312. https://www.sciencedirect.com/science/article/abs/pii/S0925231224011986?via=ihub. 
  3. Elvey, C. T. (1957-01-01). Marton, L.. ed. Aurora Borealis. 9. Academic Press. pp. 1–42. https://www.sciencedirect.com/science/article/abs/pii/S0065253908601626.