WHALE OPTIMISATION

Introduction

The Whale Optimization Algorithm (WOA) is a nature-inspired, metaheuristic algorithm developed by Seyedali Mirjalili in 2016. It mimics the bubble-net hunting strategy of humpback whales, which is a unique feeding method. The algorithm's main strength lies in its ability to explore and exploit the search space effectively, making it suitable for solving complex optimization problems.

1. Bubble-Net Hunting Strategy:

- Encircling Prey: Whales create bubbles in a spiral or circular shape to trap fish.

- Exploitation Phase: Models the spiral movement toward the prey.

- Exploration Phase: Diversifies the search by moving whales randomly across the search space.

2. Mathematical Model:

- The position of a whale in the search space represents a potential solution.

- Encircling prey is mathematically expressed as:

\[

\mathbf{D} = |\mathbf{C} \cdot \mathbf{X}^*(t) - \mathbf{X}(t)|

\]

\[

\mathbf{X}(t+1) = \mathbf{X}^*(t) - \mathbf{A} \cdot \mathbf{D}

\]

- Here, \(\mathbf{X}(t)\) is the position vector, \(\mathbf{X}^*(t)\) is the position of the best solution, \(\mathbf{A}\) and \(\mathbf{C}\) are coefficient vectors, and \(t\) denotes the current iteration.

3. Exploration vs. Exploitation:

- The algorithm switches between exploration and exploitation phases based on a probability \(p\) and the parameter \(a\), which linearly decreases from 2 to 0 over iterations.

- Exploration (random search) is enhanced when \(a > 1\) or \(a < -1\), while exploitation (searching around the best solution) is intensified when \(|a| < 1\).

Implementation Steps

1. Initialization:

- Define the search space and initialize the population of whales randomly.

- Set the algorithm parameters: population size, maximum number of iterations, and coefficients.

2. Fitness Evaluation:

- Evaluate the fitness of each whale's position.

- Identify the best solution (\(\mathbf{X}^*(t)\)) in the current population.

3. Position Update:

- For each whale, update its position using the encircling mechanism or the spiral update mechanism based on the value of \(p\).

- Ensure the new positions are within the search space boundaries.

4. Termination:

- Repeat the position update and fitness evaluation until the maximum number of iterations is reached or a satisfactory solution is found.

Applications

WOA has been applied in various domains, including:

- Engineering Optimization: Structural design, electrical engineering, and robotics.

- Machine Learning: Hyperparameter tuning, feature selection, and neural network training.

- Image Processing: Image segmentation and feature extraction.

- Economic Load Dispatch: Optimizing power generation and distribution in electrical grids.

Conclusion

The Whale Optimization Algorithm is a powerful optimization tool inspired by the natural hunting behavior of humpback whales. Its simplicity, efficiency, and versatility make it a popular choice for solving a wide range of optimization problems. With ongoing research and development, WOA continues to evolve, promising even broader applications and improved performance.

For further details and implementation examples, refer to the original papers by Mirjalili and other recent studies exploring various enhancements and applications of WOA