Brief Introduction to Grey Wolf Optimization (GWO)

Metaheuristic algorithmic frameworks are implementations of optimization algorithms that are independent of specific problems.

1. Introduction

Metaheuristic algorithmic frameworks represent a versatile approach to optimization, providing implementations that transcend specific problems. To put it simply, optimization algorithms are powerful problem-solving tools designed to find the best solution among a set of possibilities. Imagine you’re trying to find the shortest route between multiple destinations on a map — optimization algorithms can efficiently determine the most time or cost-effective path, making them invaluable across various domains, from logistics to engineering. In this article, we delve into one such metaheuristic algorithm, the Grey Wolf Optimization (GWO), exploring its inspiration from nature and its application in solving complex problems.

2. Brief Explanation

The GWO simulates the Social Hierarchy and Hunting Behaviour of the pack of grey wolves.

2.1 Social Hierarchy

The pack has four following categories. The alpha is responsible for taking decisions; the beta assists the alpha with all the decisions; the delta follows the lead of the alpha and beta and is in charge of the omega.
Each grey wolf represents a solution in the algorithm. The alpha, beta, delta, and omega represent the best, second-best, third-best, and the rest of the solutions, respectively.

2.2 Hunting behavior

The hunting behavior shows that the wolves find the location of the prey and encircle them. The alpha will lead the hunt with the help of beta and delta, accompanied by the rest of the pack. They approach, track, and chase prey. They gimmick prey by encircling and harassing them and finally attacking them when they are exhausted. This hunting behavior is behind the optimization of the problem.

3. GWO Algorithm

The behaviors explained in the above sections are used to obtain optimized solutions for the “black box” problems. The algorithm follows a social hierarchy, hence the best solutions are saved after every iteration to reach the optimal solution. As a part of the hunting mechanism, the wolves encircle the prey before attacking them.

The population size and the maximum number of iterations are initialized to find the three best solutions Xₐ, Xᵦ, Xᵧ.​​

​When the iteration = 1, we proceed as follows.

• Compute a = { 2 (1 — iteration / maxiter)
• Calculate X₁, X₂, X₃.
• Compute Xₙₑ𝓌 = X₁, X₂, X₃.
• Verify if the value lies inside the upper and lower bounds
• Perform a greedy selection. If the new value is better then update the value

Now let us look into the pseudocode to understand how the algorithm works. The above iteration goes on for maximum times to reach the optimal solution.

4. Performance optimization/Complexity Analysis

From the pseudocode, the summary of the time complexity is as follows.

• The initialization of population size(n) and the dimension of the problem(m) is denoted by O(n*m).
• The control parameters are calculated in O(n*m) time.
• Update the positions of the grey wolves also requires O(n*m) time.
• To calculate all the optimal values, we need O(n*m) time.
• The complexity also depends on the maximum number of iterations. Hence it is O(n * m * maxIter).

5. Conclusion

In this article, we have explored the adaptation of nature to solve complex problems. We examined the pseudocode and its time complexity in detail.