All you need to know about Grey Wolf Optimization

Among various optimization techniques, Grey Wolf Optimization is one of the metaheuristic optimization techniques which is inspired by the hierarchy among the wolf family and the special hunting techniques used by the grey wolves. So the Grey wolf optimization technique imitates the overall characteristics of the grey wolf colony and tries to find the optimal solution.

In this article let us try to obtain an overview of the Grey Wolf Optimization technique.

Table of Contents

1. The grey wolf optimization
2. Uses grey wolf optimization
3. Working of grey wolf optimization technique 
4. Example of using grey wolf optimization
5. Pros and cons of grey wolf optimization
6. Summary

The grey wolf optimization

Before understanding the optimization technique of the grey wolf let us try to understand why the algorithm is inspired by the social hierarchy of the grey wolf family.

The above image shows the social hierarchy distribution of grey wolves where the characteristics of each wolf category are different in the colony. The entire grey wolf optimization family is officially called a pack. So now let us try to understand the responsibilities of each of the categories of wolves in the colony.

Alpha Wolf: Alpha wolf holds the superior position in the entire grey wolf colony and holds the right to command the entire colony of grey wolves.

Beta Wolf: Beta wolves report to alpha wolves regularly and help in optimal decision-making for the alpha wolf.

Delta Wolf: Delta wolves are subordinate to the beta wolf providing constant updates to alpha and beta wolves and are superiors for omega wolves.

Omega Wolf: Omega wolves are responsible for hunting the wolves in the grey wolves colony and are responsible for taking care of younger wolves.

Characteristics of grey wolves that lead to the development of an optimization algorithm?

The grey wolves follow a special technique of hunting where the entire colony of grey wolves operates in packs or groups to hunt their prey. The selected prey is separated from the herd by the omega wolves and the selected prey is chased and attacked by the delta and beta wolves. So the unique technique of hunting followed by the grey wolves colony lead to the development of an optimization technique called Grey Wolf Optimization where the nearest optimal solution is produced using various inbuilt functionalities.

Uses of grey wolf optimization

The grey wolf optimization technique is used in various time-consuming problems such as NP-hard problems and traveling sales problems. The grey wolf optimization technique generally reduces the operational time for higher dimensional data as the algorithm breaks down the entire complex problems into subsets. The subsets of operation are provided to each agent similar to the overall hierarchy of the grey wolf colony and the best optimal solution is yielded.

So the complex problems are broken down to the respective agents in the algorithm similar to the hierarchy of grey wolves and each of the agents takes up its respective tasks and reduces the overall time consumption. All the agents in the algorithm follow certain guidelines and strategies and find the best optimal solution for the problem. 

Working of grey wolf optimization work

Before understanding how the grey wolf optimization algorithm works let us interpret the grey wolf colony in the form of optimal solution parameters.

• Alpha wolf can be termed as the best fittest solution among all the possible solutions for the problem. It is the best optimal solution produced by the optimization algorithm.
• Beta wolf can be termed as the second fittest solution among all the possible solutions for the problem. This solution will be taken up if the best optimal solution does not fit for certain solutions.
• Delta wolf can be termed as the third best solution among all the possible solutions for the problem. But the third best solution is evaluated with both the best fit and first fittest solution for all possible solutions.
• Omega wolf can be termed as the least optimal solution being produced for all the possible solutions and the least optimal solution is evaluated only by the third fittest solution and no comparison will be done with respect to the best fittest solution.

With this context of optimal solutions produced by the grey wolf optimization technique let us try to understand how the solutions produced by the algorithm are ranked as the best fittest solution among all the possible solutions.

At first, a random number of possible solutions to the problem is validated. All the possible solutions are validated with respect to a standard scale of vectors which in general is denoted as “A”. So if A>1 the possible solutions diverge from the optimal solution of the problem and if A<1 then all the possible solutions converge towards the optimal solution to find the best fittest solution to the problem. Once the best fittest solution is determined the algorithm stops iterating and the best possible solutions to the problem are ranked suitably and from the rankings provided the solutions are validated. In most cases, the best fittest solution is used and in rare cases, the second-best optimal solution is chosen for certain problems over the best fittest solution.

Example of using grey wolf optimization

Grey wolf optimization finds its major applications in tasks where the optimal solution has to be produced by reiterating the solution to achieve the desired task. As a result, the grey wolf optimization technique finds its applications in various problems like the NP-hards problem, Traveling Salesman problem, and many other AI problems. Let us try to understand how the grey wolf optimization technique helps in solving the traveling salesman problem.

Analyzing the Traveling salesman problem through Grey Wolf

Let us first try to understand the traveling salesman problem. The goal of the problem is to find the minimum path between the cities with a condition that the salesman is allowed to visit the city only once.

By interpreting the traveling salesman problem through grey wolf optimization the entire grey wolf population can be termed as different paths the salesman has to take to cover the cities, So it becomes the candidate solution to the problem. The optimal solution can be taught as the prey and here the optimal solution is the best city to start. 

So with respect to the start city, the optimization algorithm will have to yield the closest city(alpha wolf) which can be termed as the best solution to the problem, and thereby all the second nearest cities to the start city can be termed as the second best solution (beta wolf). In a similar way, the third nearest city to the start city can be termed as the third best solution (delta wolf) and all the other nearest cities to the smart city can be termed as the best solution among all the candidate solutions(omega wolf). 

The fittest solution is the optimal solution to the TSP solution and is termed the best fit solution, and the best fit solution is validated across all the best solutions produced by the grey wolf optimization.

So this is how the grey wolf optimization algorithm will be responsible to find the optimal solution for the salesman by providing the shortest distance from the starting city to the next city and also ensuring that the salesman visits each city only once.

Pros and cons of grey wolf optimization

Pros of grey wolf optimization

As grey wolf optimization techniques try to replicate the hunting characteristics of grey wolves, the optimization algorithm breaks down complex problems into different subsets and tries to yield the best possible optimal solution. The iterating process of the grey wolf optimization algorithm is faster when compared to the other optimization algorithms as they are different solutions being compared with respect to the optimal solution and ranked accordingly. This ranking technique of the grey wolf optimization makes the convergence of the models faster.

Cons of grey wolf optimization

The grey wolf optimization tries to find the optimal solution only when the best possible solution falls under the territory of the optimal solution. This makes the grey wolf optimization technique yield lower accuracies and sometimes converge to a bad solution. The best possible solution may lie out of the territory considered by the group of candidate solutions in certain cases. Moreover, the grey wolf optimization technique falls under the heuristic optimization techniques and the optimal solution produced is only near the original optimal solution and is not the best optimal solution to the problem.

Summary

Among the various optimization techniques, the grey wolf technique tries to find the optimal solution uniquely by following the overall principles of grey wolf hunting. The grey wolf optimization is a better choice for higher dimensional data and for certain problems like the traveling salesman problem. The overall algorithm produces the nearest optimal solution when compared to the best optimal solution which can be validated and if required can be optimized further as optimization of the grey wolf technique can be done with a fewer number of parameters.