How Grey Wolves Inspired more Efficient Energy Management
Dr. Seyedali "Ali" Mirjalili created the Grey Wolf Algorithm after being inspired by the hunting strategies an organization of wolves. The algorithm uses cleverly adapts the intricate organization of wolves to the general problem of optimization. Its applications are far-reaching from cloud computing to power grid management.
EXPLAINER
Intro
Many times, researchers will turn to nature as inspiration for an algorithm. One example (that I'm sure you've heard of) is artificial neural networks, whose design was inspired by the neurons within our brains. From the original artificial neural network (the perception), a whole genre of machine learning algorithms have been created.
However, this post isn't about neural networks, or even machine learning. There is another whole genre of algorithms that I want to tell you about. Swarm optimization algorithms!
Honey bees, ants, fireflies, and a whole host of different organisms coordinate with each other to achieve a goal. Whether they are communicating through pheromones, wiggle dances, or bright lights. They are usually optimizing. For instance, ants will try to find the shortest path to food by following each others pheromones, and wolves will follow a leader to encircle prey.
The algorithms developed from these observations are powerful, flexible, and, intuitive to understand, which allows them to be adopted in a variety of diverse contexts. Today, I will talk about a specific one: Grey Wolf Optimization. It has wonderful origin story and has found some surprising applications.
Origin of Grey Wolf Optimization
Dr. Seyedali Mirjalili has made a YouTube video explaining how he came up with Grey Wolf Optimization. It is a great watch if you want to know more about how he came up with the idea.
But first, to avoid confusion, I want to describe how our understanding of grey wolf behavior has evolved.
In 1947, a landmark research paper by Rudolph Schenkel theorized that wolves have a strict organizational structure where alpha wolves are the most dominant followed by beta wolves, and then omega wolves. This theory spawned an early understanding of how wolf dynamics work.
The key point of contention is that Schenkel's traditional theory claims that wolves fight for dominance and that certain wolves (omega wolves) fall to the bottom of the chain where they are used by others to vent anger and aggression.
However, this idea has proven to be inaccurate. In real life, the alpha "leader" wolf will assume its role from being the parent of other younger wolves--not being the strongest or best leader. In general, wolf organizational structure is primarily based on parental relationships, rather than infighting despite what pop culture may suggest.
In fact, omega wolves don't actually exist in the wild as they were observed in captivity!
So where does this leave Dr. Mirjalili and the Grey Wolf Optimization algorithm? As you are about to see, the model of wolf behavior that inspired the researcher was in some ways modern, but in other ways inaccurate. It is important to recognize that bio-inspired algorithms are not meant to be true to biology, but rather use insights from nature to solve problems.
Dr. Mirjalili first was inspired by a documentary he watched about wolves. He was drawn a model of wolf behavior where alpha wolves were the dominant leaders, followed by beta wolves, then delta wolves, and finally omega wolves.
He was also drawn to their strategical behavior when hunting prey. Namely how the wolves would coordinate with each other to approach, encircle, and attack big prey like bison
These observations, how the wolves organized themselves and then strategically attacked big prey may seem unrelated to energy efficiency, but bear with me.
Take a less esoteric situation like ordering inventory for a grocery store. In this situation, the bison could represent the correct amount of produce to buy (maximizing price and demand). It is hard to determine this number analytically. The GWO algorithm uses wolves to encircle and approximate this "bison" which is actually the problem we want to solve.
Although it might seem weird to swap out bison for a solution to a numerical problem. It actually enables us to apply the strategies that wolves use to hunt prey to many important optimization problems. To clear up confusion, let's examine how GWO actually works.
The Origin Story of Grey Wolf Optimization
How our Understanding of Grey Wolves has Evolved
A Simplified Explanation of GWO
Let's define what optimization is, in lay man's terms, before we dive too deep into technical details:
Optimization: is a type of problem where we have a goal and we want to find the best solution in a sea of possible solutions.
For example, if our goal was to minimize the function f(x) = |x|, all values of x are valid solutions, but we would want to search for the value that minimized the function. Obviously the answer is x = 0, but in more complicated cases when we do not know the underlying function of a system, we need to search for the best answer.
This is what Grey Wolf Algorithm does, it searches for the best possible answer to a problem by trying different possible solutions.
Okay, now let's get into the algorithm itself.
Grey Wolf Optimization starts by initializing a number of "wolves" to random solutions in the solution space.
Then we designate the top 3 best wolves as alpha, beta, and delta. The positions of these wolves remained fixed while we change the position of all the other omega wolves. The positions of these omega wolves change according a few mathematical equations that best explained by the creator himself.
The essence of what these mathematical equations are doing is as follows:
Using the three best solutions (alpha, beta, delta) to inform a guess of where the "prey" (aka best solution) is. The omega wolves will then either move towards or away from this guess
Varying whether the wolves go toward the prey or away from the prey. Generally the wolves will start by going away from the prey, and then go towards the prey towards the end of the algorithm's runtime. This is important to make sure the wolves don't get "tunnel visioned" on a specific spot
Incorporating randomness into the wolves' behavior which allows the wolves to search in many places at once.
Afterwards, the algorithm reassigns the alpha, beta, and delta based on if any wolves found better solutions. These steps are repeated until the algorithm reaches a "termination" point which is usually after a certain amount of time has passed or after a certain amount of epochs have passed.
Applications of GWO
The Grey Wolf Algorithm is very flexible and has key advantages over other algorithms in the same class. It has relatively few parameters that require tuning, is simple to implement in code, and has advanced mechanisms to avoid common pitfalls like being trapped in local minimums.
As a result, it has been adopted in the fields of machine learning, image processing, and engineering design. However, I want to focus on two more recent examples from research papers published in the Spring of 2025. These researchers made modifications of the Grey Wolf Algorithm to tackle challenges in fog-cloud computing and power grid management.
Fog-cloud computing is a system of computing that you have probably benefited from! Simply, cloud computing is when centralized big data servers handle computation and transmit information back to a client. Think of google Colab which is a service that allows you to upload code to hardware provided by google in order to train machine learning models.
Fog computing is when calculations are evaluated by device itself. This is useful for small calculations where it makes sense to save bandwidth.
As you may guess, allocating computations to data servers and retrieving them can be challenging in an interconnected environment where there is a web of servers linked up with each other. Researchers in Saudi Arabia modified the Grey Wolf Algorithm to calculate optimal task scheduling timings.
In doing so they achieved a 29% reduction in energy consumption and a 46% improvement in makespan which is how efficiency is measured in the cloud computing space.
In another example, researchers used a modified Grey Wolf Algorithm to improve the efficiency of power grid management. The researchers created a model power grid with renewable energy sources and demonstrated how a modified Grey Wolf Algorithm made improvements in grid stability as well as resource management (reflecting in a higher profit).
These are by no means an exhaustive list of the applications of the Grey Wolf Algorithm, but I'm sure you can see the benefit to society that the Grey Wolf Algorithm has produced.
Closing Note: How true is the GWO to Biology?
Okay, I'm sure if you have been following along, you may be wondering how true this algorithm really is to biology and real life.
Of course grey wolves don't actually have an "omega" class, and they obviously don't conform to the simplistic notion that the algorithm presents. Yet, in my opinion, this is excusable. The GWO algorithm only achieved its level of adoption and success due to its relative simplicity.
The Grey Wolf Algorithm used powerful analogies to how grey wolves actually hunt to motivate its conception. The patterns observed in how grey wolves weave in and out from the prey, and their general technique of being guided by more experienced wolves in the pack.
In fact, this touches on something much larger than just the GWO.
Many times people hear about researchers spending tax money or their time researching things that may not seem productive. Whether it be the behavior of wolves or something entirely different. However, the GWO algorithm and many other examples in science teach us that these projects may not have a materialistic and quantifiable benefit in the short term, they inspire innovations years down the line that do.