Recent advancements in the field of machine learning have brought Artificial Neural Networks (ANNs) to the fore once again. By leveraging insights from neuroscience, ANNs have been successfully applied to a wide range of practical scenarios. In this article, we will discuss in detail techniques such as particle swarm optimisation, backpropagation, and neural networks, which are all utilised in the development of ANNs.

## Networks of artificial neurons

Most research in the field of Artificial Intelligence (AI) revolves around Artificial Neural Networks (ANNs), which are commonly referred to as neural networks. Neural networks are capable of performing three distinct types of operations:

- The first category describes how the various neurons in the structure are linked to one another.
- In the second group, we have the procedures that are utilised to establish the link weights.
- In the end, the activation function is what controls how much energy the neurons may release in their outputs.

Backpropagation is a widely-utilised method within the field of artificial neural networks that involves the hierarchical stacking of nodes. This process involves the use of two distinct types of layers. The first layer is referred to as the “output layer” and is the last layer that is processed following the input of all necessary data. The second layer is referred to as the “hidden layer” and is the layer that lies between the output layer and the visible input layers.

## The Backpropagation Algorithm’s Various Steps

There are a few distinct phases to the backpropagation algorithm:

- A vector of input information is sent to the input layer.
- The layer of output is delivered to the output set.
- The deviation from the ideal result is determined by contrasting the two.
- According to the norms of learning, the comparison then decides how the weights should shift.

## The Backpropagation Algorithm’s Drawbacks

One of the main disadvantages of this approach is the amount of time necessary for training the models. This is due to the fact that the optimal solution is attained by the neurons operating in a reverse manner. To address this issue, scientists have formulated a more sophisticated approach referred to as Particle Swarm Optimisation. This has enabled them to minimise the training time and obtain more precise and reliable results.

The Sigmoid function, a type of activation function, is incorporated into each node of a neural network or other functions, such as the Rectified Linear Unit (ReLU). The signal generated from the input node is communicated via a weighted link, before being processed by the activation function to produce the final output.

## Using a Backpropagation Algorithm (BP)

Given the lengthy time it takes to achieve convergence, this procedure is continually repeated until the desired result is achieved. Particle swarm optimisation has become increasingly popular in recent years, leading to a decrease in the use of this method.

## Collective cognition

In 2009, Konstantinos and Michael developed a method whereby neurons pool their resources to identify the optimal resting spot, the aim of which is to uncover a comprehensive solution. This approach is analogous to a flock of birds collectively working together to reach a certain destination, as it relies on the combined efforts of all of its members.

Ant Colony Optimisation (ACO) and Particle Swarm Optimisation (PSO) are two of the most widely used techniques in the field of Swarm Intelligence. ACO is inspired by the behaviour of ants searching for food and uses graphs to find the optimal solution. PSO, on the other hand, is based on the concept of neurons (particles) working together to optimise the search process. Both methods are effective and have been successfully employed in a variety of areas.

## Optimisation via a swarm of particles

A vector termed velocity vector is used to update the positions of all swarms (neurons) as they work together to discover the global solution.

Research suggests there is little room for improvement in the following areas:

- The enlargement of the search area in a field,
- Modifications to the settings, and
- Combining using a different method, or hybridization.

Within the framework of Particle Swarm Optimisation (PSO), the initial positions of the particles are randomly assigned. The velocities and positions of the particles have no influence on the process. All particles work together to solve a problem, keeping track of the iterations that have already been completed. At the end of each cycle, a personal best (pbest) and a global best (gbest) are calculated from the data gathered. The subsequent particle locations are then modified by the random weighting of the vectors pbest and gbest.

Particle motion is characterised by an equation of motion defining a fixed velocity vector. Furthermore, the velocity update equation describes the change in velocity vectors as a function of two vectors (pbest and gbest). When solving Eq.(5), the period of swarm motion is represented by the parameter t, which is typically set to 1.0. As a result, the hive has shifted its location. Eq.(6) determines the best vector, pbest and gbest, by subtracting the dimensional element, which is then multiplied by a random variable in the range 0–1 and an acceleration constant, C1 and C2, respectively.

Velocity is an important factor to consider when studying particle swarms. It is determined by combining the total of the particles’ paths across the solution space, which are made more variable due to a random variable. The motion of particles towards either their personal best (pbest) or global best (gbest) is regulated by an equation, and acceleration constants are used to control this equation. Calculating the mean squared error (MSE) helps to reduce the amount of error that is introduced while the particles are learning. Particle swarms are preferred to backpropagation algorithms because they have the potential to reach a global solution in a shorter time frame.