Machine learning has seen remarkable strides recently, with Artificial Neural Networks (ANNs) in the limelight. Drawing from principles in neuroscience, ANNs have proven to be effective in diverse practical applications. This article will delve into specific techniques, like particle swarm optimisation, backpropagation, and neural networks that inform the development of ANNs.

## Artificial Neuron Networks

The majority of Artificial Intelligence (AI) research centres on Artificial Neural Networks (ANNs), also known as neural networks. Neural networks are capable of executing three types of distinct operations:

- The initial category outlines the manner in which the neurons in the structure are interconnected.
- The second category comprises the methods used for determining the link weights.
- Finally, it is the activation function that governs the amount of energy that neurons can release through their outputs.

In the field of Artificial Neural Networks, Backpropagation is a prevalent technique that employs hierarchical node stacking. This process occurs through two distinct layers, the “output layer” and the “hidden layer”. The output layer is the final layer processed after data input, while the hidden layer is situated between the output layer and visible input layers.

## Steps Involved in the Backpropagation Algorithm

The backpropagation algorithm can be broken down into multiple distinct phases:

- The input layer receives a vector of input data.
- The output set receives the output layer.
- The deviation from the expected outcome is evaluated by comparing the two results.
- Based on the learning rules, the outcome of the comparison determines how the weights should be adjusted.

## Limitations of the Backpropagation Algorithm

One of the primary disadvantages of using the Backpropagation Algorithm is the extensive duration required for model training due to the reverse operation of the neurons needed to attain optimal solutions. To overcome this challenge, scientists have developed a more advanced technique called Particle Swarm Optimization that has reduced the training time needed and provided more accurate and dependable outcomes.

Activation functions such as the Sigmoid function or Rectified Linear Unit (ReLU) are present in each node of a neural network. The input signal is transmitted via a weighted link and processed by the activation function to produce the ultimate output.

## Application of Backpropagation Algorithm (BP)

Due to the extended time required to reach convergence, the procedure is repeated iteratively until the desired result is obtained. In recent times, the popularity of Particle Swarm Optimization has increased, resulting in a decline in the application of this method.

## Collective Intelligence

In 2009, Konstantinos and Michael introduced a technique where neurons collaborate to determine the optimal resting point, which aims to identify a comprehensive solution. This approach is similar to a flock of birds working together to reach a specific destination by relying on the collective efforts of all group members.

Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) are among the most popular Swarm Intelligence techniques used. ACO is inspired by the way ants seek food and uses graphs to identify the best solution. On the other hand, PSO relies on the idea of neurons (particles) collaborating to enhance the search process. Both approaches are effective and have been successfully applied in various domains.

## Swarm Optimization through Particles

The velocity vector is utilized to update the positions of all swarms (neurons) as they work collectively to identify the optimum global solution.

Studies have indicated a limited scope for enhancement in the following domains:

- Expanding the search region within a domain,
- Alterations to the configurations, and
- Combining with a distinct approach or performing hybridization.

In the realm of Particle Swarm Optimization (PSO), the particles’ starting positions are randomly determined without any effect on the process. The particles operate as a team to tackle a problem and keep track of the completed iterations. After each iteration, data is gathered to determine the personal best (pbest) and global best (gbest). Next, the resulting particle positions are adjusted by randomly scaling the pbest and gbest vectors.

Particle movement is governed by an equation of motion that defines a fixed velocity vector. The velocity update equation also specifies the variation in velocity vectors based on two vectors (pbest and gbest). While solving Eq.(5), the period of swarm motion is indicated by the parameter t, usually set at 1.0. Consequently, the swarm’s location changes. Eq.(6) computes the optimal vectors, pbest and gbest, by computing the dimensional element, subtracting it, and then multiplying it by a random variable between 0 and 1, and an acceleration constant (C1 and C2, respectively).

Velocity plays a crucial role in the study of particle swarms. It is calculated by summing up the paths taken by particles across the solution space, with a random variable increasing the level of variability. Particle motion towards their personal best (pbest) or global best (gbest) is controlled by an equation using acceleration constants. The Mean Squared Error (MSE) is computed to minimize errors generated during particle learning. In comparison to backpropagation algorithms, particle swarms are preferred due to their ability to achieve a global solution more quickly.