For this question, assume that there are $100$ samples of flowers. For each sample,

two features $($petal length and petal width$)$ are measured and as shown in Figure

$2,$ each point represents a sample and its coordinates $(1,2)$ represent the values

of its two features. Both the petal length and the petal width of all samples are less

than $10$ cm$.$

We would like to divide those $100$ flower samples into five clusters and find the

corresponding cluster centres $($centroids$).$

Answer the following questions about the design of a Particle Swarm

Optimization $($PSO$)$ algorithm to determine the centroid of each cluster for this

clustering problem.

Figure $2$

$($a$)$ Write down the precise specification of a particle, i$.$e$.$ describe the contents

of a candidate solution represented by a particle. Also, give an example of

a particle based on your specification.

$[4$ marks$]$

$($b$)$ Describe a suitable fitness function and specify $($in detail$)$ all the steps

required for computing the fitness of a particle. As part of your answer,

state whether the fitness function should be minimised or maximised.

There is no need to write down a mathematical formula for the fitness

function.

$[7$ marks$]$

$($c$)$ Write down the flowchart of PSO to solve this clustering problem.

$[5$ marks$]$

$($d$)$ Identify which steps in the PSO flowchart of your answer in $($c$)$ need to be

modified if you use a Genetic Algorithm $($instead of PSO$)$ to solve this

clustering problem; and describe how to modify each of those steps when

using a Genetic Algorithm.