Since your problem is discrete selection of clusters, therefore this problem can be solved using binary PSO. You could work on this problem in two ways:
Approach 1:
1. Select lower bound to 0 and upper bound to 1
2. Define a threshold like (0.6)
3. Randomly generate population in between lower and upper bound
4. Population value greater than threshold will be 1 else 0
For instance initial population of 1st particle is [0.2 0.1 0.3 0.4 0.5 0.7 0.8 0.2 0.9 0.1] then binary equivalent of this population will be [0 0 0 0 0 1 1 0 1 0]
5. Evaluate your objective on the selected clusters. For 1st particle selected clusters will be 6,7, and 9
6. Repeat this process for all particles
7. Follow steps 4 and 5 for all updated particles in each iteration
8. Update local and global best
Approach 2:
1. Set lower and upper bound of velocity (-6 to 6 is preferable)
2. Randomly generate velocity in between lower and upper bound
3. Use Sigmoidal function to convert velocity into binary population
4. Follow steps 5 to 8 of approach 1.
You don't need to use PSO for this.
You can use the wrapper method.
You can experiment individually for all cluster sizes from 1 to 10, and you choose which cluster number results best. Experiments will be easy because the number of clusters is 10.
However, if the problem is to choose which of the 10 clusters will be more active, then it would make more sense to use a PSO-based application.
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