Improvement and Application of Fractional Particle Swarm Optimization Algorithm

Algorithm 1

IFPSO-KM algorithm.

	Input: data set
	Output: divided cluster center solution sets
	Step 1: Initialize the population and parameters, determine the value according to the SSE and Silhouette Coefficient, randomly select data sample points as the initial center point, and calculate the fitness value of each particle according to the formula.
	Step 2: Compare the fitness value of each particle with its individual extreme value , and update if the new value is better.
	Step 3: Compare the fitness value of each particle with the population extreme value , and update if the new value is better.
	Step 4: According to the velocity formula (equation (17) and position formula (equation (18)) the velocity and position of the particles are updated respectively. At the same time, the experiment uses the basic idea of GA to randomly perform mutation operations on some particles, randomly encode particles within the set number of dimensions and perform single-point mutation operations to generate new groups. Then recalculate the fitness value of the particles, and update the fitness value according to equtaion (16).
	Step 5: According to the update process of the above algorithm, the optimal cluster center point is generated.
	Step 6: Using the nearest neighbor rule in the KM algorithm, reclassify each sample to obtain a new cluster division.
	Step 7: Determine whether the termination conditions are met. If it is satisfied, output the optimal solution; otherwise, return Step 2. The termination condition is that the cluster centers obtained within a given number of iterations do not change, or the maximum number of iterations is reached.