Page 146 - Data Science Algorithms in a Week

130 Alfonso T. Sarmiento and Edgar Gutierrez

Figure 1. Optimization algorithm.

Global Search: PSO Algorithm

The algorithm used is called “local best PSO” (Engelbrecht, 2005) and is based on a
social network composed of neighborhoods related to each particle. The algorithm
maintains a swarm of particles, where each particle represents a candidate solution to the
optimization problem. These particles move across the search space communicating good
positions to each other within the neighborhood and adjusting their own position and
velocity based on these good positions. For this purpose, each particle keeps a memory of
its own best position found so far and the neighborhood best position among all the
neighbor particles. The goodness of a position is determined by using a fitness function.
The stopping condition of the algorithm is when the maximum number of iterations has
been exceeded.
The following empirical rules are recommended to guide the choice of selecting the
initial values for the parameters of the PSO algorithm.

Empirical rules for selecting the PSO parameters

Parameter Empirical rule of choice
Swarm size From 20 to 40 (Clerc, 2006)
Inertia weight In ]0,1[ (Shi and Eberhart, 1998)
Cognitive coefficient Suggestion 1.43 (Clerc, 2006)
Social coefficient Suggestion 1.43 (Clerc, 2006)
The steps of the algorithm are described in the following lines.

Step 1) Initialization:
 Set iteration k=0