Algorithms

The following algorithms are implemented:

• Particle Swarm Optimization [1] This implementation is the modified Particle Swarm Optimization where it employs an inertia weight $\omega$ that controls convergence. This implementation uses linear decay for the inertia weight, which lowers the value of $\omega$ until it reaches the default minimum of $\omega = 0.4$. The update rules for the particles are the following:

  \[x_{i+1} = x_i + v_{i+1} \\ v_{i+1} = \omega v_i + \varphi_1 \beta_1 (p_i - x_i) + \varphi_2 \beta_2 (p_g - x_i)\]

  where $\beta_1$ and $\beta_2$ are uniformly distributed random numbers; $\varphi_1$ and $\varphi_2$ are the momentum coefficients; $p_i$ is the previous individual best position and $p_g$ is the privious global best position of the population.

References