Page 179 - Data Science Algorithms in a Week

The Estimation of Cutting Forces in the Turning of Inconel 718 Assisted … 163


v i k  1 v k   1 , v ,2 i k   1 , ..., v , i d k  1  (10)
  ,1 i

to the current position xi(k):

k
x i k   1  x i   + v i k   1 (11)

The components of vi(k+1), are computed as follows:


k
k
k
v , i j k   1  v , i j    c r  ˆ y , i j    x , i j    c r  y j    x , i j   (12)
k
k
1 1, j
2 2, j

where j designates component in the search space; ω represents the inertia weight which
decreases linearly from 1 to near 0; c1, and c2 are cognitive and social parameters,
respectively, known as learning factors; and r1,j and r2,j are random numbers uniformly
distributed in the range [0, 1]. The inertia weight component causes the particle to
continue in the direction in which it was moving at iteration k. A large weight facilitates
global search, while a small one tends to facilitate fine tuning the current search area. The
cognitive term, associated with the experience of the particle, represents its previous best
position and provides a velocity component in this direction, whereas the social term
represents information about the best position of any particle in the neighborhood and
causes movement towards this particle. These two parameters are not critical for the
convergence of PSO, but fine tuning may result in faster convergence of algorithm and
alleviation of local minima. The r1,j and r2,j parameters are employed to maintain the
diversity of population.
The PSO algorithm shares many similarities with evolutionary computation
techniques such as GA. PSO algorithm are also are initialized with a randomly created
population of potential solutions and has fitness values to evaluate the population.
Furthermore, both algorithms update the population and search for the optimum with
random techniques. However, unlike GA, PSO does not have operators such as mutation
and crossover which exist in evolutionary algorithms. In PSO algorithm potential
solutions (particles) are moving to the actual optimum in the solution space by following
their own experiences and the current best particles. Compared with GA, PSO has some
attractive characteristics such are its memory which enables it to retain knowledge of
good solutions by particles of the whole swarm, simultaneously search for an optima in
multiple dimensions, mechanism of constructive cooperation and information-sharing
between particles. Due to its simplicity, robustness, easy implementation, and quick
convergence PSO optimization method has been successfully applied to a wide range of
applications. The focus of this study is to employ a PSO for optimization of the weights
and bias of the ANN model. The steps involved in process of ANN training using PSO
are shown in Table 4.