Soft Computing Techniques for Optimal Capacitor Placement - Complex System Modelling and Control Through Intelligent Soft Computations - page 603

Fig. 8 Flowchart for the
particle swarm optimization
(PSO) algorithm

In 1962, an optimum operating tracking method was devised, which was based
on set of point by forming a simplex in the factor-space and continually forming
new simplexes by re ecting one point in the hyper-plane of the remaining points. It

is a local search method designed for unconstrained optimization without using
gradient information. Following four basic procedures are used by this method to
rescale the simplex based on the local behaviour of the function: re

fl

ection,
expansion, contraction, and shrinkage. Through these procedures, the simplex can
successfully improve itself and get closer to the optimum. The algorithm for NM
simplex is outlined below and the steps are illustrated in Fig. 8 through a
two-dimensional case (N = 2).
1. Initialization: For theminimization of a function of Nvariables, create N+ 1 vertex
points to form an initial N-dimensional simplex. Evaluate the functional value at
each vertex point of the simplex. See a two-dimensional simplex exhibited in
Fig. 9 a. For the maximization case, it is convenient to transform the problem into
the minimization case by pre-multiplying the objective function by

fl

− 1.