Use of Kaczmarz´s method in intelligent-particle swarm optimization

Intelligent-particle swarm optimization algorithm (IPSO) is an improved heuristic method estimating the quadratic model of the problem in the hand. The conventional way to find the coefficients of the second order equation is to solve the nonhomogeneous linear equation (Ax = b), where A is the Vandermonde matrix. Although this method seems to be quite simple to execute, matrix inversion must be performed at every iteration. Another disadvantage is that the Vandermonde matrix must be square, which means all data from the members in population cannot be used. Therefore, in this study, the iterative Kaczmarz´s Method is integrated to IPSO. The obtained results are compared with the conventional algorithm.