Fitting nonlinear mathematical models to the cost function of the quadrafilar helix antenna optimization problem

Abstract

Here, optimization of a quadrafilar helical antenna is presented to compare the performances of objective function pairs adapted from mathematical models by using DEA with fixed weight objective function structure and SPEA2 with variable weight objective function structure from 2 different competitive multi-objective algorithms. The most important purpose in optimization problems is to find the result with the lowest cost. For this, the selection of the appropriate objective function pair is very important. The most important aim in this study is to determine the optimum objective function pair model. For this purpose, five different objective function models were derived by using nonlinear mathematical models. These objective functions are adapted from polynomial, power, exponential, gaussian and fourier mathematical models. In order to determine the most successful model without question, the objective functions adapted from the mathematical models are compared separately in both evolutionary algorithms by using different algorithm parameters and different weight coefficients. According to the results obtained, it is seen that the objective function adapted from the power mathematical model has the lowest cost. This proposed adaptation technique, which is the novelty of the study, is an efficient and reliable method to find the most appropriate objective function and the lowest cost result in optimization problems. It can also be quickly adapted to any optimization problem.