5.5 Selection of weighting factors

In Eq. (26), all the objectives are added with different weighting factors to form a single cost function. In such techniques, it is tedious and difficult to select proper weighting factor for the optimal solution. Improper set of weighting factors strongly effect on achieving the final values of the desired synthesizing parameters and hence on the performance of the optimization algorithm. Generally, some selected best results are presented without mentioning such difficulties. However, these values of the weighting factors are obtained by trial and error method [4]. Though multi-objective evolutionary algorithm (MOEA) [35, 36] can be used to solve such problems, the researchers are not comfortable with it as it has been used rarely as compared to single-objective optimization approaches.

#### 5.6 Evolutionary algorithms

It is already discussed that time-modulated antenna array synthesis problems are non-convex as well as nonlinear. Therefore, stochastic, global computational techniques are required to solve such problems. In this regard, different populationbased global searching techniques such as DE, SA, GA, PSO, ABC, and multiobjective evolutionary algorithm (MOEA) have been applied successfully to synthesize the desired pattern at the center frequency by suppressing sideband radiation to satisfactorily low levels. However, here the working principle of ABC and its implementation have been presented, and a novel approach to synthesize TMAA is discussed.
