In this paper, stochastic optimization algorithms of PSO (Particle Swarm Optimization) and APSO (Adaptive Particle Swam Optimization) are studied and compared. It is revealed that the APSO provides faster convergence and better search efficiency than the conventional PSO when they are adopted to find the global minimum of a two-dimensional function. The advantages of the APSO comes from the ability to control the inertia weight, and acceleration coefficients. To verify that the APSO is working better than the standard PSO, the design of a 10GHz microstrip patch as one of the elements of a high frequency array antenna is taken as a test-case and shows the optimized result with 5 iterations in the APSO and 28 iterations in th PSO.