A Solution Of Some Commonly Used Optimization Functions By A Hybrid Bfgs-Pso Algorithm

In this study, the development of a hybrid optimization method has been emphasized in order to eliminate the deficiencies in the structure of heuristic and numerical methods. Heuristic methods cannot guarantee the exact solution. However, they can run relatively faster than numerical methods. On the other hand, numerical methods contain strong mathematical solutions and can reach a definite solution. In our applications, one of the heuristic optimization methods, Particle Swarm Optimization (PSO) method and Broydon-Fletcher-Goldfarb-Shanno (BFGS) method, which is one of the numerical optimization methods, are aimed to reach the optimum solution more accurately and faster. In the algorithm of the developed optimization method, the solution is firstly sought with BFGS. Thus, the smallest or maximum points for the objective function are determined. Then these points are screened using PSO. Until the final result is reached, the intermediate solution points are continuously transferred between the BFGS and the PSO. Using the original BFGS and the original PSO, two different methods are proposed: BFGS first, then PSO hybrid method, and vice versa hybrid method (first PSO then BFGS); It has been applied by working on the frequently used test functions among the researchers. Experimental results have indicated that both proposed hybrid algorithm and another hybrid algorithm implemented in reverse way can reach the global optimal results in short times.