Yaygın kullanılan bazı optimizasyon fonksiyonlarının melez bir algoritma ile çözümü

Abstract

Designing a new hybrid optimization algorithm  Providing a new perspective to achieve optimized results  Designing an optimization algorithm for faster reach optimized solutionsIn 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. In our applications, Particle Swarm Optimization (PSO) method and Broydon-Fletcher-Goldfarb-Shanno (BFGS) method 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. Optimum result 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). Figure A. Recycled aggregate productionPurpose: Although numerical optimization algorithms guarantee the exact solution, they remain relatively slow. On the other hand, heuristic optimization algorithms are fast but they cannot guarantee the exact solution.From this point of view, it is aimed to design an algorithm that achieves both fast and exact solutions.Theory and Methods: In this study, it is proposed that numerical and heuristic methods can be hybridized and exact solutions can be reached faster. In the literature, hybrid optimization algorithms apply heuristic and then numerical approaches. In the developed method, the opposite way was followed. Results:The developed method was tested on the functions used in the literature for testing purposes. Accordingly, as the test function becomes more complex, the speed of the solution is slow in milliseconds according to the comparison algorithm. Conclusion:Consequently, the combination of numerical methods such as BFGS and heuristic methods such as PSO may be an appropriate approach for solution accuracy. As intended in this study, heuristics can be hybridized with other numerical methods. On the other hand, the literature research and the proposed algorithm proved that hybrid algorithms obtained better results than standard heuristics and numerical methods.