- - - Dep.of Op. Res. and Int. Tech., Faculty of Computer Sciences and Mathematics, University of Mosul, Iraq
- - - Dep.of Op. Res. and Int. Tech., Faculty of Computer Sciences and Mathematics, University of Mosul, Iraq
- - - Dep.of Op. Res. and Int. Tech., Faculty of Computer Sciences and Mathematics, University of Mosul, Iraq

In this paper, we have investigated a new spectral Quasi-Newton (QN) algorithm. New search directions of the proposed algorithm increase its stability and increase the arrival to the optimum solution with a lowest cost value and our numerical applications on the standard Firefly Algorithm (FA)and the new proposed algorithm are powerful as in meta-heuristic field. Our new proposed algorithm has quite common uses in several sciences and engineering problems. Finally, our numerical results show that the proposed technique is the best and its accuracy higher than the accuracy of the standard FA. These numerical results are compared using statistical analysis to evaluate the efficiency and the robustness of new proposed algorithm.

QN-method, self-scaling QN, Conjugate gradient, Unconstrained optimization, Firefly Algorithm