Scaling features in complex optimization problems Original Research Article

We study the scaling behavior in the ensemble approach of simulated annealing and threshold accepting considering two examples of complex optimization problems, namely Grötschelʹs traveling salesman problem and a spin glass problem with Gaussian distributions of the couplings. If scaling is present it should allow for an estimation of the ground state energy. Our numerical results show a different qualitative behavior for the two kinds of problems. Whereas scaling is present in the spin glass problem it is widely absent in the traveling salesman problem.