We study the scaling behavior in the ensemble approach of simulated annealing and threshold accepting considering two examples of complex optimization problems, namely Grotschel's 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. [References: 15]
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