  Monte Carlo optimizations of Number Partitioning and of Diophantine
approximations are microscopic realizations of `Trap Model' dynamics. This
offers a fresh look at the physics behind this model, and points at other
situations in which it may apply.
  Our results strongly suggest that in any such realization of the Trap Model,
the response and correlation functions of smooth observables obey the
fluctuation-dissipation theorem even in the aging regime. Our discussion for
the Number Partitioning problem may be relevant for the class of optimization
problems whose cost function does not scale linearly with the size, and are
thus awkward from the statistical mechanic point of view.
