A computer program product is described for solving the traveling salesman
problem in polynomial time. The probability distribution of the space of
all paths is modeled in a configurational density distribution. A
Hamiltonian is constructed specifying the costs, distance, or penalty
associated with different legs of paths encompassed in the
configurational density distribution. Starting at a maximum temperature
where free energy dominates and the penalty function plays little role,
the system is iteratively adapted to reduce the temperature in steps
incrementally chosen to preserve the linear characteristic of the
approximation, until a lower temperature state of reduced energy is
reached in which a preferred set of paths can be identified from the
configurational density distribution.