  The 0-1 integer linear programming feasibility problem is an important
NP-complete problem. This paper proposes a continuous-time dynamical system for
solving that problem without getting trapped in non-solution local minima.
First, the problem is transformed to an easier form in linear time. Then, we
propose an "impulse algorithm" to escape from local traps and show its
performance is better than randomization for escaping traps. Second, we present
the time-to-solution distribution of the impulse algorithm and compare it with
exhaustive search to see its advantages. Third, we show that the fractional
size of the basin of attraction of the global minimum is significantly larger
than $2^{-N}$, the corresponding discrete probability for exhaustive search.
Finally, we conduct a case study to show that the location of the basin is
independent of different dimensions. These findings reveal a better way to
solve the 0-1 integer linear programming feasibility problem continuously and
show that its cost could be less than discrete methods in average cases.
