  The efficiency of minimum-energy configuration searching algorithms is
closely linked to the energy landscape structure of complex systems. Here we
characterize this structure by following the time evolution of two systems,
vacancy aggregation in Fe and energy relaxation in ion-bombarded c-Si, using
the kinetic Activation-Relaxation Technique (k-ART), an off-lattice kinetic
Monte Carlo (KMC) method, and the well-known Bell-Evans-Polanyi (BEP)
principle. We also compare the efficiency of two methods for handling
non-diffusive flickering states -- an exact solution and a Tabu-like approach
that blocks already visited states. Comparing these various simulations allow
us to confirm that the BEP principle does not hold for complex system since
forward and reverse energy barriers are completely uncorrelated. This means
that following the lowest available energy barrier, even after removing the
flickering states, leads to rapid trapping: relaxing complex systems requires
crossing high-energy barriers in order to access new energy basins, in
agreement with the recently proposed replenish-and-relax model [B\'eland et
al., PRL 111, 105502 (2013)] This can be done by forcing the system through
these barriers with Tabu-like methods. Interestingly, we find that following
the fundamental kinetics of a system, though standard KMC approach, is at least
as efficient as these brute-force methods while providing the correct kinetics
information.
