  A novel family of dynamical Monte Carlo algorithms for lattice polymers is
proposed. Our central idea is to simulate an extended ensemble in which the
self-avoiding condition is systematically weakened. The degree of the
self-overlap is controlled in a similar manner as the multicanonical ensemble.
As a consequence, the ensemble --the multi-self-overlap ensemble-- contains
adequate portions of self-overlapping conformations as well as higher energy
ones. It is shown that the multi-self-overlap ensemble algorithm reproduce
correctly the canonical averages at finite temperatures of the HP model of
lattice proteins. Moreover, it outperforms massively a standard multicanonical
algorithm for a difficult example of a polymer with 8-stickers. Alternative
algorithm based on exchange Monte Carlo method is also discussed.
