  We consider the optimal paths in a $d$-dimensional lattice, where the bonds
have isotropically correlated random weights. These paths can be interpreted as
the ground state configuration of a simplified polymer model in a random
potential. We study how the universal scaling exponents, the roughness and the
energy fluctuation exponent, depend on the strength of the disorder
correlations. Our numerical results using Dijkstra's algorithm to determine the
optimal path in directed as well as undirected lattices indicate that the
correlations become relevant if they decay with distance slower than 1/r in d=2
and 3. We show that the exponent relation 2nu-omega=1 holds at least in d=2
even in case of correlations. Both in two and three dimensions, overhangs turn
out to be irrelevant even in the presence of strong disorder correlations.
