  We present an affine $sl (n+1)$ algebraic construction of the basic
constrained KP hierarchy. This hierarchy is analyzed using two approaches,
namely linear matrix eigenvalue problem on hermitian symmetric space and
constrained KP Lax formulation and we show that these approaches are
equivalent. The model is recognized to be the generalized non-linear
Schr\"{o}dinger ($\GNLS$) hierarchy and it is used as a building block for a
new class of constrained KP hierarchies. These constrained KP hierarchies are
connected via similarity-B\"{a}cklund transformations and interpolate between
$\GNLS$ and multi-boson KP-Toda hierarchies. Our construction uncovers origin
of the Toda lattice structure behind the latter hierarchy.
