  We present an improved form of the integration technique known as NDIM
(Negative Dimensional Integration Method), which is a powerful tool in the
analytical evaluation of Feynman diagrams. Using this technique we study a $%
\phi ^{3}\oplus \phi ^{4}$ theory in $D=4-2\epsilon $ dimensions, considering
generic topologies of $L$ loops and $E$ independent external momenta, and where
the propagator powers are arbitrary. The method transforms the Schwinger
parametric integral associated to the diagram into a multiple series expansion,
whose main characteristic is that the argument contains several Kronecker
deltas which appear naturally in the application of the method, and which we
call diagram presolution. The optimization we present here consists in a
procedure that minimizes the series multiplicity, through appropriate
factorizations in the multinomials that appear in the parametric integral, and
which maximizes the number of Kronecker deltas that are generated in the
process. The solutions are presented in terms of generalized hypergeometric
functions, obtained once the Kronecker deltas have been used in the series.
Although the technique is general, we apply it to cases in which there are 2$
$or$ $3 different energy scales (masses or kinematic variables associated to
the external momenta), obtaining solutions in terms of a finite sum of
generalized hypergeometric series de 1 and 2 variables respectively, each of
them expressible as ratios between the different energy scales that
characterize the topology. The main result is a method capable of solving
Feynman integrals, expressing the solutions as hypergeometric series of
multiplicity $(n-1) $, where $n$ is the number of energy scales present in the
diagram.
