  The credit on {\it reduction theory} goes back to the work of Lagrange,
Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is
voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who
created the well known LLL algorithm, and many other researchers such as L.
Babai and C. P. Schnorr who created significant new variants of basis reduction
algorithms. In this paper, we propose and investigate the efficacy of new
optimization techniques to be used along with LLL algorithm. The techniques we
have proposed are: i) {\it hill climbing (HC)}, ii) {\it lattice diffusion-sub
lattice fusion (LDSF)}, and iii) {\it multistage hybrid LDSF-HC}. The first
technique relies on the sensitivity of LLL to permutations of the input basis
$B$, and optimization ideas over the symmetric group $S_m$ viewed as a metric
space. The second technique relies on partitioning the lattice into
sublattices, performing basis reduction in the partition sublattice blocks,
fusing the sublattices, and repeating. We also point out places where parallel
computation can reduce run-times achieving almost linear speedup. The
multistage hybrid technique relies on the lattice diffusion and sublattice
fusion and hill climbing algorithms.
