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We have formulated the problem of generating periodic dense paritcle packingsas an optimization problem called the Adaptive Shrinking Cell (ASC) formulation[S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because theobjective function and impenetrability constraints can be exactly linearizedfor sphere packings with a size distribution in $d$-dimensional Euclidean space$\mathbb{R}^d$, it is most suitable and natural to solve the corresponding ASCoptimization problem using sequential linear programming (SLP) techniques. Weimplement an SLP solution to produce robustly a wide spectrum of jammed spherepackings in $\mathbb{R}^d$ for $d=2,3,4,5$ and $6$ with a diversity of disorderand densities up to the maximally densities. This deterministic algorithm canproduce a broad range of inherent structures besides the usual disordered oneswith very small computational cost by tuning the radius of the {\it influencesphere}. In three dimensions, we show that it can produce with high probabilitya variety of strictly jammed packings with a packing density anywhere in thewide range $[0.6, 0.7408...]$. We also apply the algorithm to generate variousdisordered packings as well as the maximally dense packings for $d=2,3, 4,5$and 6. Compared to the LS procedure, our SLP protocol is able to ensure thatthe final packings are truly jammed, produces disordered jammed packings withanomalously low densities, and is appreciably more robust and computationallyfaster at generating maximally dense packings, especially as the spacedimension increases.

Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming