  Given a family of feasible subsets of a ground set, the packing problem is to
find a largest subfamily of pairwise disjoint family members.
Non-approximability renders heuristics attractive viable options, while
efficient methods with worst-case guarantee are a key concern in computational
complexity. This work proposes a novel near-Boolean optimization method relying
on a polynomial multilinear form with variables ranging each in a
high-dimensional unit simplex, rather than in the unit interval as usual. The
variables are the elements of the ground set, and distribute each a unit
membership over those feasible subsets where they are included. The given
problem is thus translated into a continuous version where the objective is to
maximize a function taking values on collections of points in a unit hypercube.
Maximizers are shown to always include collections of hypercube disjoint
vertices, i.e. partitions of the ground set, which constitute feasible
solutions for the original discrete version of the problem. A gradient-based
local search in the expanded continuous domain is designed. Approximations with
polynomial multilinear form of bounded degree and near-Boolean games are also
finally discussed.
