Most
The COMPASS most-promising-area (MPA) around a current best (center) point x*. The MPA is the set of feasible points that are at least as close to x* as to every other point visited so far. Geometrically it is the intersection of:
the original problem's linear constraints (carried as originalHalfSpaces), and
one halfway hyperplane per visited point
y != x*: the half-space of points no farther fromx*than fromy. Forythis half-space isa · x <= bwitha = y - x*andb = (|y|^2 - |x*|^2) / 2, which containsx*.
A point lies in the MPA when it satisfies every halfway hyperplane and is input-feasible for the problem (box bounds, integer granularity, linear and functional constraints). The RMD sampler walks within this region; the redundancy checker can prune halfway hyperplanes that never bind.
Parameters
the problem whose feasible region the MPA refines
the current best point x*, in the problem's input order
the set of previously visited points (each in the problem's input order); the center itself, if present, contributes no constraint and is ignored
Properties
All half-spaces that define the MPA: the original constraints plus the halfway hyperplanes.
One halfway hyperplane per distinct visited point, each oriented to contain center.
The original problem's linear constraints expressed uniformly as a · x <= b half-spaces.
Functions
Returns the halfway hyperplanes that are not redundant given the problem's original half-spaces together with the remaining halfway hyperplanes — i.e. the ones that can actually bind on the MPA. Used to keep the RMD sampler's per-axis interval computation lean.
True if x lies in the most-promising area: it satisfies every halfway hyperplane and is input-feasible for the problem (which already enforces the box bounds and original linear and functional constraints).