gbp4q {gbp}

gbp4q

Description

generalized bin packing problem in 4 dimension, a.k.a bin packing problem with weight limit.

Usage

gbp4q

Format

An object of class C++Class of length 1.

Details

gbp4d init a profit vector p, a length l, a depth d, a height h, and a weight w, along with associate constraints ml, md, mh and mw. gbp4d should fit it (l, d, h, w) into bn (ml, md, mh, mw) with w on weight limit constraint and l, d, h on geometry intepretation. gbp4d solver would solve

maximize sum_j=1^n p_j k_j

subject to sum_j=1^n w_j k_j leq mw and

fit (l_j, d_j, h_j) at coordinate (x_j, y_j, z_j) such that no overlap in ml x md x mh cuboid, j = 1, ......, n

and instantiate a gbp4d object with a x-axis coordinate vector x, a y-axis coordinate vector y, a z-axis coordinate vector z, a selection vector k, and an objective o.

gbp4q solver would also select the most preferred often smallest m from a list of m(l, d, h) after determine all or the higest volume set of ld can fit into one m(l, d, h) w.r.t the weight constraint.

a gbp4q class instance has 7 fields:

- p: profit of it fit into bn <vector>

created via cluster w via gbp1d, cluster max(l, d, h) and area via gbp4d_solver_dpp_main_create_p()

- it: it position and scale <matrix>

- x, y, z, w it position and w in the bin <numeric> (w hold in bn when fit it in bn)

- l, d, h, w it scale along x, y, z and w <numeric> (w of it itself)

- bn: bn scale <matrix>

- l, d, h, w bn scale along x, y, z and w <numeric>

matrix of 4 rows and each column is a single bn

should make sure bn list are sorted via volume so that the first col is the most prefered smallest bn, and also the last col is the least prefered largest and often dominant bn

should make sure no X in front of Y if bnX dominant bnY, bnX dominant bnY if all(X(l, d, h) > Y(l, d, h)) and should always prefer Y.

should make sure bn such that l >= d or vice versa.

- k: selection indicator 0, 1 on it <vector>

- f: selection indicator 0, 1, 2, 3 on bn <vector>

f in result should have no 0 and only one of 1

- o: objective achivement volumn fit in over volumn overall <numeric>

- ok: a quick indicator of all it fit into bn? <bool>

See Also

Other gbp4q: gbp4d_solver_dpp_filt, gbp4q_checkr