A branch-and-price algorithm for the two-dimensional vector packing problem

Bin packing with lexicographic objectives for loading weight- and volume-constrained trucks in a direct-shipping system

“…Our problem is a variant of the 2D-VPP for which an early exact approach is given by Spieksma (1994). Recent exact approaches are based on BaP and are described in Heßler et al (2018) and Wei et al (2020a). General approximation results are given in Bansal et al (2016).…”

Solving Bin Packing Problems Using VRPSolver Models

“…These are the following: BraPed16 Graph compression and arc-flow model-based approach proposed in [6] and executed at a Quad-Core Intel Xeon 2.66 GHz processor, HesGscIrn18 Stabilized branch-and-price algorithm, using a labeling algorithm for RCSP in the pricing, proposed in [19] and executed at an Intel i7-5930k 3.5GHz processor. WLLH20 Branch-and-price algorithm proposed in [43] only for the 2-dimensional case, using a specially tailored 2-D binary knapsack algorithm for the pricing subproblem, executed at an Intel i7-6700 3.40GHz processor.…”

“…However, VRPSolver solved the largest number of instances, including 3 open instances in class 9 with 200 items. In [43], another algorithm could solve 5 instances in class 9 with 200 items. It can be seen in Table 4 that the other classes of instances are "easy," in the sense that all their instances are solvable in root node, without need for cutting or branching.…”

“…After that, other exact algorithms for BPP were proposed in [10,42]. Recent exact algorithms for VPP were presented in [6,19,43]. The best exact algorithms for VSBPP are those in [1,4,17,23].…”

Hybrid Heuristic Algorithm Based On Improved Rules & Reinforcement Learning for 2D Strip Packing Problem

“…Martello [3] used the branch-and-bound algorithm. In 2019 Wei [4] et al tried to eliminate the conflict between the two items by branching first, and then used dynamic programming to solve the problem of two-constraint backpacks on the leaf node. Experiments have shown the algorithm was superior to the existing branch-and-bound method.…”