A new exact method for the two-dimensional orthogonal packing problem

MPQ-trees for the Orthogonal Packing Problem

“…Note that considering the big difference between our processors and the ones used by Caprara and Monaci for their experiments, one can see that algorithms A1 and A3 are also competitive. Table 1b shows the running times on benchmarks defined in [8]. The third column corresponds to the algorithm of Clautiaux, Carlier and Moukrim [8] implemented in C on a PC (Pentium IV, 2.6 GHz).…”

“…Table 1b shows the running times on benchmarks defined in [8]. The third column corresponds to the algorithm of Clautiaux, Carlier and Moukrim [8] implemented in C on a PC (Pentium IV, 2.6 GHz). The size of the containers is (20,20) and there are 10 to 23 items to be packed.…”

“…We report the performance of our algorithm on 37 classical benchmarks for OKP-2 from [3, 2, 7, 12] (Tables 1a) and on 42 benchmarks for OPP-2 defined in [8] (Table 1b). For OKP-2 instances, we used a basic branch-and-bound procedure to select the items to be checked for feasibility.…”

“…. , D} there exists a function x d : V → Q + , such that: In this paper, we consider the bi-dimensional case, which has been the most studied so far [11,9,6,12,7,3,5,8,1]. This paper is organized as follows.…”

A hybrid evolutionary algorithm for the two-dimensional packing problem

“…He applied the branch and bound method, where the upper bound was derived from the Lagrangean relaxation of a cutting problem formulated as a zero-one integer programming problem. Descriptions of other exact methods can be found in Scheithauer and Terno (1993), Hadjiconstantinou and Christofides (1995), Fekete and Schepers (1997), Boschetti et al (2002), Caprara and Monaci (2004), and Clautiaux et al (2007).…”