An anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem

Libralesso, Luc; Fontan, Florian

doi:10.1016/j.ejor.2020.10.050

Cited by 18 publications

(9 citation statements)

References 32 publications

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“…Another anytime algorithm with similarities to rectangle search is Complete Anytime Beam Search (CABS) (Zhang 1998). As adapted by Libralesso et al (2020), CABS performs a sequence of increasing-width beam searches, dou-bling the beam width at each iteration, and retaining the best solution so far as an incumbent. It terminates when no node excluded from the beam has f (n) ≤ g(incumbent).…”

Section: Relevant Comparatorsmentioning

confidence: 99%

Beam Search: Faster and Monotonic

Lemons

López

Holte

et al. 2022

ICAPS

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Beam search is a popular satisficing approach to heuristic search problems that allows one to trade increased computation time for lower solution cost by increasing the beam width parameter. We make two contributions to the study of beam search. First, we show how to make beam search monotonic; that is, we provide a new variant that guarantees nonincreasing solution cost as the beam width is increased. This makes setting the beam parameter much easier. Second, we show how using distance-to-go estimates can allow beam search to find better solutions more quickly in domains with non-uniform costs. Together, these results improve the practical effectiveness of beam search.

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Section: Relevant Comparatorsmentioning

confidence: 99%

Beam Search: Faster and Monotonic

Lemons

López

Holte

et al. 2022

ICAPS

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“…Figure 7: e center point of item i and its NFP rectangle: (a) description of item (i); (b) the corresponding NFP (i) of item i. {(0,0), (10,0), (15,− 6), (22,10), (14,24), (0,24), (− 5,12)} 526 3 × 3 9 46 23.234 12 {(0,0), (6,− 6), (4,− 20), (20,− 12), (36,− 20), (30,− 6), (40,0), (24,0), (20,16) coincide with each other (Figure 9(a)). Using Eq.…”

Section: (B))mentioning

confidence: 99%

“…Based on the tree search algorithm proposed by Fanslau and Bortfeldt [14] for container loading problems, Bortfeldt and Jungmann [15] proposed a tree search algorithm for rectangular layout problems with guillotine cutting constraints. Libralesso and Fontan [16] presented a new anytime tree search algorithm called IMBA Liu et al [17] proposed a binary tree search algorithm for the problem of how to load a subset of a given rectangular box into a rectangular container to maximize the packaging volume.…”

Section: Introductionmentioning

confidence: 99%

Heuristic Approach for Packing Identical Rectangular Tiles in an Irregular Marble Slab

Yuan

Song

2022

Mathematical Problems in Engineering

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Packing identical rectangular tiles in a large marble slab is a necessary task. However, when the region of the marble slab is a concave set, the characteristics of the concave set make it difficult to determine whether the rectangular tiles are in the region. For this purpose, this article proposes a heuristic approach to the problem of packing identical rectangular items with orthogonal constraints in a concave irregular region. The heuristic approach uses a tree-search structure, and the final layout is built by inserting a new item in an irregular polygon. The newly inserted item must satisfy the containment and the nonoverlapping constraints associated with the irregular polygon. Regarding the containment constraint, we propose an improved slope algorithm to obtain the inner-fit polygon (IFP) of irregular polygons and rectangular items and apply IFP to determine the relative position of a rectangular item and an irregular polygon to guarantee containment constraint. Compared with existing methods, this approach can not only be used in convex regions but also in concave regions. Numerical experiments and application examples illustrate the effectiveness of the approach.

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“…This limitation is mainly imposed by the techniques employed by off-the-shelf solvers -such as branch and bound-. Such techniques explore the neighborhood of solutions obtained by the linear programming relaxation [14]. Thus, they tend to obtain integer solutions at leaf nodes; an aspect that makes them very time and storage consuming.…”

Section: Introductionmentioning

confidence: 99%