Irregular packing problems: A review of mathematical models

AAS Leao, FMB Toledo, JF Oliveira… - European Journal of …, 2020 - Elsevier
Irregular packing problems (also known as nesting problems) belong to the more general
class of cutting and packing problems and consist of allocating a set of irregular and regular …

[HTML][HTML] Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts

JJ Lastra-Díaz, MT Ortuño - European Journal of Operational Research, 2024 - Elsevier
The irregular strip-packing problem, also known as nesting or marker making, is defined as
the automatic computation of a non-overlapping placement of a set of non-convex polygons …

Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

Y Stoyan, A Pankratov, T Romanova - Journal of the Operational …, 2016 - Taylor & Francis
We further improve our methodology for solving irregular packing and cutting problems. We
deal with an accurate representation of objects bounded by circular arcs and line segments …

Placement problems for irregular objects: Mathematical modeling, optimization and applications

Y Stoyan, A Pankratov, T Romanova - … and Applications: In Honor of Ivan …, 2017 - Springer
We describe our methodology for solving NP-hard irregular placement problems. We deal
with an accurate representation of objects bounded by circular arcs and line segments and …

Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation

RP Abeysooriya, JA Bennell… - International Journal of …, 2018 - Elsevier
The paper investigates the two-dimensional irregular packing problem with multiple
homogeneous bins (2DIBPP). The literature on irregular shaped packing problems is …

A customized branch-and-bound approach for irregular shape nesting

A Wang, CL Hanselman, CE Gounaris - Journal of Global Optimization, 2018 - Springer
Abstract We study the Nesting Problem, which aims to determine a configuration of a set of
irregular shapes within a rectangular sheet of material of fixed width, such that no overlap …

A one-pass heuristic for nesting problems

I Kierkosz, M Łuczak - Operations Research and Decisions, 2019 - cejsh.icm.edu.pl
A two-dimensional cutting (packing) problem with items of irregular shape and rectangular
sheets is studied. Three types of problems are considered: single-sheet problems without …

Constraint aggregation in non-linear programming models for nesting problems

P Rocha, AM Gomes, R Rodrigues, FMB Toledo… - … science: State of the art …, 2016 - Springer
The Nesting problem is a complex problem that arises in industries where sets of pieces or
space must be efficiently placed or allocated in order to minimize wasted space or wasted …

Two-phase approach to the nesting problem with continuous rotations

P Rocha, R Rodrigues, AM Gomes, FMB Toledo… - IFAC-PapersOnLine, 2015 - Elsevier
This paper presents an approach that assists in producing highly compacted Nesting layouts
with irregular pieces using free rotations. This approach consists in the selection and …

Avoiding Internal Gaps with Heterogeneous Circle Coverings via Optimal Power Diagrams

AC Frommer, Y Diaz-Mercado - IFAC-PapersOnLine, 2024 - Elsevier
In this work, we present a strategy for distributing a collection of heterogeneous circles over
a convex domain such that there are no gaps between circles. We find optimal power …