Related papers: On Solving the Oriented Two-Dimensional Bin Packin…
This paper addresses the two-dimensional bin packing problem with guillotine constraints. The problem requires a set of rectangular items to be cut from larger rectangles, known as bins, while only making use of edge-to-edge (guillotine)…
The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot…
In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack. Each item has integral width, integral height and an associated integral profit. The goal is…
The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…
We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
Cutting and Packing problems are occurring in different industries with a direct impact on the revenue of businesses. Generally, the goal in Cutting and Packing is to assign a set of smaller objects to a set of larger objects. To solve…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate…
[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants.…
In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin…
The three-dimensional bin packing problem (3D-BPP) plays an important role in city logistics and manufacturing environments, due to its direct relevance to operational cost. Most existing literature have investigated the conventional…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
In the Two-dimensional Bin Packing (2BP) problem, we are given a set of rectangles of height and width at most one and our goal is to find an axis-aligned nonoverlapping packing of these rectangles into the minimum number of unit square…
We address the bin packing problem (BPP), which aims to maximize bin utilization when packing a variety of items. The offline problem, where the complete information about the item set and their sizes is known in advance, is proven to be…
We investigate a real-life air cargo loading problem which is a variant of the three-dimensional Variable Size Bin Packing Problem with special bin forms of cuboid and non-cuboid unit load devices (ULDs). Packing is constrained by…