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 minimized, leading to a biobjective formulation of the problem with a tradeoff between the number of bins and their heterogeneousness. An extension of the Best-Fit approximation algorithm is presented to solve the problem. Experimental investigations have been carried out on benchmark instances of different size, ranging from 100 to 1000 items. Encouraging results have been obtained, showing the applicability of the heuristic approach to the described problem.
Technische Hochschule Rosenheim（罗森海姆应用技术大学）；Technische Universität München（慕尼黑工业大学）；Institut für nachhaltige Energieversorgung（可持续能源供应研究所）；Technische Hochschule Ingolstadt（因戈尔施塔特应用技术大学）
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, practitioners can resort to heuristic and exact methodologies. Lately, machine learning is increasingly used for solving such problems. This paper considers a 2D packing problem from the furniture industry, where a set of wooden workpieces must be assigned to different modules of a trolley in the most space-saving way. We present an…
Re-evaluating LLM-based Heuristic Search: A Case Study on the 3D Packing Problem
The University of Manchester（曼彻斯特大学）；University of Manchester（曼彻斯特大学）；Department of Computer Science（计算机科学系）；Alliance Manchester Business School（曼彻斯特商业联盟学院）
Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Universität Wien（维也纳大学）
Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific problem a set of oriented rectangular items is given which must be packed into a minimum number of bins of equal size. The first algorithm proposed in this work is a randomized multi-start version of a cons…
We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple procedures of the intersection test without any exceptional handling due to geometric issues, while they often require much memory and computational effort in high-resolution. To reduce the complexity of rasterized shapes, we propose a pair of scanlines representation called the double scanline representation that merges consecutive pixels in each row and co…
Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；University of California, Los Angeles（加州大学洛杉矶分校）
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 multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performan…
Tata Consultancy Services Research and Innovation Lab（塔塔咨询服务研究与创研实验室）；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
We propose a Deep Reinforcement Learning (Deep RL) algorithm for solving the online 3D bin packing problem for an arbitrary number of bins and any bin size. The focus is on producing decisions that can be physically implemented by a robotic loading arm, a laboratory prototype used for testing the concept. The problem considered in this paper is novel in two ways. First, unlike the traditional 3D bin packing problem, we assume that the entire set of objects to be packed is not known a priori. Instead, a fixed number of upcoming objects is visible to the loading system, and they must be loaded i…
Sichuan University（四川大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Huazhong University of Science and Technology（华中科技大学）
The bin packing problem exists widely in real logistic scenarios (e.g., packing pipeline, express delivery), with its goal to improve the packing efficiency and reduce the transportation cost. In this NP-hard combinatorial optimization problem, the position and quantity of each item in the box are strictly restricted by complex constraints and special customer requirements. Existing approaches are hard to obtain the optimal solution since rigorous constraints cannot be handled within a reasonable computation load. In this paper, for handling this difficulty, the packing knowledge is extracted …
A 3D flexible bin packing problem (3D-FBPP) arises from the process of warehouse packing in e-commerce. An online customer's order usually contains several items and needs to be packed as a whole before shipping. In particular, 5% of tens of millions of packages are using plastic wrapping as outer packaging every day, which brings pressure on the plastic surface minimization to save traditional logistics costs. Because of the huge practical significance, we focus on the issue of packing cuboid-shaped items orthogonally into a least-surface-area bin. The existing heuristic methods for classic 3…
Inst. for Information Transmission Problems, Russian Academy of Sciences（俄罗斯科学院信息传输问题研究所）
The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems is suggested: (a) basic element sets (item set, bin set, item subset assigned to bin), (b) binary relation over the sets: relation over item set as compatibility, precedence, dominance; relation over items and bins (i.e., correspondence of items to bins). A special attention is targeted to the following versions of bin packing problems: (a) problem with mul…
This work aims to study and explore the use of Gene Expression Programming (GEP) in solving the on-line Bin-Packing problem. The main idea is to show how GEP can automatically find acceptable heuristic rules to solve the problem efficiently and economically. One dimensional Bin-Packing problem is considered in the course of this work with the constraint of minimizing the number of bins filled with the given pieces. Experimental Data includes instances of benchmark test data taken from Falkenauer (1996) for One-dimensional Bin-Packing Problems. Results show that GEP can be used as a very powerf…
School of Computer Science and Technology, Huazhong University of Science and Technology（华中科技大学计算机科学与技术学院）
We address a new variant of packing problem called the circle bin packing problem (CBPP), which is to find a dense packing of circle items to multiple square bins so as to minimize the number of used bins. To this end, we propose an adaptive large neighborhood search (ALNS) algorithm, which uses our Greedy Algorithm with Corner Occupying Action (GACOA) to construct an initial layout. The greedy solution is usually in a local optimum trap, and ALNS enables multiple neighborhood search that depends on the stochastic annealing schedule to avoid getting stuck in local minimum traps. Specifically, …
Bin Packing with Conflicts (BPC) are problems in which items with compatibility constraints must be packed in the least number of bins, not exceeding the capacity of the bins and ensuring that non-conflicting items are packed in each bin. In this work, we introduce the Bin Packing Problem with Compatible Categories (BPCC), a variant of the BPC in which items belong to conflicting or compatible categories, in opposition to the item-by-item incompatibility found in previous literature. It is a common problem in the context of last mile distribution to nanostores located in densely populated area…
GOPT: Generalizable Online 3D Bin Packing via Transformer-based Deep Reinforcement Learning
State Key Laboratory of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology（华中科技大学机械科学与工程学院智能制造装备与技术国家重点实验室）；BOSCH Corporate Research, China（博世中国研究中心）；State Key Laboratory of High-end Heavy-load Robots, Midea Group（美的集团高端重载机器人国家重点实验室）；Midea Corporate Research Center（美的集团企业研究中心）
