Bin Packing Research Articles

Auto-scaling edge cloud for network slicing

This paper presents a study on resource control for autoscaling virtual radio access networks (RAN slices) in next-generation wireless networks. The dynamic instantiation and termination of on-demand RAN slices require efficient autoscaling of computational resources at the edge. Autoscaling involves vertical scaling (VS) and horizontal scaling (HS) to adapt resource allocation based on demand variations. However, the strict processing time requirements for RAN slices pose challenges when instantiating new containers. To address this issue, we propose removing resource limits from slice configuration and leveraging the decision-making capabilities of a centralized slicing controller. We introduce a resource control agent (RC) that determines resource limits as the number of computing resources packed into containers, aiming to minimize deployment costs while maintaining processing time below a threshold. The RAN slicing workload is modeled using the Low-Density Parity Check (LDPC) decoding algorithm, known for its stochastic demands. We formulate the problem as a variant of the stochastic bin packing problem (SBPP) to satisfy the random variations in radio workload. By employing chance-constrained programming, we approach the SBPP resource control (S-RC) problem. Our numerical evaluation demonstrates that S-RC maintains the processing time requirement with a higher probability compared to configuring RAN slices with predefined limits, although it introduces a 45% overall average cost overhead.

A hybrid estimation of distribution algorithm for the offline 2D variable-sized bin packing problem

In this paper we present an evolutionary heuristic for the offline two-dimensional variable-sized bin packing problem. In this problem we have to pack a set of rectangles into two-dimensional variable-sized rectangular bins. The bins are divided into types, and the bins in different types have different sizes and possibly different weights (costs). There are (sufficiently) many bins from each type, and any rectangle fits into at least one bin-type. The goal is to pack the rectangles into the bins without overlap, parallel to the sides, so that the total area of the used bins (or total cost) is minimized. Our algorithm is a hybrid heuristic. It uses two different techniques to generate the descendants: either estimation of distribution algorithm and sampling the resulting probability model, or applying the usual operators of evolutionary algorithms (selection, mutation). To pack the rectangles into the bins the algorithm uses the strategy of randomly choosing one of two placement heuristics, that pack always only one group (one to three) of rectangles. It improves the quality of the solutions with three local search procedures. The algorithm has been tested on benchmark instances from the literature and has been compared with other heuristics and metaheuristics. Our algorithm outperformed the previously published results.

A variable neighborhood search framework combining improved simulated annealing search to solve the one-dimensional crating problem

The N-P problem, similar to bin packing, has a great impact on us in real life. Similar to the classical combinatorial problem, with the expansion of the problem size, usually there is no way to solve it by enumeration. The common solution is to solve by heuristic methods, in addition to the improved local search method by forbidden search or simulated annealing to solve. However, due to the multivariate nature of the bin packing problem, it is difficult to solve most of the bin packing problems by the above single method. In this paper, a variable neighborhood search combined with an improved local search is used to solve the one-dimensional bin packing problem. The method in this paper is generalizable and can easily improve the existing method to suit new problems, and the results are acceptable.

A Genetic Programming-based Framework for Semi-automated Multi-agent Systems Engineering

With the rise of new technologies, such as Edge computing, Internet of Things, Smart Cities, and Smart Grids, there is a growing need for multi-agent systems (MAS) approaches. Designing multi-agent systems is challenging, and doing this in an automated way is even more so. To address this, we propose a new framework, Evolved Gossip Contracts (EGC). It builds on Gossip Contracts (GC), a decentralised cooperation protocol that is used as the communication mechanism to facilitate self-organisation in a cooperative MAS. GC has several methods that are implemented uniquely, depending on the goal the MAS aims to achieve. The EGC framework uses evolutionary computing to search for the best implementation of these methods. To evaluate EGC, it was used to solve a classical NP-hard optimisation problem, the Bin Packing Problem (BPP). The experimental results show that EGC successfully discovered a decentralised strategy to solve the BPP, which is better than two classical heuristics on test cases similar to those on which it was trained; the improvement is statistically significant. EGC is the first framework that leverages evolutionary computing to semi-automate the discovery of a communication protocol for a MAS that has been shown to be effective at solving an NP-hard problem.

Task Containerization and Container Placement Optimization for MEC: A Joint Communication and Computing Perspective

Containers are used by an increasing number of Internet service providers to deploy their applications in multi-access edge computing (MEC) systems. Although container-based virtualization technologies significantly increase application availability, they may suffer expensive communication overhead and resource use imbalances. However, so far there has been a scarcity of studies to conquer these difficulties. In this paper, we design a workflow-based mathematical model for applications built upon interdependent multitasking composition, formulate a multi-objective combinatorial optimization problem composed of two subproblems—graph partitioning and multi-choice vector bin packing, and propose several joint task-containerization-and -container-placement methods to reduce communication overhead and balance multi-type computing resource utilization. The performance superiority of the proposed algorithms is demonstrated by comparison with the state-of-the-art task and container scheduling schemes.

BalCon — resource balancing algorithm for VM consolidation

Cloud providers handle substantial number of requests to create and delete virtual machines (VMs) on a daily basis, where the unknown sequence of requests eventually leads to resource fragmentation. To mitigate this issue, periodic consolidation of VMs into fewer number of physical hosts is an important cost-saving procedure, closely related to the vector bin-packing problem. In this paper, we propose the BalCon algorithm for consolidation that steadily reduces the number of active hosts and keeps migration costs low. BalCon classifies the cluster’s state and selects one of three heuristics to balance resources for superior consolidation. To evaluate BalCon’s performance with respect to optimality, we introduce integer programming models. BalCon finds 99.7% of the optimal solutions for over 750 problem instances. This outstanding result was achieved due to the Force Step of our algorithm, which is the key improvement detail for common heuristics. We compare BalCon with a modified Sercon heuristic using Huawei and synthetic datasets with two resources for allocation.

Hybrid branch-and-price-and-cut algorithm for the two-dimensional vector packing problem with time windows

This paper introduces the two-dimensional vector packing problem with time windows (2DVPPTW). It packs all items into identical bins to minimize the number of used bins. Items are characterized by their weights, volumes, and time windows. Items have different time requirements for delivery in many practical settings. For example, items have their time windows for packing and delivery. The 2DVPPTW is subjected to three constraints: weight, volume, and time windows. We present an integer programming (IP) model for the proposed 2DVPPTW. The IP model is reformulated into the master problem and the subproblem (SP). A hybrid branch-and-price-and-cut (H-BPC) algorithm is developed to solve the 2DVPPTW. On the basis of extensive computational experiments, the proposed H-BPC is significantly effective in comparison with the commercial branch-and-bound/cut solvers, such as CPLEX, and two exact methods. The primary reason for the computational efficiency of the H-BPC is the development of a heuristic algorithm, namely, adaptive large neighborhood search (ALNS), to solve the SP, which is usually computationally expensive. Developing the heuristic algorithm extends the works on the solution to the SPs of bin packing problems and two-dimensional vector packing problems. Two dynamic programming (DP) algorithms are also proposed to solve the SP optimally, namely, the label-setting algorithm and the maximal clique-based DP (MC_DP) algorithm. Moreover, two cooperative schemes are proposed and compared. One is composed of the ALNS and label-setting algorithm, which has a shorter computational time, and the other is composed of the ALNS and MC_DP, which can obtain more optimal solutions. Furthermore, subset-row inequalities, rounded capacity inequalities, multidimensional dual-feasible function, and incompatibility preprocessing policy help to decrease the computational burden dramatically.

Learning to Solve 3-D Bin Packing Problem via Deep Reinforcement Learning and Constraint Programming.

Recently, there is a growing attention on applying deep reinforcement learning (DRL) to solve the 3-D bin packing problem (3-D BPP). However, due to the relatively less informative yet computationally heavy encoder, and considerably large action space inherent to the 3-D BPP, existing DRL methods are only able to handle up to 50 boxes. In this article, we propose to alleviate this issue via a DRL agent, which sequentially addresses three subtasks of sequence, orientation, and position, respectively. Specifically, we exploit a multimodal encoder, where a sparse attention subencoder embeds the box state to mitigate the computation while learning the packing policy, and a convolutional neural network subencoder embeds the view state to produce auxiliary spatial representation. We also leverage an action representation learning in the decoder to cope with the large action space of the position subtask. Besides, we integrate the proposed DRL agent into constraint programming (CP) to further improve the solution quality iteratively by exploiting the powerful search framework in CP. The experiments show that both the sole DRL and hybrid methods enable the agent to solve large-scale instances of 120 boxes or more. Moreover, they both could deliver superior performance against the baselines on instances of various scales.

A machine learning optimization approach for last-mile delivery and third-party logistics

Third-party logistics is now an essential component of efficient delivery systems, enabling companies to purchase carrier services instead of an expensive fleet of vehicles. However, carrier contracts have to be booked in advance without exact knowledge of what orders will be available for dispatch. The model describing this problem is the variable cost and size bin packing problem with stochastic items. Since it cannot be solved for realistic instances by means of exact solvers, in this paper, we present a new heuristic algorithm able to do so based on machine learning techniques. Several numerical experiments show that the proposed heuristics achieve good performance in a short computational time, thus enabling its real-world usage. Moreover, the comparison against a new and efficient version of progressive hedging proves that the proposed heuristic achieves better results. Finally, we present managerial insights for a case study on parcel delivery in Turin, Italy.

A hybrid biogeography-based optimization algorithm for three-dimensional bin size designing and packing problem

The three-dimensional bin packing problem (3D-BPP) plays a critical role in logistics activities. Prior studies focus on 3D-BPP in cases where bin size is predetermined. However, bin volume utilization can be improved significantly by optimizing bin size. In this study, we propose a novel three-dimensional bin size designing and packing problem (3D-BSDPP) and a hybrid biogeography-based optimization (HBBO) algorithm to address the problem by maximizing bin volume utilization by optimizing the bin size. The HBBO combines a differential evolution algorithm with basic biogeography-based optimization to improve exploration ability, and a novel local search strategy involving three specific local search operators is proposed to accelerate the HBBO convergence. Finally, a novel heuristic packing method is employed to find a high-quality packing solution. The proposed algorithm is evaluated through experiments carried out on a practical bin packing application. The results indicate that the proposed algorithm outperforms existing algorithms in solving the 3D-BSDPP.

A symmetry-free spectrum allocation heuristic for elastic optical networks

We revisit spectrum allocation (SA), a fundamental problem in optical network design, and we explain that it can be modeled as a permutation problem. This new model eliminates spectrum symmetry, a property that presents a significant challenge to conventional spectrum allocation solutions. Accordingly, we develop parameterized first-fit (PFF), a new symmetry-free heuristic for the SA problem that has several desirable features: it explores a pre-defined subset of the solution space whose size is tailored to the available computational budget; it constructs this subset by sampling from diverse areas of the solution space rather than from the neighborhood of an initial solution; it finds solutions by applying the well-known first-fit (FF) algorithm and thus it can be deployed readily; its execution can be easily parallelized; and it is effective and efficient in finding good quality solutions.

Space Splitting and Merging Technique for Online 3-D Bin Packing

This paper introduces a novel method for online 3-D bin packing, which is a strongly NP-hard problem, based on a space splitting and merging technique. In this scenario, the incoming box is unknown and must be immediately packed. The problem has many applications in industries that use manipulators to automate the packing process. The main idea of the approach is to divide the bin into spaces. These spaces are then categorized into one of two types of data structures: main and secondary data structures. Each node in the main data structure holds the information of a space that can be used to fit a new box. Each node in the secondary data structure holds the information of a space that cannot be used to place a box. The search algorithm based on these two data structures reduces the required search effort and simplifies the organizing and editing of the data structure. The experimental results demonstrate that the proposed method can achieve a packed volume ratio of up to 83% in the case of multiple bins being used. The position of a placed box can be found within milliseconds.

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Super Intendo: Semantic Robot Programming from Multiple Demonstrations for taskable robots

When an end-user instructs a taskable robot on a new task, it is important for the robot to learn the user’s intention for the task. Knowing the user’s intention, represented as desired goal conditions, allows the robot to generalize across variations of the learned task seen at execution time. However, it has proven challenging to learn goal conditions due to the large, noisy, and complex space of goal conditions expressed by human users. This paper introduces Semantic Robot Programming with Multiple Demonstrations (SRP-MD) to learn a generative model of latent end-user task goal conditions from multiple end-user demonstrations in a shared workspace. By learning a generative model of the goal conditions, SRP-MD generalizes to task instances even when the quantity of objects to be arranged is not in the training set or novel object instances are included. At test time, a new goal is pulled from the learned generative model given the objects present in the initial scene. The efficacy of SRP-MD as a step toward taskable robots is shown on a Fetch robot learning and executing bin packing tasks in a simulated environment with grocery items.

Enhancing meta slot space space wavelength to solve blocking case in elastic optical networks

Elastic optical networks (EONs) are a promising technology for the development of flexible and wideband communication systems. The (FSU) frequency slot unit concept is used in this technology to define the bandwidth unit in the frequency domain. The use of a specified number of consecutive FSUs allows bandwidth to be assigned to a data stream in a flexible manner. Nonblocking optical switching networks are required for a successful elastic optical network operation. This article concentrates on the Wavelength Space Wavelength,Space, Wavelength switching network topologies that were previously presented. In comparison to the other architectures, the SSW switching fabric requires fewer Spectrum converters (SCs). n relation to Wavelength Space Wavelength, a prior study clarified that using the meta-slot approach reduces hardware complexity, which is measured by the number of frequency slot unit. A frequency range with one or more (FSUs) is called a meta-slot. The previous study did not discuss how to optimize the meta-slot class sizes, despite the fact that its effectiveness depends on the sizes of the meta-slot classes. Additionally, the use of meta-slots for Space Space Wavelength was not taken into account in the earlier analysis. The optimization of meta-slot class sizes is looked into in this study, and it is shown that this optimization may be modeled as the shortest path issue. For Wavelength Space Wavelength, the previously reported nonblocking conditions are contrasted with the meta-slot scheme optimized using the shortest path model. The outcome attests to the optimized meta-slot scheme's superiority. The distribution of meta-slots among S-switches is also crucial for Space Space Wavelength. The assignment of meta-slots is modeled as a bin-packing problem in the study. Thus, a well-known bin-packing heuristic can be used to find the assignment that is close to ideal. The number of S-switches is calculated for using the optimized meta-slot scheme and previously known nonblocking conditions. The outcome confirms that the meta-slot scheme benefits both Space, Wavelength and Wavelength Space Wavelength.

The Use of Machine Learning Techniques for Optimal Multicasting in 5G NR Systems

Multicasting is a key feature of cellular systems, which provides an efficient way to simultaneously disseminate a large amount of traffic to multiple subscribers. However, the efficient use of multicast services in fifth-generation (5G) New Radio (NR) is complicated by several factors, including inherent base station (BS) antenna directivity as well as the exploitation of antenna arrays capable of creating multiple beams concurrently. In this work, we first demonstrate that the problem of efficient multicasting in 5G NR systems can be formalized as a special case of multi-period variable cost and size bin packing problem (BPP). However, the problem is known to be NP-hard, and the solution time is practically unacceptable for large multicast group sizes. To this aim, we further develop and test several machine learning alternatives to address this issue. The numerical analysis shows that there is a trade-off between accuracy and computational complexity for multicast grouping when using decision tree-based algorithms. A higher number of splits offers better performance at the cost of an increased computational time. We also show that the nature of the cell coverage brings three possible solutions to the multicast grouping problem: (i) small-range radii are characterized by a single multicast subgroup with wide beamwidth, (ii) middle-range deployments have to be solved by employing the proposed algorithms, and (iii) BS at long-range radii sweeps narrow unicast beams to serve multicast users.

Arcflow Formulations and Constraint Generation Frameworks for the Two Bar Charts Packing Problem

We consider the two bar charts packing problem (2-BCPP), a recent combinatorial optimization problem whose aim is to pack a set of one-dimensional items into the minimum number of bins. As opposed to the well-known bin packing problem, pairs of items are grouped to form bar charts, and a solution is only feasible if the first and second items of every bar chart are packed in consecutive bins. After providing a complete picture of the connections between the 2-BCPP and other relevant packing problems, we show how we can use these connections to derive valid lower and upper bounds for the problem. We then introduce two new integer linear programming (ILP) models to solve the 2-BCPP based on a nontrivial extension of the arcflow formulation. Even though both models involve an exponential number of constraints, we show that they can be solved within a constraint generation framework. We then empirically evaluate the performance of our bounds and exact approaches against an ILP model from the literature and demonstrate the effectiveness of our techniques on both benchmarks inspired by the literature and new classes of instances that are specifically designed to be hard to solve. The outcomes of our experiments are important for the packing community because they indicate that arcflow formulations can be used to solve targeted packing problems with precedence constraints and also that some of these formulations can be solved with constraint generation. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.1256 .

Compliant‐based robotic 3D bin packing with unavoidable uncertainties

AbstractRobotic 3D bin packing (R‐3dBPP), aiming to place deformed cases in various sizes in the container without fences, is a comprehensive application that includes perception, planning, execution, and hardware design. Traditional studies assume that the context of the real space must be accurately perceived and represented. However, disjunctions between the planner and reality are unavoidable in R‐3dBPP, especially with low‐cost sensors. As far as the author knows, there is no practical solution. In this paper, the above assumption is discarded and the typical types of uncertainties prevalent to guide the design of the algorithms are formulated. A new online bin‐packing algorithm is proposed, keeping deformed boxes stacked in close contact with each other, so that the whole pallet is kept stable by friction between the boxes and the container. In order to meet the requirement of close contact under the non‐negligible errors from sensors and planners, a compliant‐based motion planning system is introduced. It replaces the precision‐based feedback with a compliant end‐effector and accompanying motion strategies. Last but not least, a complete online bin‐packing robot system is developed and the system's performance under the influence of the uncertainties mentioned above through simulation and physical experiments is evaluated.

A 4/3 OPT+2/3 Approximation for Big Two-Bar Charts Packing Problem

We consider the two-bar charts packing problem generalizing the strongly NP-hard bin packing problem. We prove that the problem remains strongly NP-hard even if each two-bar chart has at least one bar higher than 1/2. If the first (or second) bar of each two-bar chart is higher than 1/2, we show that the O(n2)-time greedy algorithm with lexicographic ordering of two-bar charts constructs a packing of length at most OPT+1, where OPT is optimum, and present an O(n2.5)-time algorithm that constructs a packing of length at most 4/3 ・ OPT+2/3 in the NP-hard case where each two-bar chart has at least one bar higher than 1/2.

Improved Approximation Algorithms for Bin Packing with Conflicts

Given a set of items, and a conflict graph defined on the item set, the problem of bin packing with conflicts asks for a partition of items into a minimum number of independent sets so that the total size of items in each independent set does not exceed the bin capacity. As a generalization of both classic bin packing and classic vertex coloring, it is hard to approximate the problem on general graphs. We present new approximation algorithms for bipartite graphs and split graphs. The absolute approximation ratios are shown to be [Formula: see text] and [Formula: see text] respectively, both improving the existing results.