Heterogeneous Bins Research Articles

Two-layer heuristic for the three-dimensional bin design and packing problem

The bin packing problem is a classical problem widely existing in practical applications, such as shipping, warehousing and manufacturing industries. Whereas current research mainly focuses on reducing packing costs by optimizing the packing scheme, this study explores a novel approach by redesigning the bin sizes to fit the items ready to be packed. Specifically, this study considers a general three-dimensional open dimension problem (3D-ODP) where all dimensions, i.e. length, width and height, of a number of heterogeneous bin types are unknown and need to be decided. Based on the designed bin types, the corresponding packing scheme with minimal total costs is optimized, which is referred to as a three-dimensional multiple-bin-size bin packing problem (3D-MBSBPP). The combination of 3D-ODP and 3D-MBSBPP is redefined as a three-dimensional bin design and packing problem (3D-BDPP), for which a two-layer heuristic is developed. It consists of an outer heuristic framework (i.e. genetic algorithm or differential evolution algorithm) to design bin types, and an inner deterministic constructive heuristic (i.e. placement algorithm) to generate an effective solution for the 3D-MBSBPP. Extensive simulation tests on the classical benchmark and a case study derived from an e-commerce company are conducted to verify the algorithms and deduce managerial insights.

Optimizing e-commerce warehousing through open dimension management in a three-dimensional bin packing system.

In the field of e-commerce warehousing, maximizing the utilization of packing bins is a fundamental goal for all major logistics enterprises. However, determining the appropriate size of packing bins poses a practical challenge for many logistics companies. Given the limited research on the open-size 3D bin packing problem as well as the high complexity and lengthy computation time of existing models, this study focuses on optimizing multiple-bin sizes within the e-commerce context. Building upon existing research, we propose a hybrid integer programming model, denoted as the three dimensional multiple option dimensional rectangular packing problem (3D-MODRPP), to address the multiple-bin size 3D bin packing problem. Additionally, we leverage well-established hardware and software technologies to propose a 3D bin packing system capable of accommodating multiple bin types with open dimensions. To reduce the complexity of the model and the number of constraints, we introduce a novel assumption method for 0-1 integer variables in the overlap and rotation constraints. By applying this approach, we significantly streamline the computational complexity associated with the model calculations. Furthermore, we refine the dataset by developing a customized version based on the classical Three-Dimensional One-Size Dependent Rectangular Packing Problem (3D-ODRPP) dataset, leading to improved outcomes. Through comprehensive analysis of the research results, our model exhibits remarkable advancements in addressing the strong heterogeneous bin packing problem, the weak heterogeneous bin packing problem, the actual bin packing problem, and the bin packing problem with multiple bin types and open sizes. Specifically, it significantly reduces model complexity and computation time and increases space utilization. The system designed in this study paves the way for practical applications based on the proposed model, providing researchers with broader research prospects and directions to expand the scope of investigation in the field of 3D bin packing. Consequently, this system contributes to solving complex 3D packing problems, reducing space waste, and enhancing transportation efficiency.

A Reduced Variable Neighborhood Search Approach to the Heterogeneous Vector Bin Packing Problem

The two-dimensional heterogeneous vector bin packing problem (2DHet-VBPP) consists of packing the set of items into the set of various type bins, respecting their two resource limits. The problem is to minimize the total cost of all bins. The problem, known to be NP-hard, can be formulated as a pure integer linear program, but optimal solutions can be obtained by the CPLEX Optimizer engine only for small instances. This paper proposes a metaheuristic approach to the 2DHet-VBPP, based on Reduced variable neighborhood search (RVNS). All RVNS elements are adapted to the considered problem and many procedures are designed to improve efficiency of the method. As the Two-dimensional Homogeneous-VBPP (2DHom-VBPP) is more often treated, we considered also a special version of the RVNS algorithm to solve the 2DHom-VBPP. The results obtained and compared to both CPLEX results and results on benchmark instances from literature, justify the use of the RVNS algorithm to solve large instances of these optimization problems.

New formulations for Variable Cost and Size Bin Packing Problems with Item Fragmentation

In the Bin Packing Problem with Item Fragmentation a set of items of known weight and a set of bins of limited capacity are given; the task is to find the minimum cost assignment of items to bins without exceeding their capacity. However, contrary to the classical Bin Packing Problem, items can be split and fractionally assigned to different bins at a cost. In this paper we generalize models and properties from the literature by considering a set of heterogeneous bins, possibly having different cost and capacity. We prove that such a natural extension changes substantial features of the problem. We propose both compact and extended formulations and a branch-and-price algorithm that combines column generation techniques and implicit enumeration strategies to achieve guarantees on the optimality of the solutions. We present the results of an extensive experimental campaign proving that our algorithm outperforms general purpose commercial solvers by orders of magnitude.

3D heterogeneous bin packing framework for multi-constrained problems using hybrid genetic approach

This work presents distinct methodologies in using Genetic Algorithm (GA) for optimizing Three Dimensional (3D) packing of heterogeneous shaped bins with arbitrary sizes into a prismatic container, by considering the major real time packing constraints such as load bearing constraint, placement constraint, stability constraint, overlapping constraint, orientation constraint and weight constraint. The primary aim of this research is focused in optimizing the packing of heterogeneous prismatic bins of arbitrary sizes into standard rectangular commercial containers by obeying the above mentioned packaging constraints. Different genetic approaches adopted to achieve these goals are Binary coded GA, Decimal coded GA with and without penalty fitness function, Constrained GA with maximization and minimization fitness function, Heuristic GA and Hybrid GA. GA has been used to minimize the unused void space in the interior of the container by loading as much heterogeneous bins, by satisfying the packing constraints. Tweaking Algorithm (TA) is an application dependent heuristic algorithm applied in this research and has been used to enhance the genetic output by filling the remaining unused empty space inside the container. TA has also been enhanced in converting the obtained output into packer readable box packing sequence in tabular and diagrammatical format. In general, combination of GA and TA are considerably at par compared with the heuristic techniques for box packing.

Optimal energy-efficient placement of virtual machines with divisible sizes

A key problem in the management of data centers is how to provision virtual machines based on the available physical machines, because an optimized placement can lead to significant reduction in energy consumption. This problem can be formulated as bin packing with heterogeneous bin types, where the cost of a bin depends on how full it is. We prove that under suitable conditions, an extended version of the First-Fit-Decreasing heuristic delivers optimal results for this problem.

Optimization of heterogeneous Bin packing using adaptive genetic algorithm

This research is concentrates on a very interesting work, the bin packing using hybrid genetic approach. The optimal and feasible packing of goods for transportation and distribution to various locations by satisfying the practical constraints are the key points in this project work. As the number of boxes for packing can not be predicted in advance and the boxes may not be of same category always. It also involves many practical constraints that are why the optimal packing makes much importance to the industries. This work presents a combinational of heuristic Genetic Algorithm (HGA) for solving Three Dimensional (3D) Single container arbitrary sized rectangular prismatic bin packing optimization problem by considering most of the practical constraints facing in logistic industries. This goal was achieved in this research by optimizing the empty volume inside the container using genetic approach. Feasible packing pattern was achieved by satisfying various practical constraints like box orientation, stack priority, container stability, weight constraint, overlapping constraint, shipment placement constraint. 3D bin packing problem consists of ‘n’ number of boxes being to be packed in to a container of standard dimension in such a way to maximize the volume utilization and in-turn profit. Furthermore, Boxes to be packed may be of arbitrary sizes. The user input data are the number of bins, its size, shape, weight, and constraints if any along with standard container dimension. This user input were stored in the database and encoded to string (chromosomes) format which were normally acceptable by GA. GA operators were allowed to act over these encoded strings for finding the best solution.

Multi Objective Optimization of Heterogeneous Bin Packing using Adaptive Genetic Approach

Objectives: The packing of goods in any industry is a tedious work. The proposed system evaluates the optimal packing and prediction of 3D bin packing maximize the maximize profit. Methods/Statistical Analysis: The Adaptive Genetic Algorithm (AGA) is used to solve the 3D single bin packing problem by getting the user input data such as number of bins, its size, shape, weight, and constraints if any along with standard container dimension. These inputs were stored in the database and encoded to string (chromosomes) format which were normally acceptable by AGA. Findings: The performance of the hybrid GA the Tuning algorithm is satisfactory and gives the feasible solution when compared with the other standard search algorithms. The minimum number of boxes left unloaded by using this algorithm will helps to validating the developed bin packing system. The developed Adaptive Genetic Algorithm was validated using the mathematical function. This research work is the good background of further development and analysis in this transportation domain of the following cases- Case 1: Homogenous boxes of same dimensions: all the boxes packed without gap. Case 2: Homogenous boxes of arbitrary dimensions: all the boxes packed with small gaps. Case 3: Homogenous/Heterogeneous boxes of arbitrary dimensions: all the boxes packed with gaps. Application/Improvements: The proposed adaptive genetic approach is very helpful in the logistic industries, especially for cargo packaging for export this is very helpful and can be easily implement any logistic industry.

Column generation for the variable cost and size bin packing problem with fragmentation

Bin Packing Problems with Item Fragmentation (BPPIF) are variants of classical Bin Packing in which items can be split at a price. We extend BPPIF models from the literature by allowing a set of heterogeneous bins, each potentially having a different cost and capacity. We introduce extended formulations and column generation algorithms to obtain good bounds with reasonable computing effort. We test our algorithms on instances from the literature. Our experiments prove our approach to be more effective than state-of-the-art general purpose solvers.

Vector bin packing with heterogeneous bins: application to the machine reassignment problem

In this paper, we introduce a generalization of the vector bin packing problem, where the bins have variable sizes. This generalization can be used to model virtual machine placement problems and in particular to build feasible solutions for the machine reassignment problem. We propose several families of greedy heuristics for this problem and show that they are flexible and can be adapted to handle additional constraints. We present structural properties of the machine reassignment problem, that allow us to decompose it into smaller subproblems and adapt our heuristics to them. We evaluate our heuristics on academic benchmarks of the vector bin packing problem, a randomly generated vector bin packing problem with heterogeneous bins benchmark as well as Google’s realistic instances of the machine reassignment problem.

English

This paper presents a parallel genetic algorithm for three dimensional bin packing with heterogeneous bins using Hadoop Map-Reduce framework. The most common three dimensional bin packing problem which packs given set of boxes into minimum number of equal sized bins is proven to be NP Hard. The variation of three dimensional bin packing problem that allows heterogeneous bin sizes and rotation of boxes is computationally more harder than common three dimensional bin packing problem. The proposed Map-Reduce implementation helps to run the genetic algorithm for three dimensional bin packing with heterogeneous bins on multiple machines parallely and computes the solution in relatively short time.

Balls into non-uniform bins

Balls-into-bins games for uniform bins are widely used to model randomised load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks. In this paper we consider scenarios in which non-uniform selection probabilities help to balance the load among the bins. While previous evaluations try to find strategies for identical bins, we investigate heterogeneous bins where the “capacities” of the bins might differ significantly. We look at the allocation of m balls into n bins of total capacity C where each ball has d random bin choices. For such heterogeneous environments we show that the maximum load remains bounded by lnln(n)/ln(d)+O(1)w.h.p. if the number of balls m equals the total capacity C. Further analytical and simulative results show better bounds and values for the maximum loads in special cases.

Efficient lower bounds and heuristics for the variable cost and size bin packing problem

We consider the variable cost and size bin packing problem, a generalization of the well-known bin packing problem, where a set of items must be packed into a set of heterogeneous bins characterized by possibly different volumes and fixed selection costs. The objective of the problem is to select bins to pack all items at minimum total bin-selection cost. The paper introduces lower bounds and heuristics for the problem, the latter integrating lower and upper bound techniques. Extensive numerical tests conducted on instances with up to 1000 items show the effectiveness of these methods in terms of computational effort and solution quality. We also provide a systematic numerical analysis of the impact on solution quality of the bin selection costs and the correlations between these and the bin volumes. The results show that these correlations matter and that solution methods that are un-biased toward particular correlation values perform better.

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.

The Three-Dimensional Bin Packing Problem and Its Practical Algorithm.

The three-dimensional bin packing problem (3DBPP) is orthogonally to pack a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. It is formulated as a mixed integer program (MIP) that can solve small-sized instances to optimum. For large scale of instances, a composite algorithm, aimed at solving the 3DBPP with several practical constraints, is proposed and evaluated by the lower bound and the test instances available on website. It should be noted that although the computational tests are conducted for the 3DBPP with identical bins, the proposed approach is designed for a general case with heterogeneous bins.