Bin Packing Heuristics Research Articles

Classification and evaluation of the algorithms for vector bin packing

Heuristics for Vector Bin Packing (VBP) play an important role in modern distributed computing systems and other applications aimed at optimizing the usage of multidimensional resources. In this paper we perform a systematic classification of heuristics for VBP, with the focus on construction heuristics. We bring together existing VBP algorithms and their tuning parameters, and propose new algorithms and new tuning parameters. For a less studied class of multi-bin algorithms, we explore their properties analytically, considering monotonic and anomalous behavior and approximation guarantees. For empirical evaluation, all algorithms are implemented as the Vectorpack library and assessed through extensive experiments. Our findings may serve as the basis for the development of more complex, hybrid algorithms, hyperheuristics and machine learning algorithms. The Vectorpack library can also be adjusted for addressing enhanced VBP problems with additional features, which arise in applications, especially those typical for modern distributed computing systems.

Container Allocation in Cloud Environment Using Multi-Agent Deep Reinforcement Learning

Nowadays, many computation tasks are carried out using cloud computing services and virtualization technology. The intensive resource requirements of virtual machines have led to the adoption of a lighter solution based on containers. Containers isolate packaged applications and their dependencies, and they can also operate as part of distributed applications. Containers can be distributed over a cluster of computers with available resources, such as the CPU, memory, and communication bandwidth. Any container distribution mechanism should consider resource availability and their impact on overall performance. This work suggests a new approach to assigning containers to servers in the cloud, while meeting computing and communication resource requirements and minimizing the overall task completion time. We introduce a multi-agent environment using a deep reinforcement learning-based decision mechanism. The high action space complexity is tackled by decentralizing the allocation decisions among multiple agents. Considering the interactions among the agents, we introduce a new cooperative mechanism for a state and reward design, resulting in efficient container assignments. The performances of both long short term memory (LSTM) and memory augmented-based agents are examined, for solving the challenging container assignment problem. Experimental results demonstrated an improvement of up to 28% in the execution runtime compared to existing bin-packing heuristics and the common Kubernetes industrial tool.

Optimizing the Migration of Virtual Machines in Cloud Data Centers

Dynamic resource allocation of cloud data centers is implemented with the use of virtual machine migration. Selected virtual machines (VM) should be migrated on appropriate destination servers. This is a critical step and should be performed according to several criteria. It is proposed to use the criteria of minimum resource wastage and service level agreement violation. The optimization problem of the VM placement according to two criteria is formulated, which is equivalent to the well-known main assignment problem in terms of the structure, necessary conditions, and the nature of variables. It is suggested to use the Hungarian method or to reduce the problem to a closed transport problem. This allows the exact solution to be obtained in real time. Simulation has shown that the proposed approach outperforms widely used bin-packing heuristics in both criteria.

Deep reinforcement learning for multi-objective placement of virtual machines in cloud datacenters

The ubiquitous diffusion of cloud computing requires suitable management policies to face the workload while guaranteeing quality constraints and mitigating costs. The typical trade-off is between the used power and the adherence to a service-level metric subscribed by customers. To this aim, a possible idea is to use an optimization-based placement mechanism to select the servers where to deploy virtual machines. Unfortunately, high packing factors could lead to performance and security issues, e.g., virtual machines can compete for hardware resources or collude to leak data. Therefore, we introduce a multi-objective approach to compute optimal placement strategies considering different goals, such as the impact of hardware outages, the power required by the datacenter, and the performance perceived by users. Placement strategies are found by using a deep reinforcement learning framework to select the best placement heuristic for each virtual machine composing the workload. Results indicate that our method outperforms bin packing heuristics widely used in the literature when considering either synthetic or real workloads.

Virtual Machine Placement Using JAYA Optimization Algorithm

ABSTRACTCloud computing has become more popular with the ability to run HPC applications on cloud infrastructures. Improving the energy efficiency of these data centers become important for all the cloud providers. We observe that bin-packing heuristics such as Best-Fit Decreasing for energy-aware virtual machine (VM) allocation could not provide the optimal solution to minimize the total energy consumption of the data center. In this work, we explore the virtual machines provisioning considering multi-dimensional resources and energy consumption of the data center. We propose to use JAYA algorithm for optimal placement and minimizing the energy consumption of the data center. Our simulation results show the proposed algorithm could reduce the total energy consumption up to 34% and SLA by 15% compared with the Particle Swarm Optimization and power-aware best-fit decreasing.

Minimizing the number of machines with limited workload capacity for scheduling jobs with interval constraints

• We consider a parallel machine scheduling problem. • The problem is motivated by the operation under emergency conditions of storage systems. • The relationship of the problem with other packing problems is considered. • Different heuristics and exact solution techniques are proposed. • The proposed method is able to solve large (250 jobs) instances within reduced running times. In this paper, we consider a parallel machine scheduling problem in which machines have a limited workload capacity and jobs have deadlines and release dates. The problem is motivated by the operation of energy storage management systems for microgrids under emergency conditions and generalizes some problems that have already been studied in the literature for their theoretical value. In this work, we propose heuristic and exact algorithms to solve the problem. The heuristics are adaptations of classical bin packing heuristics in which additional conditions on the feasibility of a solution are imposed, whereas the exact method is a branch-and-price approach. The results show that the branch-and-price approach is able to optimally solve random instances with up to 250 jobs within a time limit of one hour, while the heuristic procedures provide near optimal solution within reduced running times. Finally, we also provide additional complexity results for a special case of the problem.

Energy-aware VM placement algorithms for the OpenStack Neat consolidation framework

One of the main challenges in cloud computing is an enormous amount of energy consumed in data-centers. Several researches have been conducted on Virtual Machine(VM) consolidation to optimize energy consumption. Among the proposed VM consolidations, OpenStack Neat is notable for its practicality. OpenStack Neat is an open-source consolidation framework that can seamlessly integrate to OpenStack, one of the most common and widely used open-source cloud management tool. The framework has components for deciding when to migrate VMs and for selecting suitable hosts for the VMs (VM placement). The VM placement algorithm of OpenStack Neat is called Modified Best-Fit Decreasing (MBFD). MBFD is based on a heuristic that handles only minimizing the number of servers. The heuristic is not only less energy efficient but also increases Service Level Agreement (SLA) violation and consequently cause more VM migrations. To improve the energy efficiency, we propose VM placement algorithms based on both bin-packing heuristics and servers’ power efficiency. In addition, we introduce a new bin-packing heuristic called a Medium-Fit (MF) to reduce SLA violation. To evaluate performance of the proposed algorithms we have conducted experiments using CloudSim on three cloud data-center scenarios: homogeneous, heterogeneous and default. Workloads that run in the data-centers are generated from traces of PlanetLab and Bitbrains clouds. The results of the experiment show up-to 67% improvement in energy consumption and up-to 78% and 46% reduction in SLA violation and amount of VM migrations, respectively. Moreover, all improvements are statistically significant with significance level of 0.01.

Randomized Algorithms for Scheduling Multi-Resource Jobs in the Cloud

We consider the problem of scheduling jobs with multiple-resource requirements (CPU, memory, and disk) in a distributed server platform, motivated by data-parallel and cloud computing applications. Jobs arrive dynamically over time and require certain amount of multiple resources for the duration of their service. When a job arrives, it is queued and later served by one of the servers that has sufficient remaining resources to serve it. The scheduling of jobs is subject to two constraints: 1) packing constraints : multiple jobs can be served simultaneously by a single server if their cumulative resource requirement does not exceed the capacity of the server, and 2) non-preemption : to avoid costly preemptions, once a job is scheduled in a server, its service cannot be interrupted or migrated to another server. Prior scheduling algorithms rely on either bin packing heuristics which have low complexity but can have a poor throughput, or MaxWeight solutions that can achieve maximum throughput but repeatedly require to solve or approximate instances of a hard combinatorial problem (Knapsack) over time. In this paper, we propose a randomized scheduling algorithm for placing jobs in servers that can achieve maximum throughput with low complexity. The algorithm is naturally distributed and each queue and each server needs to perform only a constant number of operations per time unit. Extensive simulation results, using both synthetic and real traffic traces, are presented to evaluate the throughput and delay performance compared to prior algorithms.

Min-Sum Bin Packing

We study min-sum bin packing (MSBP). This is a bin packing problem, where the cost of an item is the index of the bin into which it is packed. The problem is equivalent to a batch scheduling problem we define, where the total completion time is to be minimized. The problem is NP-hard in the strong sense. We show that it is not harder than this by designing a polynomial time approximation scheme for it. We also show that several natural algorithms which are based on well-known bin packing heuristics (such as First Fit Decreasing) fail to achieve an asymptotic finite approximation ratio, whereas Next Fit Increasing has an absolute approximation ratio of at most 2, and an asymptotic approximation ratio of at most 1.6188. We design a new heuristic that applies Next Fit Increasing on the relatively small items and adds the larger items using First Fit Decreasing, and show that its asymptotic approximation ratio is at most 1.5604.

Semi-online task assignment policies for workload consolidation in cloud computing systems

Satisfying on-demand access to cloud computing infrastructures under quality-of-service constraints while minimising the wastage of resources is an important challenge in data centre resource management. In this paper we tackle this challenge in a semi-online workload management system allocating tasks with uncertain duration to physical servers. Our semi-online framework, based on a bin packing approach, allows us to gather information on incoming tasks during a short time window before deciding on their assignments. Our contributions are as follows: (i) we propose a formal framework capturing the semi-online consolidation problem; (ii) we propose a new dynamic and real-time allocation algorithm based on the incremental merging of bins; and (iii) an adaptation of standard bin packing heuristics with a local search algorithm for the semi-online context considered here. We provide a systematic study of the impact of varying time-period size and varying the degrees of uncertainty on the duration of incoming tasks. The policies are compared in terms of solution quality and solving time on a data-set extracted from a real-world cluster trace.Our results show that, around periods of high demand, our best policy saves up to 40% of the resources compared to the other polices, and is robust to uncertainty in the task durations. Finally, we show that small increases in the allowable time window allows a significant improvement, but that larger time windows do not necessarily improve resource usage for real world datasets.

NewBalance: Efficient Data Space Management and Algorithmic Optimization for Large‐Scale Storage Systems

Fragmentation usually occurs when data space of original storage nodes has to be reallocated to new added storage nodes during the scale-out evolution of the large-scale storage system. It greatly influences its performance and becomes a challenge to manage the whole space. We present an efficient space management framework, called NewBalance, to reduce fragmentation with the minimum data movement while keeping the storage system load balance. The space management framework has two phases including the collection phase and the allocation phase. For the collection phase, we propose a novel algorithm, called the greedy bi-direction collector, which collects enough space for the new storage nodes. For the allocation phase, we formally represent it as a variant of the bin packing problem and then utilize some bin packing heuristics including the first fitting and the best fitting to allocate collected intervals to new added storage nodes. The experimental results show that the amount of intervals can be reduced by 20%~55% and our algorithmic optimization improves the data lookup performance by at least 10% and the scale-out performance by 2X~3X.

Multi-Capacity Combinatorial Ordering GA in Application to Cloud resources allocation and efficient virtual machines consolidation

This paper describes a novel approach making use of genetic algorithms to find optimal solutions for multi-dimensional vector bin packing problems with the goal to improve cloud resource allocation and Virtual Machines (VMs) consolidation. Two algorithms, namely Combinatorial Ordering First-Fit Genetic Algorithm (COFFGA) and Combinatorial Ordering Next Fit Genetic Algorithm (CONFGA) have been developed for that and combined. The proposed hybrid algorithm targets to minimise the total number of running servers and resources wastage per server. The solutions obtained by the new algorithms are compared with latest solutions from literature. The results show that the proposed algorithm COFFGA outperforms other previous multi-dimension vector bin packing heuristics such as Permutation Pack (PP), First Fit (FF) and First Fit Decreasing (FFD) by 4%, 34%, and 39%, respectively. It also achieved better performance than the existing genetic algorithm for multi-capacity resources virtual machine consolidation (RGGA) in terms of performance and robustness. A thorough explanation for the improved performance of the newly proposed algorithm is given.

A Multi-Objective Fuzzy Ant Colony Optimization Algorithm for Virtual Machine Placement

In cloud computing, the most important challenge is to enforce proper utilization of physical resources. To accomplish the mentioned challenge, the cloud providers need to take care of optimal mapping of virtual machines to a set of physical machines. In this paper, the authors address the mapping problem as a multi-objective virtual machine placement problem (VMP) and propose to apply multi-objective fuzzy ant colony optimization (F-ACO) technique for optimal placing of virtual machines in the physical servers. VMP-F-ACO is a combination of fuzzy logic and ACO, where we use fuzzy transition probability rule to simulate the behaviour of the ants and the authors apply the same for virtual machine placement problem. The results of fuzzy ACO techniques are compared with five variants of classical ACO, three bin packing heuristics and two evolutionary algorithms. The results show that the fuzzy ACO techniques are better than the other optimization and heuristic techniques considered.

Algorithms for the bin packing problem with overlapping items

We study an extension of the bin packing problem, where packing together two or more items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as a finite set of symbols from a given alphabet. Unlike the items of Bin Packing, two such sets can share zero, one or more symbols. The problem was first introduced by Sindelar et al. (2011) under the name of VM Packing with the addition of hierarchical sharing constraints making it suitable for virtual machine colocation. Without these constraints, we prefer the more general name of Pagination. After formulating it as an integer linear program, we try to approximate its solutions with several families of algorithms: from straightforward adaptations of classical Bin Packing heuristics, to dedicated algorithms (greedy and non-greedy), to standard and grouping genetic algorithms. All of them are studied first theoretically, then experimentally on an extensive random test set. Based upon these data, we propose a predictive measure of the statistical difficulty of a given instance, and finally recommend which algorithm should be used in which case, depending on either time constraints or quality requirements.

More than bin packing: Dynamic resource allocation strategies in cloud data centers

Resource allocation strategies in virtualized data centers have received considerable attention recently as they can have substantial impact on the energy efficiency of a data center. This led to new decision and control strategies with significant managerial impact for IT service providers. We focus on dynamic environments where virtual machines need to be allocated and deallocated to servers over time. Simple bin packing heuristics have been analyzed and used to place virtual machines upon arrival. However, these placement heuristics can lead to suboptimal server utilization, because they cannot consider virtual machines, which arrive in the future. We ran extensive lab experiments and simulations with different controllers and different workloads to understand which control strategies achieve high levels of energy efficiency in different workload environments. We found that combinations of placement controllers and periodic reallocations achieve the highest energy efficiency subject to predefined service levels. While the type of placement heuristic had little impact on the average server demand, the type of virtual machine resource demand estimator used for the placement decisions had a significant impact on the overall energy efficiency.

Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints

The paper examines a new problem in the irregular packing literature that has many applications in industry: two-dimensional irregular (convex) bin packing with guillotine constraints. Due to the cutting process of certain materials, cuts are restricted to extend from one edge of the stock-sheet to another, called guillotine cutting. This constraint is common place in glass cutting and is an important constraint in two-dimensional cutting and packing problems. In the literature, various exact and approximate algorithms exist for finding the two dimensional cutting patterns that satisfy the guillotine cutting constraint. However, to the best of our knowledge, all of the algorithms are designed for solving rectangular cutting where cuts are orthogonal with the edges of the stock-sheet. In order to satisfy the guillotine cutting constraint using these approaches, when the pieces are non-rectangular, practitioners implement a two stage approach. First, pieces are enclosed within rectangle shapes and then the rectangles are packed. Clearly, imposing this condition is likely to lead to additional waste. This paper aims to generate guillotine-cutting layouts of irregular shapes using a number of strategies. The investigation compares three two-stage approaches: one approximates pieces by rectangles, the other two approximate pairs of pieces by rectangles using a cluster heuristic or phi-functions for optimal clustering. All three approaches use a competitive algorithm for rectangle bin packing with guillotine constraints. Further, we design and implement a one-stage approach using an adaptive forest search algorithm. Experimental results show the one-stage strategy produces good solutions in less time over the two-stage approach.

Adaptive selection of heuristics for assigning time slots and rooms in exam timetables

This paper presents an iterative adaptive approach which hybridises bin packing heuristics to assign exams to time slots and rooms. The approach combines a graph-colouring heuristic, to select an exam in every iteration, with bin-packing heuristics to automate the process of time slot and room allocation for exam timetabling problems. We start by analysing the quality of the solutions obtained by using one heuristic at a time. Depending on the individual performance of each heuristic, a random iterative hyper-heuristic is used to randomly hybridise the heuristics and produce a collection of heuristic sequences to construct solutions with different quality. Based on these sequences, we analyse the way in which the bin packing heuristics are automatically hybridised. It is observed that the performance of the heuristics used varies depending on the problem. Based on these observations, an iterative hybrid approach is developed to adaptively choose and hybridise the heuristics during solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme which is concerned with developing methods to design and adapt heuristics automatically. The approach is tested on the exam timetabling track of the second International Timetabling Competition, to evaluate its ability to generalise on instances with different features. The hyper-heuristic with low-level graph-colouring and bin-packing heuristics approach was found to generalise well over all the problem instances and performed comparably to the state of the art approaches.

An efficient strategy for storing and searching binary trees in WORM external memory

Consider the problem of searching and storing a massive binary tree in WORM (Write Once Read Many) secondary memory. Tree nodes are organized in pages, each of which contains a fixed number of nodes. Pages are transferred to primary memory as the tree is traversed. This work presents a new strategy for paging that aims to decrease the amount of unused space in each page as well as to reduce the total number of pages required to store the tree while also reduce the number of pages accessed for searching. The algorithm employs an efficient strategy based on bin packing for allocating unbalanced trees. Experimental results are reported comparing the performance of two bin-packing heuristics, as well as other paging strategies and B-trees. Results confirm the superior performance of the proposed approach both in terms of the number of page transfers required for searching and the page filling percentage.

Practical performance models of algorithms in evolutionary program induction and other domains

Evolutionary computation techniques have seen a considerable popularity as problem solving and optimisation tools in recent years. Theoreticians have developed a variety of both exact and approximate models for evolutionary program induction algorithms. However, these models are often criticised for being only applicable to simplistic problems or algorithms with unrealistic parameters. In this paper, we start rectifying this situation in relation to what matters the most to practitioners and users of program induction systems: performance. That is, we introduce a simple and practical model for the performance of program-induction algorithms. To test our approach, we consider two important classes of problems — symbolic regression and Boolean function induction — and we model different versions of genetic programming, gene expression programming and stochastic iterated hill climbing in program space. We illustrate the generality of our technique by also accurately modelling the performance of a training algorithm for artificial neural networks and two heuristics for the off-line bin packing problem.We show that our models, besides performing accurate predictions, can help in the analysis and comparison of different algorithms and/or algorithms with different parameters setting. We illustrate this via the automatic construction of a taxonomy for the stochastic program-induction algorithms considered in this study. The taxonomy reveals important features of these algorithms from the performance point of view, which are not detected by ordinary experimentation.

Extreme Point-Based Heuristics for Three-Dimensional Bin Packing

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the problem.