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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The purpose of this paper is to propose Extensible Markup Language (XML) data partitioning schemes that can cope with static and dynamic allocation for parallel holistic twig joins: grid metadata model for XML (GMX) and streams‐based partitioning method for XML (SPX).

GMX exploits the relationships between XML documents and query patterns to perform workload‐aware partitioning of XML data. Specifically, the paper constructs a two‐dimensional model with a document dimension and a query dimension in which each object in a dimension is composed from XML metadata related to the dimension. GMX provides a set of XML data partitioning methods that include document clustering, query clustering, document‐based refinement, query‐based refinement, and query‐path refinement, thereby enabling XML data partitioning based on the static information of XML metadata. In contrast, SPX explores the structural relationships of query elements and a range‐containment property of XML streams to generate partitions and allocate them to cluster nodes on‐the‐fly.

GMX provides several salient features: a set of partition granularities that balance workloads of query processing costs among cluster nodes statically; inter‐query parallelism as well as intra‐query parallelism at multiple extents; and better parallel query performance when all estimated queries are executed simultaneously to meet their probability of query occurrences in the system. SPX also offers the following features: minimal computation time to generate partitions; balancing skewed workloads dynamically on the system; producing higher intra‐query parallelism; and gaining better parallel query performance.

The current status of the proposed XML data partitioning schemes does not take into account XML data updates, e.g. new XML documents and query pattern changes submitted by users on the system.

Note that effectiveness of the XML data partitioning schemes mainly relies on the accuracy of the cost model to estimate query processing costs. The cost model must be adjusted to reflect characteristics of a system platform used in the implementation.

This paper proposes novel schemes of conducting XML data partitioning to achieve both static and dynamic workload balance.

Sharding of blockchains consists of partitioning a blockchain network into several sub-networks called “shards,” each shard processing and storing disjoint sets of transactions in parallel. Sharding has recently been applied to public blockchains to improve scalability through parallelism. The throughput of sharded blockchain is optimized when the workload among the shards is approximately the same. The purpose of this paper is to investigate the problem of balancing workload of account-based blockchains such as Ethereum.

Two known consensus-based distributed load-balancing algorithms have been adapted to sharded blockchains. These algorithms migrate accounts across shards to balance transaction processing times. Two methods to predict transaction processing times are proposed.

The authors identify some challenging aspects for solving the load-balancing problem in sharded blockchains. Experiments conducted with Ethereum transactions show that the two load-balancing algorithms are challenged by accounts often created to process a single transaction to optimize anonymity, while existing accounts sparsely generate transactions.

Tests in this work have been conducted on transactions originating from a blockchain platform rather than using artificially generated data distributions. They show the specificity of the load-balancing problem for sharded blockchains, which were hidden in artificial data sets.

Load balancing is an important issue for a heterogeneous distributed computing system environment that has been proven to be a nondeterministic polynomial time hard problem. This paper aims to propose a resource-aware load balancing (REAL) model for a batch of independent tasks with a centralized load balancer to make the solution appropriate for a practical heterogeneous distributed environment having a migration cost with the objective of maximizing the level of load balancing considering bandwidth requirements for migration of the tasks.

To achieve the effective schedule, load balancing issues should be addressed and tackled through efficient workload distribution. In this approach, the migration has been carried out in two phases, namely, initial migration and best-fit migration. Using the best-fit policy in migrations helps in the possible performance improvement by minimizing the remaining idle slots on underloaded nodes that remain unentertained during the initial migration.

The experimental results reveal that the proposed model exhibits a superior performance among the other strategies on considered parameters such as makespan, average utilization and level of load balancing under study for a heterogeneous distributed environment.

Design of the REAL model and a comparative performance evaluation with LBSM and ITSLB have been conducted by using MATLAB 8.5.0.

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

Cloud computing gives several on-demand infrastructural services by dynamically pooling heterogeneous resources to cater to users’ applications. The task scheduling needs to be done optimally to achieve proficient results in a cloud computing environment. While satisfying the user’s requirements in a cloud environment, scheduling has been proven an NP-hard problem. Therefore, it leaves scope to develop new allocation models for the problem. The aim of the study is to develop load balancing method to maximize the resource utilization in cloud environment.

In this paper, the parallelized task allocation with load balancing (PTAL) hybrid heuristic is proposed for jobs coming from various users. These jobs are allocated on the resources one by one in a parallelized manner as they arrive in the cloud system. The novel algorithm works in three phases: parallelization, task allocation and task reallocation. The proposed model is designed for efficient task allocation, reallocation of resources and adequate load balancing to achieve better quality of service (QoS) results.

The acquired empirical results show that PTAL performs better than other scheduling strategies under various cases for different QoS parameters under study.

The outcome has been examined for the real data set to evaluate it with different state-of-the-art heuristics having comparable objective parameters.

The advancements in the cloud computing has gained the attention of several researchers to provide on-demand network access to users with shared resources. Cloud computing is important a research direction that can provide platforms and softwares to clients using internet. However, handling huge number of tasks in cloud infrastructure is a complicated task. Thus, it needs a load balancing (LB) method for allocating tasks to virtual machines (VMs) without influencing system performance. This paper aims to develop a technique for LB in cloud using optimization algorithms.

This paper proposes a hybrid optimization technique, named elephant herding-based grey wolf optimizer (EHGWO), in the cloud computing model for LB by determining the optimal VMs for executing the reallocated tasks. The proposed EHGWO is derived by incorporating elephant herding optimization (EHO) in grey wolf optimizer (GWO) such that the tasks are allocated to the VM by eliminating the tasks from overloaded VM by maintaining the system performance. Here, the load of physical machine (PM), capacity and load of VM is computed for deciding whether the LB has to be done or not. Moreover, two pick factors, namely, task pick factor (TPF) and VM pick factor (VPF), are considered for choosing the tasks for reallocating them from overloaded VM to underloaded VM. The proposed EHGWO decides the task to be allocated in the VM based on the newly derived fitness functions.

The minimum load and makespan obtained in the existing methods, constraint measure based LB (CMLB), fractional dragonfly based LB algorithm (FDLA), EHO, GWO and proposed EHGWO for the maximum number of VMs is illustrated. The proposed EHGWO attained minimum makespan with value 814,264 ns and minimum load with value 0.0221, respectively. Meanwhile, the makespan values attained by existing CMLB, FDLA, EHO, GWO, are 318,6896 ns, 230,9140 ns, 1,804,851 ns and 1,073,863 ns, respectively. The minimum load values computed by existing methods, CMLB, FDLA, EHO, GWO, are 0.0587, 0.026, 0.0248 and 0.0234. On the other hand, the proposed EHGWO with minimum load value is 0.0221. Hence, the proposed EHGWO attains maximum performance as compared to the existing technique.

This paper illustrates the proposed LB algorithm using EHGWO in a cloud computing model using two pitch factors, named TPF and VPF. For initiating LB, the tasks assigned to the overloaded VM are reallocated to under loaded VMs. Here, the proposed LB algorithm adapts capacity and loads for the reallocation. Based on TPF and VPF, the tasks are reallocated from VMs using the proposed EHGWO. The proposed EHGWO is developed by integrating EHO and GWO algorithm using a new fitness function formulated by load of VM, migration cost, load of VM, capacity of VM and makespan. The proposed EHGWO is analyzed based on load and makespan.

Cloud computing (CC) refers to the usage of virtualization technology to share computing resources through the internet. Task scheduling (TS) is used to assign computational resources to requests that have a high volume of pending processing. CC relies on load balancing to ensure that resources like servers and virtual machines (VMs) running on real servers share the same amount of load. VMs are an important part of virtualization, where physical servers are transformed into VM and act as physical servers during the process. It is possible that a user’s request or data transmission in a cloud data centre may be the reason for the VM to be under or overloaded with data.

VMs are an important part of virtualization, where physical servers are transformed into VM and act as physical servers during the process. It is possible that a user’s request or data transmission in a cloud data centre may be the reason for the VM to be under or overloaded with data. With a large number of VM or jobs, this method has a long makespan and is very difficult. A new idea to cloud loads without decreasing implementation time or resource consumption is therefore encouraged. Equilibrium optimization is used to cluster the VM into underloaded and overloaded VMs initially in this research. Underloading VMs is used to improve load balance and resource utilization in the second stage. The hybrid algorithm of BAT and the artificial bee colony (ABC) helps with TS using a multi-objective-based system. The VM manager performs VM migration decisions to provide load balance among physical machines (PMs). When a PM is overburdened and another PM is underburdened, the decision to migrate VMs is made based on the appropriate conditions. Balanced load and reduced energy usage in PMs are achieved in the former case. Manta ray foraging (MRF) is used to migrate VMs, and its decisions are based on a variety of factors.

The proposed approach provides the best possible scheduling for both VMs and PMs. To complete the task, improved whale optimization algorithm for Cloud TS has 42 s of completion time, enhanced multi-verse optimizer has 48 s, hybrid electro search with a genetic algorithm has 50 s, adaptive benefit factor-based symbiotic organisms search has 38 s and, finally, the proposed model has 30 s, which shows better performance of the proposed model.

User’s request or data transmission in a cloud data centre may cause the VMs to be under or overloaded with data. To identify the load on VM, initially EQ algorithm is used for clustering process. To figure out how well the proposed method works when the system is very busy by implementing hybrid algorithm called BAT–ABC. After the TS process, VM migration is occurred at the final stage, where optimal VM is identified by using MRF algorithm. The experimental analysis is carried out by using various metrics such as execution time, transmission time, makespan for various iterations, resource utilization and load fairness. With its system load, the metric gives load fairness. How load fairness is worked out depends on how long each task takes to do. It has been added that a cloud system may be able to achieve more load fairness if tasks take less time to finish.

This paper aims to develop the Dragonfly-based exponential gravitational search algorithm to VMM strategy for effective load balancing in cloud computing. Due to widespread growth of cloud users, load balancing is the essential criterion to deal with the overload and underload problems of the physical servers. DEGSA-VMM is introduced, which calculates the optimized position to perform the virtual machine migration (VMM).

This paper presents an algorithm Dragonfly-based exponential gravitational search algorithm (DEGSA) that is based on the VMM strategy to migrate the virtual machines of the overloaded physical machine to the other physical machine keeping in mind the energy, migration cost, load and quality of service (QoS) constraints. For effective migration, a fitness function is provided, which selects the best fit that possess minimum energy, cost, load and maximum QoS contributing toward the maximum energy utilization.

For the performance analysis, the experimentation is performed with three setups, with Setup 1 composed of three physical machines with 12 virtual machines, Setup 2 composed of five physical machines and 19 virtual machines and Setup 3 composed of ten physical machines and 28 virtual machines. The performance parameters, namely, QoS, migration cost, load and energy, of the proposed work are compared over the other existing works. The proposed algorithm obtained maximum resource utilization with a good QoS at a rate of 0.19, and minimal migration cost at a rate of 0.015, and minimal energy at a rate of 0.26 with a minimal load at a rate of 0.1551, whereas with the existing methods like ant colony optimization (ACO), gravitational search algorithm (GSA) and exponential gravitational search algorithm, the values of QoS, load, migration cost and energy are 0.16, 0.1863, 0.023 and 0.29; 0.16, 0.1863, 0.023 and 0.28 and 0.18, 0.1657, 0.016 and 0.27, respectively.

This paper presents an algorithm named DEGSA based on VMM strategy to determine the optimum position to perform the VMM to achieve a better load balancing.

The n‐dimensional direct search algorithm, DIRECT, developed by Jones, Perttunen, and Stuckman has attracted recent attention from the multidisciplinary design optimization community. Since DIRECT only requires function values (or ranking) and balances global exploration with local refinement better than n‐dimensional bisection, it is well suited to the noisy function values typical of realistic simulations. While not efficient for high accuracy optimization, DIRECT is appropriate for the sort of global design space exploration done in large scale engineering design. Direct and pattern search schemes have the potential to exploit massive parallelism, but efficient use of massively parallel machines is non‐trivial to achieve. A fully‐distributed control version of DIRECT that is designed for massively parallel (distributed memory) architectures is presented. Parallel results are presented for a multidisciplinary design optimization problem – configuration design of a high speed civil transport.