Efficient Heuristic Algorithm Research Articles

Router Activation Heuristics for Energy-Saving ECMP and Valiant Routing in Data Center Networks

This paper addresses the energy conservation problem in computing systems. The focus is on energy-efficient routing protocols. We formulated and solved a network-wide optimization problem for calculating energy-aware routing for the recommended network configuration. Considering the complexity of the mathematical models of data center networks and the limitations of calculating routing by solving large-scale optimization problems, and methods described in the literature, we propose an alternative solution. We designed and developed several efficient heuristics for equal-cost multipath (ECMP) and Valiant routing that reduce the energy consumption in the computer network interconnecting computing servers. Implementing these heuristics enables the selection of routing paths and relay nodes based on current and predicted internal network load. The utility and efficiency of our methods were verified by simulation. The test cases were carried out on several synthetic network topologies, giving encouraging results. Similar results of using our efficient heuristic algorithm and solving the optimization task confirmed the usability and effectiveness of our solution. Thus, we produced well-justified recommendations for energy-aware computing system design to conclude the paper.

A Three-Stage model for Clustering, Storage, and joint online order batching and picker routing Problems: Heuristic algorithms

The online shopping center is an electronic commerce where customer orders arrive over time. The joint online order batching and picker routing is essential for managing online shopping, as it allows for the retrieval of products from storage locations as order arrival timings become known. Meanwhile, the picker routing performance is substantially affected by the product allocation to storage locations, whereas the success of the storage assignment depends on the product grouping. In order to handle such a system, this study offers a novel three-stage model, the first stage of which aims to classify products according to various available capacity levels to maximize similarity measures among products. The second stage determines the assignments of the obtained classes to carriers and storage locations in a multi-block 3D warehouse to minimize the total transportation costs and the energy costs of carriers. The third stage provides a joint online order batching and picker routing model in a picker-to-parts system to minimize completion time in the 3D warehouse. Since learning effects affect the search and pick times, and pickers’ horizontal and vertical velocities are dissimilar, these crucial factors are considered for calculating travel time of pickers. In addition, two efficient heuristic algorithms are proposed to solve the developed models in the first two stages, and an effective online 2-competitive heuristic algorithm is developed to solve the proposed model in the third stage. Moreover, a broad range of numerical experiments illustrates the validity and applicability of the proposed models and solution approaches. What is more, a competitive analysis evaluates the effectiveness of the proposed online heuristic algorithm. The results reveal that the developed hierarchical framework can provide high-quality solutions in a reasonable time and reduce the total cost and makespan by 35.65% and 12.48% on average, respectively.

Maximizing Heterogeneous Server Utilization with Limited Availability Times for Divisible Loads Scheduling on Networked Systems

Most of the available divisible-load scheduling models assume that all servers in networked systems are idle before workloads arrive and that they can remain available online during workload computation. In fact, this assumption is not always valid. Different servers on networked systems may have heterogenous available times. If we ignore the availability constraints when dividing and distributing workloads among servers, some servers may not be able to start processing their assigned load fractions or deliver them on time. In view of this, we propose a new multi-installment scheduling model based on server availability time constraints. To solve this problem, we design an efficient heuristic algorithm consisting of a repair strategy and a local search strategy, by which an optimal load partitioning scheme is derived. The repair strategy guarantees time constraints, while the local search strategy achieves optimality. We evaluate the performance via rigorous simulation experiments and our results show that the proposed algorithm is suitable for solving large-scale scheduling problems employing heterogeneous servers with arbitrary available times. The proposed algorithm is shown to be superior to the existing algorithm in terms of achieving a shorter makespan of workloads.

Bounded Wang tilings with integer programming and graph-based heuristics

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling problem and offer four integer programming formulations to construct valid or nearly-valid Wang tilings: a decision, maximum-rectangular tiling, maximum cover, and maximum adjacency constraint satisfaction formulations. To facilitate a finer control over the resulting tilings, we extend these programs with tile-based, color-based, packing, and variable-sized periodic constraints. Furthermore, we introduce an efficient heuristic algorithm for the maximum-cover variant based on the shortest path search in directed acyclic graphs and derive simple modifications to provide a 1/2 approximation guarantee for arbitrary tile sets, and a 2/3 guarantee for tile sets with cyclic transducers. Finally, we benchmark the performance of the integer programming formulations and of the heuristic algorithms showing that the heuristics provide very competitive outputs in a fraction of time. As a by-product, we reveal errors in two well-known aperiodic tile sets: the Knuth tile set contains a tile unusable in two-way infinite tilings, and the Lagae corner tile set is not aperiodic.

Crossover Rate Sorting in Adaptive Differential Evolution

Differential evolution (DE) is a popular and efficient heuristic numerical optimization algorithm that has found many applications in various fields. One of the main disadvantages of DE is its sensitivity to parameter values. In this study, we investigate the effect of the previously proposed crossover rate sorting mechanism on modern versions of DE. The sorting of the crossover rates, generated by a parameter adaptation mechanism prior to applying them in the crossover operation, enables the algorithm to make smaller changes to better individuals, and larger changes to worse ones, resulting in better exploration and exploitation. The experiments in this study were performed on several modern algorithms, namely L-SHADE-RSP, NL-SHADE-RSP, NL-SHADE-LBC and L-NTADE and two benchmark suites of test problems, CEC 2017 and CEC 2022. It is shown that crossover rate sorting does not result in significant additional computational efforts, but may improve results in certain scenarios, especially for high-dimensional problems.

Service Home Identification of Multiple-Source IoT Applications in Edge Computing

The real-time communication requirement of the Internet of Things (IoT) applications promotes the convergence of IoT and Mobile Edge Computing (MEC). The MEC paradigm greatly shortens the IoT service delay by leveraging cloudlets (edge servers) of MEC in the proximity of IoT devices. Considering limited computing and storage resources in an MEC network, it is challenging to provide efficient IoT-enabled service provisioning in such a network. In this article, we study the service home identification problem of service provisioning for multi-source IoT applications in an MEC network, by identifying a service home (cloudlet) of each multi-source IoT application for its data processing, querying and storage. Each multi-source IoT application consists of multiple sources located at different geographical locations and each source uploads its data stream via a gateway (its nearby access point) to the MEC network and the uploaded data then is aggregated with the stream data of the other sources of the IoT application at the service home. We here focus on two novel service home identification problems: the service operational cost minimization problem with the aim to minimize the total service operational cost by admitting as many multi-source IoT applications as possible, and the online throughput maximization problem with the aim to maximize the number of multi-source IoT application requests admitted. We first show that both the problems are NP-hard. We then formulate an Integer Linear Programming (ILP) solution to the service operational cost minimization problem, and propose a randomized algorithm with high probability and a deterministic approximation algorithm respectively, at moderate resource capacity violations. We third develop an efficient heuristic algorithm for the problem without any resource violation. Furthermore, we deal with the online throughput maximization problem under an assumption that multi-source IoT application requests arrive one by one without the knowledge of future arrivals, for which we formulate an Integer Linear Programming (ILP) solution to its offline version, followed by devising an online algorithm with competitive ratio. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are promising, and outperform their comparison counterparts.

Coordinating Multiple Light-Trails in Multicast Elastic Optical Networks With Adaptive Modulation

Optical multicasting has been considered resource efficient for multicast services. Light-tree and light-trail are two technologies that support optical multicasting while the former requires many splitters and thus experiences significant power loss. In this paper, we consider using the light-trail technology for the accommodation of multicast requests in elastic optical networks with adaptive modulation. For better spectrum efficiency, we consider accommodating each multicast by multiple light-trails. We formulate the problem by Mixed Integer Linear Programming (MILP) and propose efficient heuristic algorithms. For the impact of accommodation sequence on the algorithm performance, apart from the traditional sequence among different requests, we consider an additional sequence among the destinations of a multicast. For efficient multicast accommodation, we propose several strategies and compare their performances through a range of cases. To avoid a destination occupying excessive resources in certain cases of joining multiple light-trails, we propose an efficient algorithm to delete some duplicated destinations. Numerical results show that the proposed heuristic algorithms significantly outperform a benchmark algorithm and one performs close to the optimal MILP. Also, the algorithm for deleting certain destination replicas largely reduces the spectrum and transmitter usages, up to 41% and 20% for the cases considered, respectively.

A New Algorithm for Real-Time Scheduling and Resource Mapping for Robot Operating Systems (ROS)

A new version of a robot operating system (ROS-2) has been developed to address the real-time and fault constraints of distributed robotics applications. However, current implementations lack strong real-time scheduling and the optimization of response time for various tasks and applications. This may lead to inconsistent system behavior and may affect system performance. This article presents a new and efficient heuristic scheduling algorithm for the ROS-2 framework to improve resource mapping and system scheduling for robotics applications. The proposed scheduling design includes grouping callbacks into executors, assigning executor priority, and sequencing callbacks inside executors. The timing constraints and functional properties are expressed in the formal design model, and real-time scheduling is performed with respect to the timing constraints. The benefits of the proposed solution are demonstrated by a set of experimental results. Using this algorithm, it is shown that the number of executors needed to schedule a set of callbacks is minimized and the system schedulability is maximized for loaded and overloaded cases.

Joint Task Offloading, Resource Sharing and Computation Incentive for Edge Computing Networks

Edge computing is a promising technology to enable edge servers (ESs) to share computing resources for task offloading. Due to the selfish characteristic of the ESs, how to design an efficient computation incentive mechanism with the appropriate task offloading and resource allocation strategies is an essential issue. In this letter, a contract-based framework is proposed to deal with the joint task offloading, resource sharing and computation incentive (TORSCI) issue under the asymmetric information scenario. A three-dimensional task-resource-reward contract is investigated to motivate the potential ESs to participate in resource sharing. Then, based on the individual rationality and incentive compatibility conditions, the joint TORSCI optimization problem is formulated to achieve the maximum utility of the cloud server. By deriving necessary and sufficient conditions, an optimal contract is designed to obtain the joint task offloading, resource sharing and computation incentive strategy with an efficient heuristic algorithm. Simulation results demonstrate the efficiency of our proposed contract-based incentive approach.

An Efficient Heuristic Algorithm for Flow Shop Scheduling Problem with Periodic Machine Specific Halting and Preventive Maintenance Operations

An Efficient Heuristic Algorithm for Flow Shop Scheduling Problem with Periodic Machine Specific Halting and Preventive Maintenance Operations

An efficient heuristic algorithm for solving a multi-vessel quay crane scheduling problem in container terminals

As an important node of a multimodal container transport hub, the container terminal occupies a critical position in the whole process of container transportation and the global supply chain network. With the increasing size of container vessels, improving the handling efficiency of multiple vessels at berth in a given port becomes a complex problem to solve. We formulate a mixed-integer linear programming model to minimise the vessel services time, the total completion and travel times of quay cranes (QCs) among multiple vessels. To solve the proposed model, we develop a particle swarm optimisation (PSO) algorithm incorporated with a tailored initial-solution generation algorithm. Furthermore, a couple of acceleration strategies are designed to improve the solution quality and shorten computation time. The results of numerical experiments on real-life instances validate the proposed model and the efficiency of the proposed algorithm.

An Influence Maximization Algorithm Based on Improved K-Shell in Temporal Social Networks

Influence maximization of temporal social networks (IMT) is a problem that aims to find the most influential set of nodes in the temporal network so that their information can be the most widely spread. To solve the IMT problem, we propose an influence maximization algorithm based on an improved K-shell method, namely improved K-shell in temporal social networks (KT). The algorithm takes into account the global and local structures of temporal social networks. First, to obtain the kernel value <i>Ks</i> of each node, in the global scope, it layers the network according to the temporal characteristic of nodes by improving the K-shell method. Then, in the local scope, the calculation method of comprehensive degree is proposed to weigh the influence of nodes. Finally, the node with the highest comprehensive degree in each core layer is selected as the seed. However, the seed selection strategy of KT can easily lose some influential nodes. Thus, by optimizing the seed selection strategy, this paper proposes an efficient heuristic algorithm called improved K-shell in temporal social networks for influence maximization (KTIM). According to the hierarchical distribution of cores, the algorithm adds nodes near the central core to the candidate seed set. It then searches for seeds in the candidate seed set according to the comprehensive degree. Experiments show that KTIM is close to the best performing improved method for influence maximization of temporal graph (IMIT) algorithm in terms of effectiveness, but runs at least an order of magnitude faster than it. Therefore, considering the effectiveness and efficiency simultaneously in temporal social networks, the KTIM algorithm works better than other baseline algorithms.

In-network Placement of Reusable Computing Tasks in an SDN-based Network Edge

Edge computing is aimed to support compute-intensive data-hungry interactive applications which can hardly run on resource-constrained consumer devices and may suffer from running in the cloud due to the long data transfer delay. The edge network nodes' heterogeneous and limited (compared to the cloud) capabilities make the computing task placement a challenge. In this paper, we propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-network</i> task placement strategy aimed at minimizing the edge network resources usage. The proposal specifically accounts for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-limited reusable</i> computing tasks, i.e., tasks whose output can be cached to serve requests from different consumers for a certain time. Caching such results, during their time validity, achieves the twofold benefit of reducing the service provisioning time and improving the edge resource utilization, by avoiding redundant computations and data exchange. The devised strategy is implemented as a network application of a Software-defined Networking Controller in charge of overseeing the edge domain. We formulate the optimal task placement through an integer linear programming problem, and we define an efficient heuristic algorithm that well approximates the solution achieved through a standard optimal solver. Achieved results show that the proposal successfully meets the targeted objectives in a wide variety of simulated scenarios, by outperforming benchmark solutions.

An efficient heuristic algorithm for solving a multi-vessel quay crane scheduling problem in container terminals

An efficient heuristic algorithm for solving a multi-vessel quay crane scheduling problem in container terminals

SFC Design and VNF Placement Based on Traffic Volume Scaling and VNF Dependency in 5G Networks

The development of Fifth-Generation (5G) mobile communication technology has remarkably promoted the spread of the Internet of Things (IoT) applications. As a promising paradigm for IoT, edge computing can process the amount of data generated by mobile intelligent devices in less time response. Network Function Virtualization (NFV) that decouples network functions from dedicated hardware is an important architecture to implement edge computing, deploying heterogeneous Virtual Network Functions (VNF) (such as computer vision, natural language processing, intelligent control, etc.) on the edge service nodes. With the NFV MANO (Management and Orchestration) framework, a Service Function Chain (SFC) that contains a set of ordered VNFs can be constructed and placed in the network to offer a customized network service. However, the procedure of NFV orchestration faces a technical challenge in minimizing the network cost of VNF placement due to the complexity of the changing effect of traffic volume and the dependency on the VNF relationship. To this end, we jointly optimize SFC design and VNF placement to minimize resource cost while taking account of VNF dependency and traffic volume scaling. First, the problem is formulated as an Integer Linear Programming (ILP) model and proved NP-hard by reduction from Hamiltonian Cycle problem. Then we proposed an efficient heuristic algorithm called Traffic Aware and Interdependent VNF Placement (TAIVP) to solve the problem. Compared with the benchmark algorithms, emulation results show that our algorithm can reduce network cost by 10.2% and increase service request acceptance rate by 7.6% on average.

Off-site protection against service function forwarder failures in NFV

Many internet applications in the emerging 5G/6G networks require ultra-reliable and low-latency communications (URLLC) services. To deliver URLLC services flexibly and efficiently, network function virtualization (NFV) is employed to enable network slicing. NFV deploys service function chains (SFCs) consisting of service functions (SFs) and service function forwarders (SFFs) to deliver services. It is possible for SFFs in an SFC to fail when forwarding traffic to specified SF instances. Protecting SFF failures in NFV is challenging since multiple SF instances may fail simultaneously as a result of a single SFF failure. This work investigates how to protect the SF instances against the SFF failures while minimizing the cost of backup computing resources. We formulate a new problem called SFF-driven multi-instance failures and protection (SMFP), and prove its NP-hardness. We propose an efficient heuristic algorithm, namely, SFF-centralized resource optimization (FCRO), which is based on the proposed techniques of backup auxiliary transferring, backup cost-effectiveness selection, and adaptive fit backup. Our experimental results demonstrate that the proposed FCRO is effective and significantly outperforms the schemes directly extended from the existing work.

Optimal decisions in stochastic graphs with uncorrelated and correlated edge weights

Stochastic graph models and algorithms for the computation of different stochastic shortest path problems (SSPPs) continue to play an important role in various fields of computer science and operations research, with recent applications ranging from vehicle routing to social networks and decision problems in finance. In this paper, we first introduce stochastic graph models where weights to pass an edge in a graph are, possibly correlated, random variables. Depending on the application context and the interpretation of uncertain edge weights, random variables either model the time to pass an edge or describe a reward one gains by traversing an edge. For modeling the random variables discrete phase type distributions are used. Several algorithms for the computation of optimal policies which depend on the current weight upon arriving at a vertex while still exploiting weight dependencies among edges are developed. It will be shown that with correlated edge weights the stochastic shortest path problems become PSPACE-complete and the solution of instances with a bounded number of phases is NP-hard such that for an exact computation of the shortest path, algorithms from partially observable Markov decision processes (POMDPs) or mixed integer linear programming (MILP) have to be applied. Alternatively, an efficient heuristic algorithm can be used which often yields good or even optimal results with a small effort.

Location Selection of Metro-Based Distribution Nodes for Underground Logistics System with Bi-Level Programming Model

The main purpose of the study was to apply symmetry principles to general mathematical modeling based on a bi-level programming model in order to select the optimal nodes of the underground metro-based logistics system (M-ULS). The first step was to select the metro stations as alternative logistics distribution nodes based on the existing metro network. Secondly, given the requirements of suppliers and demanders, a bi-level programming model was built based on symmetry principles to minimize the total cost of logistics distribution nodes, including construction cost, transport cost, and fixed cost. The third objective was to use an efficient heuristic algorithm to solve the model to obtain the optimal location of the nodes of the logistics distribution. Lastly, Nanjing’s Metro Line 2 was used as an example to validate the efficacy of the proposed model. The results of the case indicate that it is possible to deliver goods from logistics distribution nodes to demanders using the excess capacity of the metro, and the proposed bi-level programming model for M-ULS can be used to select suitable metro stations as distribution nodes and achieve the lowest cost on both the supply and demand sides of logistics while still ensuring the green and efficient transport of logistics services. References and suggestions for planning and selecting the location of logistics distribution nodes based on the metro network in the future can be found in this article.

A Cross-Layer Optimization Framework for Index-Coded NOMA in Cache-Aided F-RANs

This paper studies cached-aided multicast transmissions in fronthaul fog radio access networks (F-RANs). While index coding and cached-aided non-orthogonal multiple access (NOMA) are techniques commonly used for utilizing cache contents to save transmit energy, there is a lack of general framework to integrate them. This work proposes index-coded NOMA and dynamic coded-NOMA to investigate energy performance of the integration of index coding and NOMA under whole-file and subfile caching, respectively. Besides, dynamic cache space allocation is applied to both caching schemes, which allocates cache sizes to the fog access points (F-APs) according to their large-scale channel conditions. For index-coded NOMA, the general grouping problem is proved to be NP-hard and optimal solutions for some special cases are given. Furthermore, efficient heuristic grouping algorithms are proposed. For dynamic coded-NOMA, we obtain the closed-form minimum transmit energy. The numerical results validate the good performance of our proposed algorithms. Index-coded NOMA and dynamic coded-NOMA have comparable performance and both of them save much energy than the existing schemes. When there are 12 F-APs under small-cache scenarios, index-coded NOMA saves energy by 70.3% compared to traditional NOMA.

Online Rerouting and Rescheduling of Time-Triggered Flows for Fault Tolerance in Time-Sensitive Networking

Time-sensitive networking (TSN) is an industry-standard networking protocol that is widely deployed in safety-critical industrial and automotive networks thanks to its quality-of-service (QoS) mechanisms, esp. deterministic transmission and bounded end-to-end delay for time-triggered (TT) flows. In this article, we focus on TT flows and address the issue of fault tolerance against permanent and transient faults with both spatial and temporal redundancy. We present an efficient heuristic algorithm for online incremental rerouting and rescheduling of disrupted flows, assuming the paths and schedules of existing flows stay fixed. It is complementary to and can be combined with offline routing and scheduling algorithms for achieving fault tolerance based on frame replication and elimination for reliability (FRER) (IEEE 802.1CB). Performance evaluation shows that our approach is able to better recover the system’s degree of redundancy (DoR) and has a higher acceptance rate than related work.