Integer Linear Programming Solution Research Articles

A genetic algorithm method for improving suboptimal sensor arrangements in coverage and connectivity problems

This paper is concerned with the solution of a Coverage and Connectivity Problem (CCP). The proposed method performs the placement of sensors forming a connected Wireless Sensor Network (WSN) to fully cover a Field of Interest (FoI). Full coverage is attained despite the presence of opaque obstacles that impair both sensing and communication. To this end, we leverage set operations involving polygons to tessellate the free space. Moreover, we propose the concept of CR-visibility to assess the total area coverage of a polygon by a sensor. The deployment of the minimal number of sensors to completely cover the FoI is cast into the form of an Integer Linear Program (ILP). Two different formulations of connectivity constraints are appended to the ILP. The first one is necessary and sufficient for connectivity, whereas the second alternative is only sufficient. While the number of inequalities in the former grows combinatorially with the number of sensors, the growth is linear in the latter, rendering it more computationally appealing for real-sized FoI. Lastly, we formulate an unconstrained version of the CCP, which is solved by a Genetic Algorithm (GA) with integer variables. We present a small simulation scenario for initial illustration of the proposed method, and a larger, real-life scenario based on the map of an actual urban setting. The results obtained with the real-life scenario show that: (i) high-quality solutions can be obtained in short computation times by imposing the sufficient constraints for connectivity; (ii) the large number of inequalities associated to the necessary and sufficient constraints render the numerical solution impractical; (iii) by using random initialization, the GA solution of the unconstrained problem requires more sensors than the ILP solution with the sufficient connectivity constraint; (iv) including that ILP solution in the initial population of the GA enables it to find a sensor placement that requires fewer sensors.

Long-term upgrade strategies in multiband and multifiber optical transport networks

Flexible-grid optical transport networks (OTNs) are currently undergoing a massive scale upgrade to bandwidth variable transceivers (BVTs) to cater to the exponential Internet traffic growth. Network operators seeking to plan future capacity in a scalable manner can also add additional bands of operations or additional fibers in the OTN. We propose two strategies for planning multiband upgrades in OTNs, which use an integer linear programming (ILP) solution and a heuristic solution with a reinforcement learning (RL)-based extension. Network simulation studies on three differently sized OTNs show that the heuristic and its RL-based extension perform extremely close to the optimal ILP-based solution while reducing execution times drastically. Finally, a techno-economic study based on what we believe to be a novel cost model highlights the cost-per-bit-per-second savings through carefully planned upgrades.

The Floor Is Lava: Halving Natural Genomes with Viaducts, Piers, and Pontoons.

Whole Genome Duplications (WGDs) are events that double the content and structure of a genome. In some organisms, multiple WGD events have been observed while loss of genetic material is a typical occurrence following a WGD event. The requirement of classic rearrangement models that every genetic marker has to occur exactly two times in a given problem instance, therefore, poses a serious restriction in this context. The Double-Cut and Join (DCJ) model is a simple and powerful model for the analysis of large structural rearrangements. After being extended to the DCJ-Indel model, capable of handling gains and losses of genetic material, research has shifted in recent years toward enabling it to handle natural genomes, for which no assumption about the distribution of markers has to be made. The traditional theoretical framework for studying WGD events is the Genome Halving Problem (GHP). While the GHP is solved for the DCJ model for genomes without losses, there are currently no exact algorithms utilizing the DCJ-Indel model that are able to handle natural genomes. In this work, we present a general view on the DCJ-Indel model that we apply to derive an exact polynomial time and space solution for the GHP on genomes with at most two genes per family before generalizing the problem to an integer linear program solution for natural genomes.

Digital Twin-Assisted, SFC-Enabled Service Provisioning in Mobile Edge Computing

Mobile Edge Computing (MEC) has been identified as a desirable computing paradigm that provides efficient and effective services for various applications, while meeting stringent service delay requirements. Orthogonal to the MEC computing paradigm, Network Function Virtualization (NFV) technology is another enabling technology that provides the network resource management with great flexibility and scalability, where the instances of Virtual Network Functions (VNFs) are deployed in edge servers as Service Function Chains (SFCs) for SFC-enabled services. Although reliable service provisioning in MEC environments is fundamentally important, the deployed VNF instances usually are not reliable, which can be affected by their software implementation, their execution duration, the workload among edge servers, and so on. Empowered by digital twin techniques, the states of VNF instances can be maintained by their digital twins in a real-time manner and their reliability can be accurately predicted through their digital twins. In this paper, we study digital twin-assisted, SFC-enabled reliable service provisioning in MEC networks by exploiting the dynamics of VNF instance reliability. We concentrate on two novel optimization problems of reliable service provisioning: the service cost minimization problem, and the dynamic service admission maximization problem. We first show their NP-hardness. We then formulate an Integer Linear Program (ILP) solution, and devise an approximation algorithm with a constant approximation ratio for the service cost minimization problem. We thirdly provide an ILP solution to the offline version of the dynamic service admission maximization problem. Built upon this offline ILP solution, we also develop an online algorithm with a provable competitive ratio for the problem, by adopting the primal-dual dynamic updating technique. We finally evaluate the performance of the proposed algorithms via simulations. Simulation results demonstrate that the proposed algorithms outperform their comparison benchmarks, and improve the performance of their comparison counterparts by no less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10.2 \%$</tex-math></inline-formula> .

Near-Optimal and Collaborative Service Caching in Mobile Edge Clouds

In this paper, we study the problem of service caching in an MEC network under a service market with multiple network service providers competing for both computation and bandwidth resources in terms of Virtual Machines (VMs) in the MEC network. We first propose an Integer Linear Program (ILP) solution and a randomized rounding algorithm, for the problem without VM sharing among different network service providers. We then devise a distributed and stable game-theoretical mechanism for the problem with VM sharing among network service providers, with the aim to minimize the social cost of all network service providers, through introducing a novel cost sharing model and a coalition formation game. We also analyze the performance guarantee of the proposed mechanism, Strong Price of Anarchy (SPoA). We thirdly consider the cost- and delay-sensitive service caching problem with temporal VM sharing, and propose a mechanism with provable SPoA. We finally evaluate the performance through extensive simulations and a real world test-bed implementation. Experimental results demonstrate that the proposed algorithms outperform existing approaches by achieving at least 40% lower social cost via service caching and resource sharing among different network service providers.

An energy-aware combinatorial auction-based virtual machine scheduling model and heuristics for green cloud computing

Considering the increasing demand for cloud computing, and the financial and environmental impact of the increasing energy consumption trend of data centers, improving energy efficiency is vital for cloud service providers. In this study, an energy-aware virtual machine scheduling model is proposed which is based on the multi-unit nondiscriminatory combinatorial auction. The model includes a powerful bidding language that allows users to declare their complicated virtual machine requests using logical AND and OR relations along with the time constraints. The study also presents the formal definition of the model and the associated optimization problem for determining the optimum schedule and energy-efficient placement of VMs on physical servers. The optimization problem is formulated using integer linear programming and several heuristic solution methods including the Genetic Algorithm are proposed for this problem. The performances of the model and the proposed heuristics are assessed on a comprehensive test suite. The proposed model is estimated to provide approximately a 37% improvement in revenues, and the solution methods are estimated to provide high-quality solutions within only 5% of the optimum which enable the model to be deployed in large-scale clouds.

Multi-agent deep reinforcement learning for user association and resource allocation in integrated terrestrial and non-terrestrial networks

Integrating the terrestrial network with non-terrestrial networks to provide radio access as anticipated in the beyond 5G networks calls for efficient user association and resource allocation strategies. In this work, a weighted sum single objective optimization problem that maximizes the total network data rate while minimizing the mobility-induced handoffs and prioritizing service provisioning of mission-critical users in the integrated terrestrial and non-terrestrial network is formulated. The problem’s complexity is reduced by solving the defined problem in two phases; the user association followed by the resource distribution phase. Several proposed approaches to the user association sub-problem utilize a central node that requires nearly-complete information, which may not be available in real time. On the contrary, this paper proposes a centralized training and distributed execution multi-agent dueling double deep Q network (MA3DQN) solution. Each user collects the channel state and access node loading information in this approach and makes an association decision that considers its quality of service requirements. The algorithm’s performance is validated through comparison with the genetic algorithm (GA), the integer linear programming (ILP), a heuristic approximation-based solution, the greedy approach, and the random user association (RUA) algorithm. Moreover, the paper simulates the multi-agent deep Q network solution as an additional benchmark algorithm. Simulation results reveal that as the number of users in the network increases, the acquired data rate of the MA3DQN is within 0.48% and 0.4% of that achieved by the GA and ILP, respectively, and outperforms all other algorithms. Notably, the proposed MA3DQN algorithm presents the best running time, attaining a gain of 99.9% over the GA algorithm, which performs the poorest among the algorithms characterized by polynomial worst-case time complexity. Besides, the MA3DQN approach maintains a handoff probability of zero, unlike the ILP, the approximation-based, greedy, and RUA solutions.

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.

IoT-Aerial Base Station Task Offloading With Risk-Sensitive Reinforcement Learning for Smart Agriculture

Aerial base stations (ABSs) allow smart farms to offload processing responsibility of complex tasks from internet of things (IoT) devices to ABSs. IoT devices have limited energy and computing resources, thus it is required to provide an advanced solution for a system that requires the support of ABSs. This paper introduces a novel multi-actor-based risk-sensitive reinforcement learning approach for ABS task scheduling for smart agriculture. The problem is defined as task offloading with a strict condition on completing the IoT tasks before their deadlines. Moreover, the algorithm must also consider the limited energy capacity of the ABSs. The results show that our proposed approach outperforms several heuristics and the classic Q-Learning approach. Furthermore, we provide a mixed integer linear programming solution to determine a lower bound on the performance, and clarify the gap between our risk-sensitive solution and the optimal solution, as well. The comparison proves our extensive simulation results demonstrate that our method is a promising approach for providing a guaranteed task processing services for the IoT tasks in a smart farm, while increasing the hovering time of the ABSs in this farm.

Optimal Generator Policy for Hybrid Fuel UAV under Airspace Noise Restrictions

Here we study an optimal control problem involving energy management of a hybrid-fuel Unmanned Aerial Vehicle (UAV). The planning problem for a hybrid-fuel platform involves determining the path while managing the energy resources, which includes a policy for power modality switching whenever applicable. The hybrid-fuel platform considered here involves a generator and battery pack combined in a series fashion as energy sources on-board a UAV. Also included in the problem are the noise restrictions, which place constraints on generator operation depending on the airspace location. These emulate possible restrictions on UAV noise that occur in military surveillance missions or in urban path planning, where the collective noise of many UAVs, some with combustion engines, may be restricted in certain areas or times of the day. We present a hybrid methodology which starts from an initial path and generator pattern obtained from a mixed integer linear program (MILP) solution. The generator pattern from the discrete solution is then refined in an optimal control framework with an objective to minimize fuel usage, while considering the nonlinear battery and generator dynamics and noise-restriction constraints. Optimal control problem is solved with a nonlinear program solver, IPOPT. Numerical results are presented and analyzed with varying path lengths and scenarios. This work aims to serve as an initial study of this hybrid-fuel UAV problem within an optimal control framework, which can be extended to refinement of both the generator pattern and the trajectory in tandem, while considering vehicle and power dynamics that are often ignored in discrete path planning solutions.

IMSI Sharing-Based Dynamic and Flexible Traffic Aggregation for Massive IoT Networks

International mobile subscriber identity (IMSI) sharing-based aggregated communication aims to connect multiple Internet of Things (IoT) devices to the mobile operator’s core network over the same subscriber line. IoT devices with low data rates and long data sending intervals are first grouped together and assigned the same subscriber identity. They then take turns to perform their data exchanges using the same cellular connection, yielding huge savings in resource (e.g., number of active bearers) usage. Current solutions however do not consider different device traffic characteristics, the flexibility in traffic patterns, and dynamic network environments where new IoT devices join and existing ones leave the network. In this article, we study the problem of the grouping of IoT devices that will share the same subscriber identity based on their traffic patterns which can also be slightly shifted. We also study the efficient regrouping of these devices as the set of devices in the network changes. We first solve the optimal grouping and traffic aggregation problem for the initial and updated network states using integer linear programming (ILP). Then, to avoid the high complexity of ILP solutions, we develop heuristic-based solutions. Through extensive simulations, we show that heuristic-based algorithms can provide close to optimal ILP-based results while running much faster. The results also show that shifting-based grouping provides more resource saving compared to no-shifting-based aggregation and the proposed solution for dynamic environments can maintain the resource saving with a much lower complexity.

Real-Time Advanced Energy-Efficient Management of an Active Radial Distribution Network

This article elucidates a new real-time optimization framework for advanced energy-efficient management of active radial distribution networks. The proposed energy management process leverages the benefits of simultaneous deployment of online direct load control (DLC) and conservation voltage reduction (CVR) for decreasing peak energy demand. Initially the proposed problem is designed as a time-coupled stochastic mixed integer nonconvex programming (MINCP) to accommodate long-term offline beneficial aspects in real-time optimization framework, which is later simplified using merger of Queueing theory and Lyapunov optimization. A successive mixed integer linear programming (s-MILP) solution approach is proposed for accurate and fast convergence of the revised MINCP framework. The efficacy of the developed strategy is evaluated after comparing with two-benchmark energy management models (viz. offline and online greedy algorithm) by demonstrating on modified IEEE 69-bus test system. Further scalability of the proposed approach is validated by testing on large distribution networks.

Exact solution of network flow models with strong relaxations

We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig–Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.

CAMDNN: Content-Aware Mapping of a Network of Deep Neural Networks on Edge MPSoCs

Machine Learning (ML) workloads are increasingly deployed at the edge. Enabling efficient inference execution while considering model and system heterogeneity remains challenging, especially for ML tasks built with a network of DNNs. The challenge is to maximize the utilization of all available resources on the multiprocessor system on a chip (MPSoC) at the same time. This becomes even more complicated because the optimal mapping for the network of DNNs can vary with input batch sizes and scene complexity. In this paper, a holistic hierarchical scheduling framework is presented to optimize the execution time for a network of DNN models on an edge MPSoC at runtime, considering varying input characteristics. The framework consists of a local and a global scheduler. The local scheduler maps individual DNNs in the inference pipeline to the best-performing hardware unit while the global scheduler customizes an Integer Linear Programming (ILP) solution to instantiate DNN remapping. To minimize scheduler runtime overhead, an imitation learning (IL) based scheduler is used that approximates the ILP solutions. The proposed scheduling framework (CAMDNN) was implemented on a Qualcomm Robotic RB5 platform. CAMDNN resulted in lower execution time of up to 32% than HEFT, and by factors of 6.67X, 5.6X and 2.17X than the CPU-only, GPU-only and Central Queue schedulers.

Maximizing Throughput of Delay-Sensitive NFV-Enabled Request Admissions via Virtualized Network Function Placement

Network Function Virtualization (NFV) has attracted significant attention from both industry and academia as an important paradigm change in network service provisioning. Most existing studies on admissions of NFV-enabled requests focused on deploying dedicated Virtualized Network Function (VNF) instances to serve each individual request without exploring the sharing of VNF instances among multiple user requests. However, with ever-growing demands of user services, exclusive usages of VNF instances in most networks drastically degrade the network performance and largely under-utilize the VNF instance resources. In this paper, we jointly explore two different VNF instance scaling techniques, horizontal scaling and vertical scaling techniques, to improve the network throughput while minimizing the operational cost of the network, where horizontal scaling that migrates some existing VNF instances from their current locations to new locations to allow the VNF instances to be shared by multiple requests to reduce the resource consumption and operational cost of the network, and vertical scaling that instantiates new VNF instances to meet the demands of new request admissions if existing VNF instances sharing becomes more expensive or the end-to-end delay requirements of currently executing requests will be violated. We first propose a unified framework of maximizing the network throughput, by admitting as many as NFV-enabled requests while meeting the end-to-end delay requirements of the admitted requests. We then provide an Integer Linear Programming (ILP) solution for the problem when the problem size is small. Otherwise, we devise an efficient algorithm through a non-trivial reduction that reduces the problem to the minimum-weight feedback arc set problem and the generalized assignment problem (GAP). We finally conduct experiments to evaluate the performance of the proposed algorithm. Experimental results demonstrate that the proposed algorithm outperforms a baseline algorithm and achieves a performance on a par with its optimal ILP solution.

A customized genetic algorithm for bi-objective routing in a dynamic network

The article presents a proposed customized genetic algorithm (CGA) to find the Pareto frontier for a bi-objective integer linear programming (ILP) model of routing in a dynamic network, where the number of nodes and edge weights vary over time. Utilizing a hybrid method, the CGA combines a genetic algorithm with dynamic programming (DP); it is a fast alternative to an ILP solver for finding efficient solutions, particularly for large dimensions. A non-dominated sorting genetic algorithm (NSGA-II) is used as a base multi-objective evolutionary algorithm. Real data are used for target trajectories, from a case study of application of a surveillance boat to measure greenhouse-gas emissions of ships on the Baltic sea. The CGA’s performance is evaluated in comparison to ILP solutions in terms of accuracy and computation efficiency. Results over multiple runs indicate convergence to the efficient frontier, with a considerable computation speed-up relative to the ILP solver. The study stays as a model for hybridizing evolutionary optimization and DP methods together in solving complex real-world problems.

Request Reliability Augmentation With Service Function Chain Requirements in Mobile Edge Computing

Provisioning reliable network services for mobile users in edge computing environments is the top priority of network service providers, as unreliable services will result in tremendous losses of revenues and customers. In this paper, we study a novel service reliability augmentation problem in a mobile edge computing (MEC) network, where mobile users request network services with service function chain (SFC) and reliability expectation requirements. To enhance the service reliability of user requests, it is a common practice to make use of redundant virtualized network function (VNF) instance placement in case the primary VNF instance fails. We aim to augment the service reliability of each admitted request to its specified reliability expectation, subject to computing capacity on each cloudlet. To this end, we first formulate a novel service reliability augmentation problem for each request with an SFC and a reliability expectation requirement, by augmenting its reliability through redundant VNF instance deployment. We then show that the problem is NP-hard, and provide an admission framework of user requests by placing primary VNF instances of network functions in the SFC to different cloudlets. We then deal with the service reliability augmentation problem of an admitted request under the assumption that all secondary VNF instances of each primary VNF instance must be placed into the cloudlets no more than <inline-formula><tex-math notation="LaTeX">$l$</tex-math></inline-formula> hops from the cloudlet of its primary VNF instance for a fixed <inline-formula><tex-math notation="LaTeX">$l$</tex-math></inline-formula> with <inline-formula><tex-math notation="LaTeX">$1\leq l \leq n-1$</tex-math></inline-formula> , where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of cloudlets in the network, for which we formulate an integer linear program solution, and develop a randomized algorithm with a good approximation ratio and high probability, at the expense of moderate resource constraint violations. We also devise a deterministic heuristic for the problem without any resource violation. We third study the service reliability augmentation problem for a set of admitted requests by extending the proposed algorithm for the service reliability augmentation problem for a single request admission. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithms are promising, and their empirical results are superior to their analytical counterparts.

Algorithms for hierarchical and semi-partitioned parallel scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming (ILP) formulation for the job assignment subproblem, and show how to turn arbitrary ILP solutions into valid schedules. We also derive a polynomial-time 2-approximation algorithm for the problem. Extensions that incorporate memory capacity constraints are also discussed.

Optimal control and learning for cyber‐physical systems

Optimal control and learning for <scp>cyber‐physical</scp> systems

Dynamic Hierarchical Caching Resource Allocation for 5G-ICN Slice

Network slicing and Multiple-Access Edge Computing (MEC) are key technologies in fifth-generation (5G) networks. The flexible programmability of network slicing and the decentralization of MEC facilitate the deployment of Information-Centric Networking (ICN). The caching feature of ICN can provide users with low-latency data services. Although many existing works have addressed the cache deployment problem or the cache optimization problem, most of them do not consider the issue of caching resource allocation in the dynamic and hierarchical environment. Dynamic deployment of cache nodes can improve the operator’s revenue as much as possible while accurately allocating the caching resources can reduce the user-requested latency. Therefore, in this study, a problem of the operator’s expected revenue maximization is presented in an environment combining dynamic deployment of the MECs and the caching-enabled node ICN-Gateway (ICN-GW). To solve this problem, we propose an optimal stopping theory (OST)-based dynamic hierarchical caching resources allocation (ODH-CRA) algorithm. The algorithm consists of three parts. Firstly, an Integer Linear Programming (ILP) solution is proposed to determine the optimal deployment of the MECs. This method determines the optimal location and number of the MECs by considering deployment costs and service requirement costs synthetically. Secondly, a redeployment technique based on the OST is proposed to determine the best redeployment time of the MECs according to the values of latency violations and the service latency requirements. Finally, an improved elite genetic algorithm (IEGA) is proposed to find the optimal solution of the hierarchical caching resource allocation. This method searches the optimal scheme by maximizing the operator’s revenue joint caching costs and energy consumption. Ultimately, we perform a series of simulation experiments to compare the proposed method’s performance to dynamic and hierarchical methods. Our solution can effectively reduce the latency for users’ requesting, improve the revenue of ICN Communication Service Provider (ICSP), and provide an effective caching resource allocation scheme for the next generation of Internet of Things (IoT) networks.