Proposed Integer Linear Programming Model Research Articles

A branch-and-price algorithm for integrating urban rail crew scheduling and rostering problems

Crew planning, involving how to best schedule crew members during a given period, is a significant problem for urban rail transit companies. This paper proposes a new integer linear programming (ILP) model that can simultaneously optimize urban rail crew scheduling and rostering problems. The proposed ILP model is a set partitioning-based model with only one type of important duty selection variable that connects the two-level problem and circumvents the drawbacks of conventional approaches that usually formulate the crew scheduling and rostering problems separately and couple these two problems through linking constraints. This study demonstrates that the structure of the underlying network used to model the problem enables the development of an effective, heuristic branch-and-price procedure. The study compares the proposed approach with two other decomposition methods, namely Lagrangian relaxation and alternating direction method of multipliers (ADMM), on problems of different sizes and shows that the method provides lower bounds that are on average 16.4% better than Lagrangian relaxation and 5.03% better than ADMM, respectively. Furthermore, the study shows that, with an average optimality gap of 3.28%, the proposed approach obtains high-quality integer solutions to the integrated problem.

The maximum length car sequencing problem

This paper introduces the maximum length car sequencing problem to support the assembly operations of a multinational automotive company. We propose an integer linear programming (ILP) formulation to schedule the maximum number of cars without violating the so-called option constraints. In addition, we present valid combinatorial lower and upper bounds, which can be calculated in less than 0.01 s, as well as binary and iterative search algorithms to solve the problem when good primal bounds are not readily available. To quickly obtain high-quality solutions, we devise an effective iterated local search algorithm, and we use the heuristic solutions as warm start to further enhance the performance of the exact methods. Computational results demonstrate that relatively low gaps were achieved for benchmark instances within a time limit of ten minutes. We also conducted an instance space analysis to identify the features that make the problem more difficult to solve. Moreover, the instances reflecting the company’s needs could be solved to optimality in less than a second. Finally, simulations with real-world demands, divided into shifts, were conducted over a period of four months. In this case, we use the proposed ILP model in all shifts except the last one of each month, for which we employ an alternative ILP model to sequence the unscheduled cars, adjusting the pace of the assembly line in an optimal fashion. The results pointed out that the latter was necessary in only one of the months.

An Integer Linear Programming Model for the Examination Timetabling Problem: A Case Study of a University in Thailand

This paper considers the examination timetabling problem (ETTP) at the College of Industrial Technology (CIT) of the King Mongkut’s University of Technology North Bangkok in Thailand. A new integer linear programming (ILP) formulation for the ETTP at the CIT is presented. The objectives were to minimize both the number of examination days (the main objective) and the number of rooms used throughout the entire examination period (the secondary objective). In this paper, a course can have multiple sections, and an examination room can accommodate exams for more than one course section. To illustrate the proposed ILP model, real data on courses acquired from the CIT were used to generate two test problems: a small problem and a large problem. The small problem included 32 courses with 69 sections. The large problem included 73 courses with 341 sections, which was the real data required for generating the midterm examination timetable for all first‐year courses in the first semester of 2021. Both problems were solved using the CPLEX solver software. The results show that the proposed model could find an optimal examination timetable for the small problem with a computational time of 2 min and 46 s. It also could find a good feasible midterm examination timetable that satisfied the requirements of the CIT for the large problem within the 2‐h time limit, much less time than that compared to manual scheduling by the CIT’s administrative staff. The obtained midterm examination timetable required five examination days and could reduce 104 examination rooms compared to assigning each course section to a separate examination room. The proposed ILP model can be used in a real‐life situation and can be a good option to generate an optimal schedule or a good feasible schedule for examinations at the CIT or other institutions that have similar requirements.

Security-aware 5G RAN slice mapping with tiered isolation in physical-layer secured metro-aggregation elastic optical networks using heuristic-assisted DRL

The optical transport network (OTN) encryption technology is attractive to solve the physical-layer security in services for the light-path provision process. This paper mainly explores the security-aware 5G radio access network (RAN) slice mapping problem with the tiered isolation (TI) policy, which decides the solution for aggregating service into the physical-layer secured metro-aggregation elastic optical networks (MA-EONs). We first introduce the physical-layer secured OTNs and illustrate their differences from the traditional optical networks. Then, we formulate the 5G RAN slice mapping problem in physical-layer secured MA-EONs as an exact integer linear programming (ILP) model to minimize the average cost (AC), which consists of the number of utilized processing pools (PPs)/general-purpose processors (GPPs)/virtual machines (VMs), and maximum frequency slot index (MFSI) on the light-paths, meanwhile satisfying the given slice’s latency, isolation, and security requirements. After that, to overcome the non-scalability problem of the ILP model, a heuristic-assisted deep reinforcement learning (HA-DRL) algorithm is proposed to obtain a near-optimal solution for large-scale network scenarios, where the classical shortest path algorithm is employed in the DRL to shrink the size of the exploration space and accelerate the convergence process. Finally, we evaluate the proposed ILP model and HA-DRL algorithm through extensive simulations. Simulation results indicate that our proposed HA-DRL method can find approximate solutions to the ILP model in the small-scale network scenario. Furthermore, the HA-DRL method can also achieve higher resource efficiency compared with benchmark heuristic first-fit algorithms in the large-scale network scenario. In comparison to the first-fit algorithm benchmark, the proposed HA-DRL can achieve up to 9.4% AC reduction in large-scale network scenarios.

Optimized Allocation of Fault Transmitters for Improving the Recloser-Fuse Coordination

New technologies are currently delivering protective devices that can enhance the design of protection coordination in modern distribution systems. This paper proposes an integer linear programming (IP) model to find the optimal location of a Fault Transmitter (FT) in the distribution system. The proposed IP model provides the optimal FT allocation considering the minimization of sustained interruption frequency and momentary interruption duration. A study of the appropriate number of FT reveals the best alternative in the proposed adaptive protection scheme. A Monte Carlo simulation with a richer representation of stochastic fault scenarios is used for further evaluation of the solutions obtained with the proposed IP model. The combined strategies allow full-scale studies of the optimal allocation of FT in distribution systems. The results of studies using two test systems certify the benefits of the proposed strategy in fuse-saving coordination and in reducing the total duration of the momentary interruption, which can cause power quality problems.

Network Function Virtualization in Elastic Optical Networks

In Network Function Virtualization (NFV), traditional purpose-built proprietary middle-boxes are replaced with virtual network function (VNF) instances that are deployed over generic hardware; network traffic flows are steered through a sequence of VNF instances (i.e., that forms a service function chain) after resolving the VNF Forward Graph Embedding (FGE) problem. NFV eases the network management and fosters the agile deployment of network services, thus enabling a foremost solution to address issues of traditional enterprise networks. With the everlasting Internet traffic growth, in this work, we extend the provision of NFV upon Elastic Optical Networks (EONs) that deliver abundant elastic and fine-granular bandwidth for connections between VNFs. We systematically examine the integrated NFV-EON architecture, and investigate one key enabler, namely the FGE-EON problem, where one has to coordinate the allocation of computing resources (as in a typical FGE problem) and the assignment of optical bandwidth (i.e., spectrum allocation in EONs). The contributions of this work are multi-fold. The FGE-EON problem is proven to be NP-Complete for the first time. An Integer Linear Programming (ILP) model is developed to address FGE-EON problem of small instances. Despite its complexity, with novel modeling techniques, the proposed ILP model maintains a compact structure even after accounting for VNF sharing and VNF co-location together for the first time. For large scale problems, we design a heuristic algorithm based on layered graph that is shown to be near-optimal in our evaluations.

Fortune: A New Fault-Tolerance TSV Configuration in Router-Based Redundancy Structure

In three-dimensional integrated circuits (3D-ICs), through silicon via (TSV) is a critical technique in providing vertical connections. However, yield is one of the key obstacles to adopt the TSV-based 3D-ICs technology in the industry. Various fault-tolerance structures using redundant TSVs to repair faulty functional TSVs have been proposed in the literature for yield and reliability enhancement. However, the TSV repair paths under delay constraint cannot always be generated due to the lack of appropriate repair algorithms. In this article, we propose an effective TSV repair strategy for the router-based TSV redundancy architecture, taking into account the delay overhead. First, we prove that the router-based fault-tolerance structure configuration (RFSC) with the delay constraint is equivalent to the length-bounded multicommodity flow (LBMCF) problem. Then, an integer linear programming (ILP) formulation with acceptable scalability is presented to solve the LBMCF problem. The experimental results demonstrate that, compared with state-of-the-art fault-tolerance designs, the proposed ILP model can provide higher yield and lower delay overhead.

Delay-aware and resource-efficient service function chain mapping in inter-datacenter elastic optical networks

Network function virtualization (NFV) is emerging as a promising paradigm for network architectures. By migrating network functions from dedicated hardware appliances to software instances running in a virtualized environment, NFV promises to offer a more flexible way to deploy and manage service function chains (SFCs). When deploying these SFCs to users, the network operators require not only the user’s demands (e.g., end-to-end delay) to be satisfied, but require the cost of SFC mapping to be minimized (e.g., resource consumption). To fulfill these two goals, in this paper, we have investigated how to realize the delay-aware and resource-efficient SFC mapping in inter-datacenter elastic optical networks. We first formulate an integer linear programming (ILP) model to solve the problem exactly. The main optimization goal in the ILP model is to jointly minimize resource consumption and end-to-end delay to achieve optimal virtual network function placement. Then, a delay-aware and load-balancing mapping algorithm (DALB-MA) is proposed to obtain a near-optimal solution in a reasonable amount of time. Finally, we evaluate the proposed ILP model and heuristic algorithms via extensive simulations. The results indicate that the proposed ILP model and the DALB-MA outperform the benchmarks in terms of block rate, average cost, number of CPUs used, maximum frequency slot index, and delay margin gain.

Optimal planning and design of SRLG-aware survivable LR-PON for wireless and FTTx networks

Protection to optical network units (ONUs) against failure of their distribution fibers (DFs) in a long-reach passive optical network (LR-PON) is highly desirable to provide uninterrupted internet services to the users. In practical network scenarios, DFs form shared-risk link groups (SRLGs). The existing SRLG-aware protection schemes depend on residual bandwidth of ONUs. Therefore, they are cost-inefficient and also fail to satisfy high reliability requirements (RRs). We for the first time propose a nonresidual bandwidth based partial protection scheme and related architecture to provide partial protection to ONUs against a single SRLG failure. Following the proposed scheme, we formulate an integer linear programming (ILP)-based optimization problem to provision backup DFs and network components for providing protection with the minimum protection cost. To meet the strict delay requirement for real-time applications, the proposed ILP model restricts the length of backup DFs to be employed to restore the traffic transmission. As the proposed ILP model becomes computationally intractable for large networks, we also propose a heuristic scheme that provides fairly close results to that of the ILP model. We assess the performance of the proposed partial protection scheme in terms of protection cost and total length of backup DFs (TLBDF). Through exhaustive simulation study we show that the proposed partial protection scheme not only satisfies high RRs but also requires much lower protection cost and TLBDF as compared to the existing SRLG-aware protection schemes.

Privacy-Aware Collaborative Task Offloading in Fog Computing

Numerous new applications have been proliferated with the mature of 5G, which generates a large number of latency-sensitive and computationally intensive mobile data requests. The real-time requirement of these mobile data has been accommodated well by fog computing in the past few years, mainly through offloading tasks to fog nodes in the vicinity. On the other hand, the user-privacy hidden in the Internet-of-Things (IoT) data has not been sufficiently considered in the presence of insecure fog nodes. It is risky to offload an entire mission-critical task to just one fog node or several fog nodes owned by the same service provider (SP), especially when the SP is marked with low-security credit and tends to collect data information of users for malicious use. To address this issue, we classify IoT user tasks based on their security requirements, divide them into different numbers of smaller fragments, and, finally, offload the segments of a task to multiple fog nodes owned by the same or various SPs according to their security requirements. The selected fog nodes will collaboratively serve the divided fragments to avoid the possible damage caused by the leak of sensitive data due to compromised fog nodes of malicious SPs. For this, we propose an integer linear programming (ILP) model and a dynamic programming algorithm to maximize the number of successfully served IoT data tasks with satisfactory security requirements while minimizing the end-to-end transmission delay. The numerical results show that the proposed ILP model and algorithm can significantly increase the successful provisioning ratio for tasks with high-security requirements.

Cost-optimal architecture design for adaptive multi-stage TWDM-PON with PtP WDM overlay

Toward greenfield time and wavelength division multiplexed passive optical network (TWDM-PON) deployment in access segment, optimal network planning, and resource provisioning need to be explored in the planning phase to reduce capital expenditure (CapEx) and operational expenditure (OpEx). To address the issue, we propose an integer linear programming (ILP)-based optimization framework to design cost-efficient adaptive multi-stage TWDM-PON architecture, where an optimal number of cascaded splitting stages are used to minimize the combined expenditure comprising the CapEx and OpEx. Point-to-point WDM overlay over TWDM-PON is incorporated, wherein we reserve some wavelengths per optical line terminal (OLT) port to equip the heavily loaded (congested) optical network units (ONUs) with dedicated wavelengths. The ILP model offers the complete interconnection details from OLT to all ONUs providing the minimum combined expenditure, and selects the optimal number and locations of remote nodes (RNs) among the candidate RN locations for passive device placement, the types (either arrayed waveguide grating or power splitter) and splitting ratios of passive devices, and the number of splitting stages. Network constraints, such as the minimum guaranteed traffic rate to each ONU, the maximum number of ONUs with dedicated wavelengths per OLT port, and the maximum number of users per OLT port are taken into consideration. We compare the performance of the proposed TWDM-PON design model with the existing studies on greenfield PON design in terms of the cost savings, methodology features, and limitations. The proposed ILP model is further extended to design cost-optimal single-stage and adaptive multi-stage time division multiplexed PONs (TDM-PONs), and the expenditure for all models are estimated. We also investigate the variation in signal-to-noise ratio due to variation in the number of cascade stages. The models provide globally optimal solutions within a reasonable time bound with all constituent sub-problems and constraints jointly taken into consideration.

Two-phase node deployment for target coverage in rechargeable WSNs using genetic algorithm and integer linear programming

Node deployment is a matter of considerable concern in designing wireless sensor networks (WSNs). This paper studies this issue in the context of rechargeable WSNs (RWSNs). We propose an efficient algorithm, namely node deployment for target coverage in RWSNs (NDTCR), which determines the number and positions of installed sensors in two phases. The first phase applies genetic algorithm to construct a mesh over a subset of positions. The mentioned mesh covers the targets and connects them to the sink. In the second phase of NDTCR, we propose an integer linear programming (ILP) model to install some sensors at each position of the mesh. The advantage of applying the first phase is that it prunes the solution space considerably. Therefore, the proposed ILP model can be solved in a reasonable time. The experimental results demonstrate that NDTCR requires 29% fewer sensors on average in comparison with the previous approaches.

Analysis of Taklinear Performance and Integer Linear Programming Models in Nurses Scheduling Problems

Almost all hospitals schedule nurses' work shifts manually, which is not effective, mistakes in scheduling nurses in hospitals can make them not work optimally so that they are prone to making mistakes and will endanger every patient in the hospital. In the research will be proposed integer linear programming model and branch and bound method, the purpose of this study is to develop an optimization model of nurse scheduling problems at the hospital. The optimization model will minimize the total deviation of nurses' working days from the standard workdays, the optimization model implemented in hospitals is processed using LINGO software.

Integer linear programming model for allocation and migration of data blocks in the STT‐RAM‐based hybrid caches

Spin-transfer torque random access memory (STT-RAM) has emerged as an eminent choice for the larger on-chip caches due to high density, low static power consumption and scalability. However, this technology suffers from long latency and high energy consumption during a write operation. Hybrid caches alleviate these problems by incorporating a write-friendly memory technology such as static random access memory along with STT-RAM technology. The proper allocation of data blocks has a significant effect on both performance and energy consumption in the hybrid cache. In this study, the allocation and migration problem of data blocks in the hybrid cache is examined and then modelled using integer linear programming (ILP) formulations. The authors propose an ILP model with three different objective functions which include minimising access latency, minimising energy and minimising energy-delay product in the hybrid cache. Evaluations confirm that the proposed ILP model obtains better results in terms of energy consumption and performance compared to the existing hybrid cache architecture.

Static routing, modulation, spectrum, and space allocation in space division multiplexed-elastic optical networks with bundles of single-mode fiber

Space division multiplexed (SDM) elastic optical network (EON) is considered to be a promising scheme for large-capacity optical communication networks. The static routing, modulation, spectrum, and space allocation (RMSSA) in SDM-EONs with bundles of single-mode fiber is studied. Considering the computational complexity of resource allocation formulation, a path-based integer linear programming (ILP) formulation with fewer variables and constraints is modeled to solve the static RMSSA problem. Then a heuristic algorithm named local optimal RMSSA (LO-RMSSA) is proposed to be applicable in large-scale network scenarios. The calculated metrics are the maximum index of utilized frequency slots, the local spectrum resource utilization, and the runtime of algorithms. The results show that the proposed ILP model and LO-RMSSA algorithm get higher computational efficiency with other metrics no worse than the existing one.

An ILP-based CapEx and OpEx efficient multi-stage TDM/TWDM PON design methodology

Abstract With reference to huge investment needed for greenfield passive optical network (PON) deployment, it is immensely important to define procedures and algorithms aimed towards optimal layout and network planning to reduce the overall expenditure due to capital expenditure and operational expenditure as much as possible. We propose an integer linear programming (ILP) based optimization model that explores optimal network dimensioning and placement of network equipment at appropriate locations so as to minimize the overall expenditure. Based on the number of users [optical network units (ONUs)], user’s bandwidth demand, power budget, maximum distance from optical line terminal (OLT) to users, available number of wavelengths and OLT ports, and geographical locations of ONUs, OLT and candidate locations of remote nodes (RNs), the model selects the number, type, splitting ratio and locations of passive devices. The RN device type is selected to be either power splitter or array waveguide grating. Optimal PON architecture is appropriately identified to be time division multiplexing or time-and wavelength division multiplexing (TWDM) depending on the requirement. It provides complete interconnection details among all devices, the overall expenditure, the number of OLT ports and the number and associated data rates of wavelengths to be used. We show exhaustive results for two deployment regions (viz. urban and rural) with different number of ONUs and bandwidth demands from users.We also show result with actual locations of OLT, ONUs and RNs selected from Google map. The proposed ILP model has low computational complexity and offers optimal solution within a reasonable time limit, without requiring a heuristic approach that provides a sub-optimal solution. The TWDM-PON conforms to next-generation PON stage 2 (NG-PON2) specifications and can be used as a useful tool for setting up NG-PON2.

Robust Train Timetabling and Stop Planning with Uncertain Passenger Demand

The integrated Train Timetabling and Stop Planning (TTSP) problem calls for determining the optimal timetables for a given set of trains, while choosing, for each train, the subset of stations where it will stop. Both the timetable and the stop plan are determined based on the passenger demand, i.e. on the number of passengers travelling between an origin and a destination stations. In this work, we study the Robust TTSP (RTTSP), where passenger demand is considered to be uncertain, as it is often the case in real practice. We propose an Integer Linear Programming (ILP) model for RTTSP based on Light Robustness, an effective technique introduced in [Fischetti, M., and M. Monaci, Light robustness In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Lecture Notes in Computer Science 5868 (2009), 61–84. Springer, Berlin Heidelberg]. We test the proposed ILP model on real-world data of the Wuhan-Guangzhou high-speed railway corridor under different demand scenarios.

Task Placement Across Multiple Public Clouds With Deadline Constraints for Smart Factory

The smart factory of Industry 4.0 has been regarded as a solution for handling the increasing production complexity caused by growing global economy and demand for customized products. Besides, it will make the interactions between humans, machines, and products become a highly competitive area for market capitalization in the near feature. Nowadays, cloud computing with the high performance of computing and self-service access plays an important role in realizing smart factor. To minimize the overall cost of company in a heterogeneous cloud environment, including multiple public clouds, while ensuring a proper level of quality-of-service, task placement across multiple public clouds is a critical problem, where task deadlines and long-haul data transmission costs between smart factory and different clouds must be considered. We formulate this task placement problem as an integer linear program (ILP) to minimize company cost under the task deadline constraint. With extensive simulations, we evaluate the performance of our proposed ILP model in heterogeneous public clouds with finite and infinite resources.

Energy‐efficient multigroup communication

AbstractWireless devices are widely used to monitor and control multiple groups within the context of machine‐to‐machine applications. The Constrained Application Protocol provides communication capabilities for applications that demand periodic monitoring of multiple groups. Because of the energy constraints of the devices used, a key challenge is to extend the network lifetime. Data aggregation solutions have been proposed to reduce the amount of network traffic and increase energy efficiency. However, for periodic monitoring of multiple groups, current data aggregation solutions do not exploit the potential of combining multiple payloads in a single message. In addition, solutions in literature are unable to take advantage of the communication interactions that occur when there is traffic originating from different groups. To fill this gap, this paper focuses on a nontraditional data aggregation approach, named two‐tier aggregation, that applies the idea of inserting many payloads in 1 message to efficiently gather data from multiple groups, introducing novelty on how the messages are assembled. An integer linear programming model is proposed to maximize the network lifetime in multiple group scenarios. The proposed formulation guarantees the energy efficiency of two‐tier aggregation and defines an upper bound for the heuristics. The evaluation shows the lifetime upper bound obtained by the proposed integer linear programming model on different network sizes and compares it to state‐of‐the‐art heuristic solutions.

Virtual-Pod-Assisted Routing and Resource Assignment in Elastic All-Optical Intra-Datacenter Networks

The service requests of intra-datacenter networks (intra-DCNs) are different from the traffic demands of traditional transport networks in the following features. First, the latter is typically generated between dedicated node pairs that only require sufficient transmission bandwidth. Intra-DCN service requests, in contrast, require IT resources, such as computational, memory and storage resources, in addition to the transmission bandwidth. Second, for a given intra-DCN service request, any intra-DCN node that can provide the required IT resources can serve as a destination node (i.e., anycast). Thus, this type of network poses an important research problem of routing and spectrum/IT resource assignment (RSIA). To support these features, we first develop an integer linear programming (ILP) model to address the static RSIA problem, and then to propose efficient heuristic algorithms to address the dynamic RSIA issues, subject to the intra-DCNs’ limited network resources. The results of the proposed ILP model and heuristic algorithms are compared with the traditional network models and algorithms. It is found that the proposed ILP model and heuristic algorithms perform much better than the traditional approaches in terms of using intra-DCN network resources and reducing the service-request blocking probability.