Proposed Integer Linear Programming Model Research Articles

Joint Optimization of Resource Allocation for Elastic Optical Intra-Datacenter Network

The ever-increasing demand for cloud services is posing serious challenges to the scalability of the computing, storing, and networking infrastructure deployed inside the datacenters. To address these challenges, we formulate the integer linear program (ILP) model to minimize the spectrum and the switch port usage by exploiting transparent multi-hop connection capability in elastic optical interconnect architecture for datacenters. The proposed ILP model not only takes into account the networking resources but also the other resources (such as computing and storage) in order to achieve a joint resource optimization in intra-datacenter networks. The optimal results show that substantial savings in both spectrum and switching resources can be achieved by properly tuning the objective function of the proposed optimization strategy.

A branch-and-price framework for optimal virtual network embedding

Network virtualization promises a future Internet that can facilitate technology revolutions via decoupling the traditional Internet Service Providers (ISPs) into the infrastructure providers (InPs), and the service providers (SPs). This separation introduces an extra layer of abstraction, thus allowing independent innovations at both the hardware level and service level. In this paper, we study the fundamental virtual network embedding (VNE) problem in network virtualization, which aims at mapping the virtual network request of the SPs to the substrate networks managed by the InPs. Given the NP-Completeness of the VNE problem, prior approaches primarily rely on the solving of the link-based Integer Linear Programming (ILP) formulations, relaxations, and heuristics. In this study, we first present a compact path-based ILP model. Moreover, we present a branch-and-price framework that embeds a column generation process to solve the proposed ILP model. Our framework can lead to optimal solution to the VNE problem, or near optimal solution with per-instance guarantee on its closeness to the optimal solution.

An algorithm and upper bounds for the weighted maximal planar graph problem

In this paper, we investigate the weighted maximal planar graph (WMPG) problem. Given a complete, edge-weighted, simple graph, the WMPG problem involves finding a subgraph with the highest sum of edge weights that is maximal planar, namely, it can be embedded in the plane without any of its edges intersecting, and no additional edge can be added to the subgraph without violating its planarity. We present a new integer linear programming (ILP) model for this problem. We then develop a cutting-plane algorithm to solve the WMPG problem based on the proposed ILP model. This algorithm enables the problem to be solved more efficiently than previously reported algorithms. New upper bounds are also provided, which are useful in evaluating the quality of heuristic solutions or in generating initial solutions for meta-heuristics. Computational results are reported for a set of 417 test instances of size varying from 6 to 100 nodes including 105 instances from the literature and 312 randomly generated instances. The computational results indicate that instances with up to 24 nodes can be solved optimally in reasonable computational time and the new upper bounds for larger instances significantly improve existing upper bounds.

Communication-Constrained Regionalization of Power Systems for Synchrophasor-Based Wide-Area Backup Protection Scheme

The evolving wide-area measurement system technology offers new opportunities for backup protection of transmission lines to avert the misoperation of conventional relays against system disturbances and prevent system instability. Since wide-area backup protection (WABP) is to operate at the range of a few hundred milliseconds, the delays associated with data and command communications and algorithm execution can be a troublesome issue in a large-scale power system. This paper briefly reviews a WABP scheme based on positive-sequence voltage phasor direct and indirect measurements. To overcome the problem of WABP delays, an integer linear programming (ILP) model is proposed to divide the power system into several protection regions. This process is accomplished in three stages in which the number and location of measurement devices (MDs), the number and boundary of protection regions, and the location of protection rooms, as well as the total number of communication links between MDs and protection rooms are optimized. The proposed WABP scheme is implemented in each region and individually protects the associated transmission lines. Execution of the proposed ILP model on different test systems reveals that with regionalization of the systems, WABP schemes can reliably be used in practice.

A cross layer optimization modeling for a periodic WSN application

Wireless Sensor Network (WSN) enables pervasive, ubiquitous, and seamless communication with the physical world. This paper investigates an optimal cross-layer optimization for WSN with periodic application. A joint energy efficient routing with minimum delay scheduling optimization model is proposed in this paper. The problem is formulated as an Integer Linear Program (ILP) model. The proposed ILP model has multi objectives cost function. The main objective of the proposed model is to maximize network lifetime and to minimize delay. The proposed ILP model represents the operation of Energy-Efficient Distributed Schedule-Based (EEDS) protocol. The ILP model is solved for different network configurations. The solution obtained by solving the proposed ILP model is compared with EEDS simulation results. Although the two solutions show similar behavior, the ILP solution outperforms the solution obtained by EEDS simulation by 28.3%. Moreover, the optimal solutions assuming different objectives are compared together.

Mathematical programming strategies for solving the minimum common string partition problem

Abstract The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover, on the basis of the integer linear programming model we develop a deterministic 2-phase heuristic which is applicable to larger problem instances. The results show that provenly optimal solutions can be obtained for problem instances of small and medium size from the literature by solving the proposed integer linear programming model with CPLEX. Furthermore, new best-known solutions are obtained for all considered problem instances from the literature. Concerning the heuristic, we were able to show that it outperforms heuristic competitors from the related literature.

An optimal dynamic resources partitioning auction model for virtual private networks

In this paper, we consider the problem of optimizing the Internet Service Provider (ISP) profit by providing a periodic Dynamic Partitioning (DP) model for utilizing network resources in the context of Virtual Private Networks (VPN). In literature, Complete Sharing (CS), Complete Partitioning (CP), and Bandwidth Borrowing (BR) techniques have been proposed for resource allocation where the following limitations can be noticed: VPN operators can exaggerate about their required resources, resources might be underutilized, and optimal bandwidth utilization is not guaranteed. To overcome the above limitations, we propose to dynamically partition the resources over different QoS classes through periodic auctions that can reduce the reasoning of exaggeration and maximize the ISP profit. Thus, we formulate our problem based on the Integer Linear Programming (ILP) that allows us to maximize the ISP profit and provides the optimal: (1) set of profitable VPN connections, (2) bandwidth division of each network link among QoS classes, and (3) routing scheme for the accepted demand. Furthermore, the proposed ILP model allows us to study the sensitivity of the ISP profit to a targeted revenue objective.

An Optimal Energy Efficient and Minimum Delay Scheduling for Periodic WSN Applications

Wireless Sensor Network (WSN) enables pervasive, ubiquitous, and seamless communication with the physical world. This paper investigates an optimal cross-layer joint routing and scheduling problem for WSN with periodic data collection. The problem is formulated as an Integer Linear Program (ILP) model such that a joint scheduling and routing is developed to maximize network lifetime and minimize delay. In this paper, an ILP model with multi objective cost function is proposed. The proposed ILP model represents the operation of Energy-Efficient Distributed Schedule-Based (EEDS) protocol. The ILP model is solved for different network configurations. The optimal solutions assuming different objectives are compared.

A simulated annealing algorithm for the job shop cell scheduling problem with intercellular moves and reentrant parts

This paper addresses the problem of scheduling parts in job shop cellular manufacturing systems by considering exceptional parts that need to visit machines in different cells and reentrant parts which need to visit some machines more than once in non-consecutive manner. Initially, an integer linear programming (ILP) model is presented for the problem to minimize the makespan, which considers intercellular moves and non-consecutive multiple processing of parts on a machine. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed to solve the problem. To increase the efficiency of the search algorithm, a neighborhood structure based on the concept of blocks is applied. Subsequently, the efficiency of the ILP model and the performance of the proposed SA are assessed over a set of problem instances taken from the literature. The proposed ILP model was coded in Lingo 8.0 and the solution obtained by the proposed SA was compared to the optimal values. The computational results demonstrate that the proposed ILP model and SA algorithm are effective and efficient for this problem.

Minimizing completion time with maintenance schedule in a manufacturing system

PurposeIn practical environments, machines subject to maintenance are prevalent in many production systems. This paper aims to find a schedule that minimizes the completion time (or equivalently, the total setup time) subject to maintenance and due dates.Design/methodology/approachAn efficient heuristic is presented to provide the near‐optimal solution for the problem. The performance of the heuristic is evaluated by comparing its solution with the optimal solution obtained from the integer linear programming model.FindingsIn many production systems, the sequence‐dependent setup time of a job cannot be ignored when a switch between two different jobs occurs. The paper studies the sequence‐dependent setup time problem with periodic maintenance, where several maintenances are required. Computational results show that problems with larger time interval and smaller maintaining time can produce a smaller completion time.Practical implicationsHere an efficient heuristic is developed to provide the near‐optimal schedule for the problem. The proposed integer linear programming model is also presented to provide the optimal schedule. However, the proposed heuristic and the integer linear programming model developed in the paper are appropriate for those companies where maintenance is performed periodically and the sequence‐dependent setup times of their jobs are required.Originality/valueThe paper presents the heuristic and the integer linear programming model to deal with sequencing and maintenance problems.

A chance constrained programming model for short-term liner ship fleet planning problems

This article deals with a short-term Liner Ship Fleet Planning (LSFP) problem with cargo shipment demand uncertainty for a single liner container shipping company. The cargo shipment demand uncertainty enables us to propose a chance constraint for each liner service route, which guarantees that the liner service route can satisfy the customers’ demand at least with a predetermined probability. Assuming that cargo shipment demand between any two ports on each liner service route is normally distributed, this article develops an integer linear programming model with chance constraints for the short-term LSFP problem. The proposed integer linear programming model can be efficiently solved by any optimization solver such as CPLEX. Finally, a numerical example is carried out to assess the model and analyze impact of the chance constraints and cargo shipment demand.

Uncovering signal transduction networks from high-throughput data by integer linear programming

Signal transduction is an important process that transmits signals from the outside of a cell to the inside to mediate sophisticated biological responses. Effective computational models to unravel such a process by taking advantage of high-throughput genomic and proteomic data are needed to understand the essential mechanisms underlying the signaling pathways. In this article, we propose a novel method for uncovering signal transduction networks (STNs) by integrating protein interaction with gene expression data. Specifically, we formulate STN identification problem as an integer linear programming (ILP) model, which can be actually solved by a relaxed linear programming algorithm and is flexible for handling various prior information without any restriction on the network structures. The numerical results on yeast MAPK signaling pathways demonstrate that the proposed ILP model is able to uncover STNs or pathways in an efficient and accurate manner. In particular, the prediction results are found to be in high agreement with current biological knowledge and available information in literature. In addition, the proposed model is simple to be interpreted and easy to be implemented even for a large-scale system.