Integrated Integer Linear Program Research Articles

Route Selection and Distribution Cost of Express Delivery: An Urban Metro Network Based Study

Route selection and distribution costs of express delivery based on the urban metro network, referred to as metro express delivery (MeD), is addressed in this study. Considering the characteristics of express delivery transportation and the complexity of the urban metro network, three distribution modes of different time periods are proposed and a strict integrated integer linear programming model is developed to minimize total distribution costs. To effectively solve the optimal problem, a standard genetic algorithm was improved and designed. Finally, the Ningbo subway network is used as an example to confirm the practicability and effectiveness of the model and algorithm. The results show that when the distribution number of express delivery packages is 1980, the three different MeD modes can reduce transportation costs by 40.5%, 62.0%, and 59.0%, respectively. The results of the case analysis will help guide express companies to collaborate with the urban metro network and choose the corresponding delivery mode according to the number of express deliveries required.

Service-oriented train timetabling with collaborative passenger flow control on an oversaturated metro line: An integer linear optimization approach

With the drastic increase of travel demands in urban areas, more and more metro lines are nowadays suffering from oversaturated situations, leading to the accumulation of passengers on platforms with potential accident risks. To further improve the service quality and reduce accident risks, this paper proposes an effective method for collaboratively optimizing the train timetable and accurate passenger flow control strategies on an oversaturated metro line. Through considering the dynamic characteristics of passenger flow, a rigorous integrated integer linear programming model is firstly formulated to minimize the total passenger waiting time at all of involved stations, in which the train timetable provides a service-oriented operation plan and optimal passenger flow control is imposed to avoid congestion on platforms within the transportation capacities. To solve the problem of interest efficiently, a hybrid algorithm, which combines an improved local search and CPLEX solver, is designed to search for high-quality solutions. Finally, two sets of numerical experiments, including a small-scale case and a real-world instance with operation data of the Beijing metro system, are implemented to demonstrate the performance and effectiveness of the proposed approaches.

Rescheduling through stop-skipping in dense railway systems

Based on the analysis of the railway system in the Paris region in France, this paper presents a rescheduling problem in which stops on train lines can be skipped and services are retimed to recover when limited disturbances occur. Indeed, in such mass transit systems, minor disturbances tend to propagate and generate larger delays through the shared use of resources, if no action is quickly taken. An integrated Integer Linear Programming model is presented whose objective function minimizes both the recovery time and the waiting time of passengers. Additional criteria related to the weighted number of train stops that are skipped are included in the objective function. Rolling-stock constraints are also taken into account to propose a feasible plan. Computational experiments on real data are conducted to show the impact of rescheduling decisions depending on key parameters such as the duration of the disturbances and the minimal turning time between trains. The trade-off between the different criteria in the objective function is also illustrated and discussed.

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

The integration of distribution and routing constitutes the Inventory Routing Problem (IRP), an important aspect of Vendor Managed Inventory (VMI) systems. IRP involves decisions on timing of deliveries, sizes of shipments and routing of vehicles. In the context of supply chain collaboration, the scope of IRP expands to include replenishments at the depot. This paper studies an IRP involving multiple products from different suppliers, a central depot (CD) and a set of warehouses. We develop an integrated Integer Linear Programming (ILP) model to determine the optimal replenishments from suppliers to the CD as well as the routing schedules of vehicles from CD to the multiple warehouses over the defined time horizon. We propose an extended three-phase heuristic called CARE (Clustering, Allocation, Routing -Extended). In the heuristic, the replenishment schedules, from suppliers to the CD (for multiple products in the defined time horizon), is solved using a dynamic programming (DP) model. The routing schedules of vehicles from CD to the multiple warehouses is then modeled and solved as a capacitated IRP (CIRP) problem. With the replenishment schedules as an input from the DP model, the CIRP is solved in three-phases: Cluster the nodes, Allocate to these nodes and Route delivery vehicles through clusters of nodes. Three variants of heuristics are proposed based on the changes to the routing phase – CARE1, CARE2, and CARE3. Computational results for a broad range of test instances yield promising results and show usefulness of the solution approaches. Particularly, the proposed heuristics outperformed CPLEX upper bounds for larger problems with lesser computational effort. The average improvement obtained by the heuristics over CPLEX upper bounds for 15 and 20 warehouse problems, respectively, are: CARE1 – 0.94% and 3.6%, CARE2 – 1.36% and 4.26%, CARE3 – 2.87% and 6.08%. We also show that the results from the proposed heuristic are statistically better than the CPLEX upper bounds. The proposed approaches can easily be implemented into existing VMI systems.

Design of Disaster-Resilient Optical Datacenter Networks

Survivability against disasters-both natural and deliberate attacks, and spanning large geographical areas-is becoming a major challenge in communication networks. Cloud services delivered by datacenter networks yield new opportunities to provide protection against disasters. Cloud services require a network substrate with high capacity, low latency, high availability, and low cost, which can be delivered by optical networks. In such networks, path protection against network failures is generally ensured by providing a backup path to the same destination (i.e., a datacenter), which is link-disjoint to the primary path. This protection fails to protect against disasters covering an area which disrupts both primary and backup paths. Also, protection against destination (datacenter) node failure is not ensured by a generic protection scheme. Moreover, content/service protection is a fundamental problem in a datacenter network, as the failure of a datacenter should not cause the disappearance of a specific content/service from the network. So content placement, routing, and protection of paths and content should be addressed together. In this work, we propose an integrated Integer Linear Program (ILP) to design an optical datacenter network, which solves the above-mentioned problems simultaneously. We show that our disaster protection scheme exploiting anycasting provides more protection, but uses less capacity than dedicated single-link failure protection. We show that a reasonable number of datacenters and selective content replicas with intelligent network design can provide survivability to disasters while supporting user demands. We also propose ILP relaxations and heuristics to solve the problem for large networks.

Design of fault tolerant wireless sensor networks satisfying survivability and lifetime requirements

Sensor networks are deployed to accomplish certain specific missions over a period of time. It is essential that the network continues to operate, even if some of its nodes fail. It is also important that the network is able to support the mission for a minimum specified period of time. Hence, the design of a sensor network should not only provide some guarantees that all data from the sensor nodes are gathered at the base station, even in the presence of some faults, but should also allow the network to remain functional for a specified duration. This paper considers a two-tier, hierarchical sensor network architecture, where some relay nodes, provisioned with higher power and other capabilities, are used as cluster heads. Given a distribution of sensor nodes in a sensor network, finding the locations to place a minimum number of relay nodes such that, each sensor node is covered by at least one relay node, is known to be a computationally difficult problem. In addition, for successful and reliable data communication, the relay nodes network needs to be connected, as well as resilient to node failures. In this paper, a novel integrated Integer Linear Program (ILP) formulation is proposed, which, unlike existing techniques, not only finds a suitable placement strategy for the relay nodes, but also assigns the sensor nodes to the clusters and determines a load-balanced routing scheme. Therefore, in addition to the desired levels of fault tolerance for both the sensor nodes and the relay nodes, the proposed approach also meets specified performance guarantees with respect to network lifetime by limiting the maximum energy consumption of the relay nodes.

Relay node placement with energy and buffer constraints in wireless sensor networks using mobile data collector

Higher-powered relay nodes, used as cluster heads in hierarchical sensor networks, can improve network performances. Most existing relay node placement strategies consider only stationary nodes, where data are routed to the base station(s), possibly using multiple hops. We consider a relay node based network, where a Mobile Data Collector (MDC) collects data from each relay node and delivers the collected data to the base station. This reduces the energy dissipation of the relay nodes by relieving them of the burden of transmitting data over longer distances. The issue is to find the minimum number of relay nodes, along with their locations, such that network coverage and lifetime requirements are satisfied. We present an integrated Integer Linear Program (ILP) formulation that determines an optimal relay node placement scheme, which ensures that there is no data loss due to buffer overflow and the energy dissipation does not exceed a specified level.

Synergistic execution of stream programs on multicores with accelerators

The StreamIt programming model has been proposed to exploit parallelism in streaming applications on general purpose multicore architectures. The StreamIt graphs describe task, data and pipeline parallelism which can be exploited on accelerators such as Graphics Processing Units (GPUs) or CellBE which support abundant parallelism in hardware. In this paper, we describe a novel method to orchestrate the execution of a StreamIt program on a multicore platform equipped with an accelerator. The proposed approach identifies, using profiling, the relative benefits of executing a task on the superscalar CPU cores and the accelerator. We formulate the problem of partitioning the work between the CPU cores and the GPU, taking into account the latencies for data transfers and the required buffer layout transformations associated with the partitioning, as an integrated Integer Linear Program (ILP) which can then be solved by an ILP solver.We also propose an efficient heuristic algorithm for the work partitioning between the CPU and the GPU, which provides solutions which are within 9.05% of the optimal solution on an average across the benchmark suite. The partitioned tasks are then software pipelined to execute on the multiple CPU cores and the Streaming Multiprocessors (SMs) of the GPU. The software pipelining algorithm orchestrates the execution between CPU cores and the GPU by emitting the code for the CPU and the GPU, and the code for the required data transfers. Our experiments on a platform with 8 CPU cores and a GeForce 8800 GTS 512 GPU show a geometric mean speedup of 6.84X with a maximum of 51.96X over a single threaded CPU execution across the StreamIt benchmarks. This is a 18.9% improvement over a partitioning strategy that maps only the filters that cannot be executed on the GPU -- the filters with state that is persistent across firings -- onto the CPU.

Software pipelining showdown

This paper is a scientific comparison of two code generation techniques with identical goals --- generation of the best possible software pipelined code for computers with instruction level parallelism. Both are variants of modulo scheduling , a framework for generation of software pipelines pioneered by Rau and Glaser [RaG181], but are otherwise quite dissimilar.One technique was developed at Silicon Graphics and is used in the MIPSpro compiler. This is the production compiler for SGI's systems which are based on the MIPS R8000 processor [Hsu94]. It is essentially a branch--and--bound enumeration of possible schedules with extensive pruning. This method is heuristic because of the way it prunes and also because of the interaction between register allocation and scheduling.The second technique aims to produce optimal results by formulating the scheduling and register allocation problem as an integrated integer linear programming ( ILP 1 ) problem. This idea has received much recent exposure in the literature [AlGoGa95, Feautrier94, GoAlGa94a, GoAlGa94b, Eichenberger95], but to our knowledge all previous implementations have been too preliminary for detailed measurement and evaluation. In particular, we believe this to be the first published measurement of runtime performance for ILP based generation of software pipelines.A particularly valuable result of this study was evaluation of the heuristic pipelining technology in the SGI compiler. One of the motivations behind the McGill research was the hope that optimal software pipelining, while not in itself practical for use in production compilers, would be useful for their evaluation and validation. Our comparison has indeed provided a quantitative validation of the SGI compiler's pipeliner, leading us to increased confidence in both techniques.