Showing papers on "Integer programming published in 2019"

A Cooperative Partial Computation Offloading Scheme for Mobile Edge Computing Enabled Internet of Things

Abstract: With the evolutionary development of latency sensitive applications, delay restriction is becoming an obstacle to run sophisticated applications on mobile devices. Partial computation offloading is promising to enable these applications to execute on mobile user equipments with low latency. However, most of the existing researches focus on either cloud computing or mobile edge computing (MEC) to offload tasks. In this paper, we comprehensively consider both of them and it is an early effort to study the cooperation of cloud computing and MEC in Internet of Things. We start from the single user computation offloading problem, where the MEC resources are not constrained. It can be solved by the branch and bound algorithm. Later on, the multiuser computation offloading problem is formulated as a mixed integer linear programming problem by considering resource competition among mobile users, which is NP-hard. Due to the computation complexity of the formulated problem, we design an iterative heuristic MEC resource allocation algorithm to make the offloading decision dynamically. Simulation results demonstrate that our algorithm outperforms the existing schemes in terms of execution latency and offloading efficiency.

Stochastic dual dynamic integer programming

Abstract: Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, such as nested Benders’ decomposition and its stochastic variant, stochastic dual dynamic programming (SDDP), which proceed by iteratively approximating these functions by cuts or linear inequalities, have been established as effective approaches. However, it is difficult to directly adapt these algorithms to MSIP due to the nonconvexity of integer programming value functions. In this paper we propose an extension to SDDP—called stochastic dual dynamic integer programming (SDDiP)—for solving MSIP problems with binary state variables. The crucial component of the algorithm is a new reformulation of the subproblems in each stage and a new class of cuts, termed Lagrangian cuts, derived from a Lagrangian relaxation of a specific reformulation of the subproblems in each stage, where local copies of state variables are introduced. We show that the Lagrangian cuts satisfy a tightness condition and provide a rigorous proof of the finite convergence of SDDiP with probability one. We show that, under fairly reasonable assumptions, an MSIP problem with general state variables can be approximated by one with binary state variables to desired precision with only a modest increase in problem size. Thus our proposed SDDiP approach is applicable to very general classes of MSIP problems. Extensive computational experiments on three classes of real-world problems, namely electric generation expansion, financial portfolio management, and network revenue management, show that the proposed methodology is very effective in solving large-scale multistage stochastic integer optimization problems.

The zwicky transient facility: Surveys and scheduler

Abstract: We present a novel algorithm for scheduling the observations of time-domain imaging surveys. Our integer linear programming approach optimizes an observing plan for an entire night by assigning targets to temporal blocks, enabling strict control of the number of exposures obtained per field and minimizing filter changes. A subsequent optimization step minimizes slew times between each observation. Our optimization metric self-consistently weights contributions from time-varying airmass, seeing, and sky brightness to maximize the transient discovery rate. We describe the implementation of this algorithm on the surveys of the Zwicky Transient Facility and present its on-sky performance.

Energy Systems Integration in Smart Districts: Robust Optimisation of Multi-Energy Flows in Integrated Electricity, Heat and Gas Networks

Abstract: Smart districts can provide flexibility from emerging distributed multi-energy technologies, thus bringing benefits to the district and the wider energy system. However, due to nonlinearity and modeling complexity, constraints associated with the internal energy network (e.g., electricity, heat, and gas) and operational uncertainties (for example, in energy demand) are often overlooked. For this purpose, a robust operational optimization framework for smart districts with multi-energy devices and integrated energy networks is proposed. The framework is based on two-stage iterative modeling that involves mixed integer linear programming (MILP) and linear approximations of the nonlinear network equations. In the MILP optimization stage, the time-ahead set points of all controllable devices (e.g., electrical and thermal storage) are optimized considering uncertainty and a linear approximation of the integrated electricity, heat, and gas networks. The accuracy of the linear model is then improved at a second stage by using a detailed nonlinear integrated network model, and through iterations between the models in the two stages. To efficiently model uncertainty and improve computational efficiency, multi-dimensional linked lists are also used. The proposed approach is illustrated with a real U.K. district; the results demonstrate the model’s ability to capture network limits and uncertainty, which is critical to assess flexibility under stressed conditions.

Efficient Search for Diverse Coherent Explanations

Abstract: This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed polytope" and show how this can be used with an integer programming solver to efficiently find coherent counterfactual explanations i.e. solutions that are guaranteed to map back onto the underlying data structure, while avoiding the need for brute-force enumeration. We also look at the problem of diverse explanations and show how these can be generated within our framework.

Joint Energy Efficient and QoS-Aware Path Allocation and VNF Placement for Service Function Chaining

Abstract: Service function chaining (SFC) allows the forwarding of traffic flows along a chain of virtual network functions (VNFs). Software defined networking (SDN) solutions can be used to support SFC to reduce both the management complexity and the operational costs. One of the most critical issues for the service and network providers is the reduction of energy consumption, which should be achieved without impacting the Quality of Service. In this paper, we propose a novel resource allocation architecture which enables energy-aware SFC for SDN-based networks, considering also constraints on delay, link utilization, server utilization. To this end, we formulate the problems of VNF placement, allocation of VNFs to flows, and flow routing as integer linear programming (ILP) optimization problems. Since the formulated problems cannot be solved (using ILP solvers) in acceptable timescales for realistic problem dimensions, we design a set of heuristic to find near-optimal solutions in timescales suitable for practical applications. We numerically evaluate the performance of the proposed algorithms over a real-world topology under various network traffic patterns. Our results confirm that the proposed heuristic algorithms provide near-optimal solutions (at most 14% optimality-gap) while their execution time makes them usable for real-life networks.

Optimized Energy Aware 5G Network Function Virtualization

Abstract: In this paper, network function virtualization (NVF) is identified as a promising key technology that can contribute to energy-efficiency improvement in 5G networks. An optical network supported architecture is proposed and investigated in this work to provide the wired infrastructure needed in 5G networks and to support NFV towards an energy efficient 5G network. In this architecture the mobile core network functions as well as baseband function are virtualized and provided as VMs. The impact of the total number of active users in the network, backhaul/fronthaul configurations and VM inter-traffic are investigated. A mixed integer linear programming (MILP) optimization model is developed with the objective of minimizing the total power consumption by optimizing the VMs location and VMs servers’ utilization. The MILP model results show that virtualization can result in up to 38% (average 34%) energy saving. The results also reveal how the total number of active users affects the baseband virtual machines (BBUVMs) optimal distribution whilst the core network virtual machines (CNVMs) distribution is affected mainly by the inter-traffic between the VMs. For real-time implementation, two heuristics are developed, an Energy Efficient NFV without CNVMs inter-traffic (EENFVnoITr) heuristic and an Energy Efficient NFV with CNVMs inter-traffic (EENFVwithITr) heuristic, both produce comparable results to the optimal MILP results. Finally, a Genetic algorithm is developed for further verification of the results.

Automatic reconstruction of fully volumetric 3D building models from oriented point clouds

Abstract: We present a novel method for reconstructing parametric, volumetric, multi-story building models from unstructured, unfiltered indoor point clouds with oriented normals by means of solving an integer linear optimization problem. Our approach overcomes limitations of previous methods in several ways: First, we drop assumptions about the input data such as the availability of separate scans as an initial room segmentation. Instead, a fully automatic room segmentation and outlier removal is performed on the unstructured point clouds. Second, restricting the solution space of our optimization approach to arrangements of volumetric wall entities representing the structure of a building enforces a consistent model of volumetric, interconnected walls fitted to the observed data instead of unconnected, paper-thin surfaces. Third, we formulate the optimization as an integer linear programming problem which allows for an exact solution instead of the approximations achieved with most previous techniques. Lastly, our optimization approach is designed to incorporate hard constraints which were difficult or even impossible to integrate before. We evaluate and demonstrate the capabilities of our proposed approach on a variety of complex real-world point clouds.

A Deep Learning-Based Approach to Power Minimization in Multi-Carrier NOMA With SWIPT

Abstract: Simultaneous wireless information and power transfer (SWIPT) and multi-carrier non-orthogonal multiple access (MC-NOMA) are promising technologies for future fifth generation and beyond wireless networks due to their potential capabilities in energy-efficient and spectrum-efficient system designs, respectively. In this paper, the joint downlink resource allocation problem for a SWIPT-enabled MC-NOMA system with time switching-based receivers is investigated, where pattern division multiple access (PDMA) technique is employed. We focus on minimizing the total transmit power of the system while satisfying the quality-of-service requirements of each user in terms of data rate and harvested power. The corresponding optimization problem is a non-convex and a mixed integer programming problem which is difficult to solve. Different from the conventional iterative searching-based algorithms, we propose an efficient deep learning-based approach to determine an approximated optimal solution. Specifically, we employ a typical class of deep learning model, namely, deep belief network (DBN), where the detailed procedure of the developed approach consists of three parts, i.e., data preparation, training, and running. The simulation results demonstrate that the proposed DBN-based approach can achieve similar performance of power consumption to the exhaustive search method. Furthermore, the results also confirm that MC-NOMA with PDMA outperforms MC-NOMA with sparse code multiple access, single-carrier non-orthogonal multiple access, and orthogonal frequency division multiple access in terms of power consumption in SWIPT-enabled systems.

Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

Abstract: Unit commitment (UC) is a key operational problem in power systems for the optimal schedule of daily generation commitment. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning horizon is decided before the uncertainty is realized, or a multistage stochastic programming model with relatively small scenario trees to ensure tractability. We propose a new type of decomposition algorithm, based on the recently proposed framework of stochastic dual dynamic integer programming (SDDiP), to solve the multistage stochastic unit commitment (MSUC) problem. We propose a variety of computational enhancements to SDDiP, and conduct systematic and extensive computational experiments to demonstrate that the proposed method is able to handle elaborate stochastic processes and can solve MSUCs with a huge number of scenarios that are impossible to handle by existing methods.

Day-Ahead Dispatch of Integrated Electricity and Natural Gas System Considering Reserve Scheduling and Renewable Uncertainties

Abstract: For secure operation of integrated electricity and natural gas system (IEGS), reserve is a useful support to manage renewable uncertainties and N − 1 contingencies. Thus, a day-ahead economic dispatch model of IEGS with reserve scheduling is presented in this paper. Considering the uncertainty of gas flow direction, a novel second-order cone (SOC) relaxation of Weymouth equation is designed to address the nonconvexity. Then, the proposed robust nonconvex model is mathematically transformed into a solvable mixed integer second-order cone programming (MISOCP) problem. To guarantee the tightness of SOC relaxation and achieve accurate dispatch solutions, MISOCP results are corrected accordingly by the multi-slack-node gas flow calculation with the Newton–Raphson method. Numerical cases are performed on IEEE 39-bus-15-node and IEEE 118-bus-40-node test IEGSs, demonstrating the proposed approach is feasible and effective for exact IEGS day-ahead dispatch and the proposed MISOCP model can provide a more economic dispatch solution with a shorter computational time than conventional MISOCP and mixed integer linear programming (MILP) models.

A branch-and-price algorithm for the heterogeneous fleet green vehicle routing problem with time windows

Abstract: Heterogeneous fleet vehicles can be used to reduce carbon emissions. We propose an improved branch-and-price (BAP) algorithm to precisely solve the heterogeneous fleet green vehicle routing problem with time windows (HFGVRPTW). In the improved BAP, to speed up the solution for the pricing problem, we develop a multi-vehicle approximate dynamic programming (MVADP) algorithm that is based on the labeling algorithm. The MVADP algorithm reduces labels by integrating the calculation of pricing problems for all vehicle types. In addition, to rapidly obtain a tighter upper bound, we propose an integer branch method. For each branch, we solve the master problem with the integer constraint by the CPLEX solver using the columns produced by column generation. We retain the smaller of the obtained integer solution and the current upper bound, and the branches are thus reduced significantly. Extensive computational experiments were performed on the Solomon benchmark instances. The results show that the branches and computational time were reduced significantly by the improved BAP algorithm.

Optimal Economic Schedule for a Network of Microgrids With Hybrid Energy Storage System Using Distributed Model Predictive Control

Abstract: In this paper, an optimal procedure for the economic schedule of a network of interconnected microgrids with hybrid energy storage system is carried out through a control algorithm based on distributed model predictive control (DMPC). The algorithm is specifically designed according to the criterion of improving the cost function of each microgrid acting as a single system through the network mode operation. The algorithm allows maximum economical benefit of the microgrids, minimizing the degradation causes of each storage system, and fulfilling the different system constraints. In order to capture both continuous/discrete dynamics and switching between different operating conditions, the plant is modeled with the framework of mixed logic dynamic. The DMPC problem is solved with the use of mixed integer linear programming using a piecewise formulation, in order to linearize a mixed integer quadratic programming problem.

Learning optimal classification trees using a binary linear program formulation (extended abstract)

Abstract: We provide a new formulation for the problem of learning the optimal classification tree of a given depth as a binary linear program. A limitation of previously proposed Mathematical Optimization formulations is that they create constraints and variables for every row in the training data. As a result, the running time of the existing Integer Linear programming (ILP) formulations increases dramatically with the size of data. In our new binary formulation, we aim to circumvent this problem by making the formulation size largely independent from the training data size. We show experimentally that our formulation achieves better performance than existing formulations on both small and large problem instances within shorter running time.

An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System

Abstract: In this paper, the mixed integer linear programming (MILP) for solving unit commitment (UC) problems in a hybrid power system containing thermal, hydro, and wind power have been studied. To promote its efficiency, an improved MILP approach has been proposed, while the symmetric problem in MILP formulas has been solved by reforming hierarchical constraints. Experiments on different scales have been conducted to demonstrate the effectiveness of the proposed approach. The results indicate a dramatic efficiency promotion compared to other popular MILP approaches in large scale power systems. Additionally, the proposed approach has been applied in UC problems of the hybrid power system. Two indexes, fluctuation degree and output degree, have been proposed to investigate the performance of renewable energy sources (RES). Several experiments are also implemented and the results show that the integration of pumped hydroelectric energy storage (PHES) can decrease the output of thermal units, as well as balance wind power fluctuation according to the load demand.

The Zwicky Transient Facility: Surveys and Scheduler

Abstract: We present a novel algorithm for scheduling the observations of time-domain imaging surveys. Our Integer Linear Programming approach optimizes an observing plan for an entire night by assigning targets to temporal blocks, enabling strict control of the number of exposures obtained per field and minimizing filter changes. A subsequent optimization step minimizes slew times between each observation. Our optimization metric self-consistently weights contributions from time-varying airmass, seeing, and sky brightness to maximize the transient discovery rate. We describe the implementation of this algorithm on the surveys of the Zwicky Transient Facility and present its on-sky performance.

User Association and Path Planning for UAV-Aided Mobile Edge Computing With Energy Restriction

Abstract: Mobile edge computing (MEC) provides computational services at the edge of networks by offloading tasks from user equipments (UEs). This letter employs an unmanned aerial vehicle (UAV) as the edge computing server to execute offloaded tasks from the ground UEs. We jointly optimize user association, UAV trajectory, and uploading power of each UE to maximize sum bits offloaded from all UEs to the UAV, subject to energy constraint of the UAV and quality of service (QoS) of each UE. To address the non-convex optimization problem, we first decompose it into three subproblems that are solved with integer programming and successive convex optimization methods respectively. Then, we tackle the overall problem by the multi-variable iterative optimization algorithm. Simulations show that the proposed algorithm can achieve a better performance than other baseline schemes.