Mixed-integer Programming Problem Research Articles

DRL-Based Offloading for Computation Delay Minimization in Wireless-Powered Multi-Access Edge Computing

Wireless power transfer (WPT) and edge computing have been validated as effective ways to solve the energy-limited problem and computation-capacity-limited problem of wireless devices (WDs), respectively. This paper studies the wireless-powered multi-access edge computing (WP-MEC) network, where WDs conduct either local computing or task offloading for their individable computation tasks. We aim to minimize total computation delay (TCD) when each WD has a computation task to execute, referred to as the total computation delay minimization (TCDM) problem, by jointly optimizing the offloading-decision, WPT duration, and transmission durations of offloading WDs. The TCDM problem is a mixed integer programming (MIP) problem that is challenging to efficiently obtain the optimal or near-optimal solution. To tackle this challenge, we decompose the TCDM problem into the sub-problem of optimizing the WPT duration and transmission durations, and the top-problem of optimizing the offloading decision. For the nonconvex sub-problem, we design a worst-WD-adjusting (WDA) algorithm to efficiently obtain its optimal solution. For the top-problem, under the time-varying channel conditions, traditional optimization methods are hard to determine the optimal or near-optimal offloading decision within the channel coherence duration. To fast obtain the near-optimal offloading decision, we propose a deep neural networks (DNN)-based deep reinforcement learning (DRL) model, which takes the sub-problem solving as one component for utility evaluation. Finally, numerical results demonstrate that the proposed online DRL-based offloading algorithm achieves the near-minimal TCD with low computational complexity, and is suitable for the fast-fading WP-MEC network.

Optimal constellation design based on satellite ground tracks for Earth observation missions

In this study, we propose an optimal constellation determination method for Earth observation satellites. First, orbit requirements for the interferometric synthetic aperture radar (InSAR) observation are mathematically formulated. From these requirements, we can obtain nadir trajectories (ground tracks) of the chief satellites of the constellation. The optimal constellation determination problem is modeled as a multi-objective mixed integer programming problem. Then, a metaheuristic optimization method is applied to the resultant problem to optimize the number and configuration of satellite ground tracks and orbital planes. The proposed method enables us to design optimal satellite constellation configurations according to the mission conditions such as the observation area and the acceptable altitude range.

Distributed Graph-Based Optimization of Multicast Data Dissemination for Internet of Vehicles

The Internet of Vehicles (IoV) is a promising paradigm for autonomous driving, where the sensing data from the onboard sensors can be disseminated and processed cooperatively via vehicle-to-vehicle links. Autonomous vehicles can share their local views for cooperative, reliable, and robust driving decisions. However, the limited wireless resources may become the bottleneck with the increasing number of vehicles. The technical challenges also arise from the decentralized control, the spatial couplings of decisions, and the complexity of combinatorial optimization. This paper proposes a novel fully distributed graph-based approach to jointly optimize multicast link establishment with data dissemination and processing decisions by only exchanging partial information among neighboring vehicles. The mixed-integer programming problem aims to maximize system energy efficiency while achieving maximum data throughput. We prove that maximizing data processing throughput is submodular optimization to find the local optimum efficiently. The optimization of data dissemination and processing is reformulated to a minimum-cost maximum-flow problem in a three-layer graph, and efficiently solved by exploiting the graphical interdependence. Both simulation-generated and trace-based datasets are evaluated to validate the effectiveness of the proposed approach in terms of data throughput and energy efficiency.

A novel deep policy gradient action quantization for trusted collaborative computation in intelligent vehicle networks

The openness of the intelligent vehicle network makes it easy for selfish or untrustworthy vehicles to maliciously occupy limited resources in the mobile edge network or spread malicious information. However, most of the existing trust models rely on evaluating vehicles or data at the application level. For selfish or forgery attacks in intelligent vehicle networks, we propose a trusted deep reinforcement learning (DRL) cybersecurity approach for computation offloading to evaluate the safety and reliability performance in IoT edge networks, including our intelligent system model and a Deep Policy Gradient Action Quantization (DPGAQ) scheme. By introducing a reputation record table and designing a highly decisive communication trusted computing mode, we can accurately predict the untrusted selfish attack of vehicle in the task offloading of the Internet of things. Furthermore, in the multi-vehicle scenario, because the trusted offloading decision is a mixed integer programming problem, which leads to the dimension explosion of channel state and space, we propose a joint action-value quantization with attention mechanism to approximate the continuous actions values to a limited number of discrete values. Because it is not only inefficient but also unnecessary to generate high-dimensional decision actions in each time frame, we prune the infeasible action decisions by order preserving pruning to reduce the computational complexity of training and achieve efficient training on the premise of ensuring accuracy. To verify the feasibility and effectiveness of our proposed algorithm, millions of channels of edge vehicle networks are used as the input data. The simulation results show that compared with the benchmark trust model, DPGAQ achieves more than 72% reputation level, and improves 11%, 10% and 11% respectively in precision, recall and F-score.

Sum Rate Optimization Scheme of UAV-Assisted NOMA under Hardware Impairments

In the unmanned aerial vehicle (UAV) assisted non-orthogonal multiple access (NOMA) networks, the practical hardware impairments (HIs) and resource allocation is still a challenging problem. Most existing research on resource allocation algorithms for UAV communication is considered with the ideal hardware condition. However, the impact of HIs on system performance cannot be ignored, especially in the case of high bit rates. Considering the HIs, most studies are from the perspective of performance analysis. The resource allocation of UAV relay-assisted NOMA systems is investigated in this paper with HIs. We aim to maximize the sum rate by jointly optimizing the deployment of UAV and transmit power. To address this problem, we first transformed the mixed integer programming problem (MIPP) into a standard convex optimization problem based on successive convex approximation (SCA) technology. Then, we introduced the Lagrangian dual transformation and quadratic transform methods to solve the power allocation problem. Finally, we propose an effective iterative algorithm to achieve an approximate optimal solution. Numerical results demonstrate that the proposed algorithm achieved better performance in terms of the sum rate compared with other benchmark schemes.

SWHORD simulator: A platform to evaluate energy transition targets in future energy systems with increasing renewable generation, electric vehicles, storage technologies, and hydrogen systems

This paper presents the simulation platform SWHORD, specially designed for the analysis of future energy systems under energy transition targets. The model is implemented in GAMS as a cost minimization mixed integer programming problem of a hydro-thermal power system, which includes high penetration of non-dispatchable renewable generation, storage technologies, electric vehicles, and hydrogen systems. Simulations are performed on an hourly basis for one year of operation, enabling the evaluation of both short-term dynamics and the seasonal behaviour of the system and including the hourly power generation profile by technology, fuel and emission costs, CO2 emissions and storage levels, as well as the renewable curtailment needed to balance the system. The model was validated by backtesting with historical data of the Portuguese power system and, from a comprehensive statistical analysis of the dispatchable generation, it is concluded that the simulation results present a good fit with the real data. An illustrative use case is presented to evaluate the consistency of the Portuguese targets for 2030. Simulation results put in evidence the advantages of the SWHORD simulator to study the complex interactions among the new drivers of future energy systems, such as electric vehicles, storage technologies, and hydrogen systems.

UAV-assisted multi-tier computing framework for IoT networks

Next-generation wireless networks are expected to support a massive amount of Internet of Things (IoT) devices in delivering a wide range of novel resource-intensive applications. IoT devices, despite their enhanced capabilities, fall short of meeting the computational requirements of these applications within a strict deadline. This paper leverages a hierarchical computational model where IoT devices offload their computational tasks to a number of unmanned aerial vehicles (UAVs) that can be deployed in a way to establish strong line-of-sight links. Being equipped with computational resources, UAVs process part of the tasks within the set time threshold while the other tasks are transferred to edge and cloud servers for potential processing. This work aims at optimizing the number and position of deployed UAVs, IoT-to-UAV association, resource allocation, and task offloading to UAVs, edge servers, and the cloud, while ensuring various system constraints. The problem is formulated as a mixed integer programming problem and solved using successive convex approximation. An efficient solution is then proposed to decompose the main problem into two subproblems that are solved iteratively. The first subproblem minimizes the number of IoT clusters and positions a UAV to serve each cluster while the second subproblem maximizes the percentage of admitted tasks using the resulting number of UAVs determined by the first subproblem. As long as not all devices are fully served, an additional UAV is introduced and the two subproblems are solved repeatedly. The proposed decomposition solution has been evaluated as a function of various system parameters and application use cases to show optimized performance and high scalability.

Channel capacity and power allocation of MIMO visible light communication system

In this paper, the channel capacity of the multiple-input multiple-output (MIMO) visible light communication (VLC) system is investigated under the peak, average optical and electrical power constraints. Finding the channel capacity of MIMO VLC is shown to be a mixed integer programming problem. To address this open problem, we propose an inexact gradient projection method to find the channel capacity-achieving discrete input distribution and the channel capacity of MIMO VLC. Also we derive both upper and lower bounds of the capacity of MIMO VLC with the closed-form expressions. Furthermore, by considering practical discrete constellation inputs, we develop the optimal power allocation scheme to maximize transmission rate of MIMO VLC system. Simulation results show that more discrete points are needed to achieve the channel capacity as SNR increases. Both the upper and lower bounds of channel capacity are tight at low SNR region. In addition, comparing the equal power allocation, the proposed power allocation scheme can significantly increase the rate for the low-order modulation inputs.

Digital twin-assisted knowledge distillation framework for heterogeneous federated learning

In this paper, to deal with the heterogeneity in federated learning (FL) systems, a knowledge distillation (KD) driven training framework for FL is proposed, where each user can select its neural network model on demand and distill knowledge from a big teacher model using its own private dataset. To overcome the challenge of train the big teacher model in resource limited user devices, the digital twin (DT) is exploit in the way that the teacher model can be trained at DT located in the server with enough computing resources. Then, during model distillation, each user can update the parameters of its model at either the physical entity or the digital agent. The joint problem of model selection and training offloading and resource allocation for users is formulated as a mixed integer programming (MIP) problem. To solve the problem, Q-learning and optimization are jointly used, where Q-learning selects models for users and determines whether to train locally or on the server, and optimization is used to allocate resources for users based on the output of Q-learning. Simulation results show the proposed DT-assisted KD framework and joint optimization method can significantly improve the average accuracy of users while reducing the total delay.

Grouped variable selection with discrete optimization: Computational and statistical perspectives

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the ℓ0-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with smooth components. Our algorithmic framework consists of approximate and exact algorithms. The approximate algorithms are based on coordinate descent and local search, with runtimes comparable to popular sparse learning algorithms. Our exact algorithm is based on a standalone branch-and-bound (BnB) framework, which can solve the associated mixed integer programming (MIP) problem to certified optimality. By exploiting the problem structure, our custom BnB algorithm can solve to optimality problem instances with 5×106 features and 103 observations in minutes to hours—over 1000 times larger than what is currently possible using state-of-the-art commercial MIP solvers. We also explore statistical properties of the ℓ0-based estimators. We demonstrate, theoretically and empirically, that our proposed estimators have an edge over popular group-sparse estimators in terms of statistical performance in various regimes. We provide an open source implementation of our proposed framework.

Joint Training and Resource Allocation Optimization for Federated Learning in UAV Swarm

Unmanned aerial vehicles (UAVs) have been widely used to perform search and tracking tasks in military and civil fields. To perform these tasks autonomously, a swarm of multiple UAVs need to be endowed with intelligence through machine learning (ML). However, the traditional centralized ML cannot be directly applied in UAV networks, since it is challenging to transmit raw data with limited bandwidth and energy budget. As a distributed manner, federated learning (FL) is more suitable for UAV networks than traditional ML schemes in order to boost edge intelligence for UAVs. Considering the limited energy supply of UAVs, we study how to minimize UAVs’ overall training energy consumption by jointly optimizing the local convergence threshold, local iterations, computation resource allocation, and bandwidth allocation, subject to the FL global accuracy guarantee and maximum training latency constraint. The formulated nonconvex mixed-integer programming problem is solved by a joint training and resource allocation optimization algorithm. In addition, we also study how to solve the problem considering fairness among different UAVs by changing the objective to minimizing the maximum energy consumption of UAVs, and extend the aforementioned approach to this problem. Our simulation results show that while satisfying both the training accuracy and latency constraints, the proposed algorithm can reduce more UAVs’ overall training energy consumption and the maximum energy consumption in the UAV swarm than four baseline schemes.

Joint Deployment and Resource Management for VLC-Enabled RISs-Assisted UAV Networks

In this paper, the problem of the deployment and resource management for visible light communication (VLC)-enabled, reconfigurable intelligent surfaces (RISs)-assisted unmanned aerial vehicle (UAV) networks is investigated. In the considered model, UAVs provide terrestrial users with wireless services and illumination simultaneously. Moreover, RISs are utilized to further improve the channel quality between UAVs and users. This joint placement and resource management problem is constructed aiming at acquiring the optimal UAV deployment, RISs phase shift, user and RIS association that satisfies the users’ needs with minimum consumption of the UAVs’ energy. An iterative algorithm that alternately optimizes continuous and binary variables is proposed to solve this mixed-integer programming problem. Specifically, RISs phase shift optimization is solved by phases alignment method and semidefinite program algorithm. Next, the successive convex approximation algorithm is proposed to settle the UAV deployment problem. The user and RIS association variables are relaxed to the continuous ones before adopting the dual method to find the optimal solution. Moreover, a greedy algorithm is proposed as an alternative to RIS association optimization with low complexity. Simulation results show that the proposed two schemes harvest the superior performance of 34.85% and 32.11% energy consumption reduction over the case without RIS, respectively.

The Evaluation and Improvement of the Production Processes of an Automotive Industry Company via Simulation and Optimization

Production delays are significant problems for the loss of goodwill of the customers and the loss of profits associated with them. The delays may accrue as a result of insufficient resource planning and poorly designed unsatisfactory procedures. In this study, a new mathematical model is proposed to optimize the production processes by minimizing production delays, and a simulation model is developed to test the alternative facility designs. The purpose is to increase customer satisfaction by ensuring that the products are delivered timely and preventing lost sales in an automotive company that manufactures garbage collectors by using real data. The mixed-integer programming problem related to the minimization of production delays is solved by the GAMS CPLEX 24.1.3 software. In this way, the total delay in the production area is minimized by the mathematical model to prevent labor and time loss. Accordingly, the alternative designs are investigated for the improvement of the production processes by using discrete system simulation. A system analysis is performed to determine the bottlenecks in the production processes by developing a simulation model via the ARENA simulation software. With the proposed facility layout alternatives, the delays are eliminated, the total production time is reduced, and an increase in production efficiency is observed.

Optimal voyage scheduling of all-electric ships considering underwater radiated noise

Underwater radiated noise (URN) emanating from ships can adversely impact the life functions of certain marine mammals that rely on sound to navigate, communicate, and locate prey. This paper formulates an optimal voyage scheduling problem to mitigate the impact of URN on sensitive marine species by choosing amongst different possible paths and specifying the cruising speed along the selected path. We focus on all-electric ships (AESs) owing to their greater flexibility for speed regulation by coordinating an integrated power system. The proposed optimization model schedules generators and energy storage devices toward minimizing the operation cost while satisfying constraints pertinent to URN levels and atmospheric greenhouse gas (GHG) emissions, the electric power network and operational limits, and expected voyage timelines, culminating in a mixed-integer nonlinear programming problem. To promote computational tractability, we approximate the nonlinear relationships for URN, propulsion load, and fuel consumption with piecewise linear functions. This leads to a mixed-integer second-order cone programming problem, which enables convergence to the global optimum and computationally efficient solutions. We illustrate the effectiveness of the proposed model in curbing URN levels and GHG emissions with numerical case studies involving an 18-node ship test system.

Scheduling Advertising on Cable Television

Scheduling Advertising on Cable Television Advertisement scheduling is a daily essential operational process in the television business. Efficient distribution of viewers among advertisers allows the television network to satisfy contracts and increase ad sale revenues. Ad scheduling is a challenging multiperiod, mixed-integer programming problem in which the network must create schedules to meet advertisers’ campaign goals and maximize ad revenues. Each campaign must meet a specific target group of viewers and a unique set of constraints. Moreover, the number of viewers is uncertain. To solve this problem, S. Souyris, S. Seshadri, and S. Subramanian develop and implement a practical approach that combines mathematical programming and machine learning to create daily schedules. According to standard business metrics and the small integer programming gap, these schedules are of high quality. Using their methods, leading networks in the United States and India experience a 3% to 5% revenue increase, which translates to about $60 million annually for one prominent user.

Cost-Aware DU Placement and Flow Routing in 5G Packet xHaul Networks

Packet-switched xHaul networks based on Ethernet technology are considered a promising solution for assuring convergent, cost-effective transport of diverse radio data traffic flows in dense 5G radio access networks (RANs). A challenging optimization problem in such networks is the placement of distributed processing units (DUs), which realize a subset of virtualized baseband processing functions on general-purpose processors at selected processing pool (PP) facilities. The DU placement involves the problem of routing of related fronthaul and midhaul data flows between network nodes. In this work, we focus on developing optimization methods for joint placement of DUs and routing of flows with the goal to minimize the overall cost of PPs activation and processing in the network, which we refer to as the PPC-DUP-FR problem. We account for limited processing and transmission resources as well as for stringent latency requirements of data flows in 5G RAN. The latency constraint makes the problem particularly difficult in a packet-switched xHaul network since it involves the non-linear and dynamic estimation of the latencies caused by buffering of packets in the switches. The latency model that we apply in this work is based on worst-case calculations with improved latency estimations that skip from processing the co-routed, but non-affecting flows. We use a mixed-integer programming (MIP) approach to formulate and solve the PPC-DUP-FR optimization problem. Moreover, we develop a heuristic method that provides optimized solutions to larger PPC-DUP-FR problem instances, which are too complex for the MIP method. Numerical experiments performed in different network scenarios indicate on the effectiveness of the heuristic in solving the PPC-DUP-FR problem. In particular, the heuristic achieves up to 63% better results than MIP (at the MIP optimality gap equal to 76%) in a medium-size mesh network, in which the MIP problem is unsolvable for higher traffic demands within reasonable runtime limits. In larger networks, MIP is able to provide some results only for the PPC-DUP-FR problem instances with very low traffic demands, whereas the solutions generated by the heuristic are at least 83% better than the ones achieved with MIP. Also, the analysis performed shows a significant impact of the PP cost factors considered and of the level of cost differentiation of PP nodes on the overall PP cost in the network. Finally, simulation results of a case-study packet xHaul network confirm the correctness of the latency model used.

Array Scheduling With Power and Bandwidth Allocation for Simultaneous Multibeam Tracking Low-Angle Targets in a VHF-MIMO Radar

The very high frequency (VHF) radar suffers from the multipath interference and false alarms when tracking low-angle targets. The co-located multiple-input multiple-output (MIMO) radar technique can mitigate these adverse effects with waveform diversity. However, the limited resources restrict the potential of the VHF-MIMO radar. In this paper, an array scheduling with power and bandwidth allocation (ASPBA) strategy is proposed for the VHF-MIMO radar tracking low-angle targets. The predicted posterior Cramér-Rao lower bound (PCRLB) under the multipath interference and measurement origin uncertainty (MOU) effects is derived to serve as the optimization metric. The measurement amplitude information (AI) is incorporated into the PCRLB to facilitate target detection and tracking. It is shown that the ASPBA problem is a mixed integer programming and NP-hard problem, where the array, power, and bandwidth allocation variables are both coupled in the objective and constraints. An efficient three-stage-based solution is proposed for problem-solving. The approximated relationship among three variables is derived using Hölder's inequality, and an auxiliary variable is introduced to describe the array contribution. Thereby, the array scheduling is determined by a heuristic rounding algorithm, and the power and bandwidth allocation are achieved using the approximated relationship. Simulation results confirm the effectiveness and efficiency of the proposed ASPBA strategy, compared with state-of-the-art algorithms. It is also shown that the target height is a main factor that influences the resource allocation results in the low-angle tracking scenario.

Optimal Micro-PMU Placement for Improving State Estimation Accuracy via Mixed-integer Semidefinite Programming

Micro-phasor measurement units (µPMUs) with a micro-second resolution and milli-degree accuracy capability are expected to play an important role in improving the state estimation accuracy in the distribution network with increasing penetration of distributed generations. Therefore, this paper investigates the problem of how to place a limited number of µPMUs to improve the state estimation accuracy. Combined with pseudo-measurements and supervisory control and data acquisition (SCADA) measurements, an optimal µPMU placement model is proposed based on a two-step state estimation method. The E-optimal experimental criterion is utilized to measure the state estimation accuracy. The nonlinear optimization problem is transformed into a mixed-integer semidefinite programming (MISDP) problem, whose optimal solution can be obtained by using the improved Benders decomposition method. Simulations on several systems are carried out to evaluate the effective performance of the proposed model.

A unit commitment based-co-optimization of generation and transmission expansion planning to mitigate market power

• A unit-commitment-based generation and transmission expansion planning model is proposed. • The planning problem is subject to the market power's constraint. • The scenario-based model is structured as a mixed-integer bi-level programming (MIBP). • The lower-level problem computes the must-run generation (MRG) as a market index. • An exact algorithm using the reformulation-and-decomposition technique is utilized to attain the optimal solution. This paper aims to construct a novel strategy for coordinated generation and transmission expansion planning (CGTEP) considering market power. The integrated model constitutes bi-level programming from a centralized planning point of view. The upper level seeks to minimize the investment and operation cost subject to technical constraints, while the lower level's objective is to mitigate the market power. A stochastic unit commitment-based approach is employed at the upper level to find the least-cost solution and at the lower level to minimize the transmission-constrained market power index. Since the lower level contains integer variables, it is impossible to utilize the Karush-Kuhn-Tucker (KKT) conditions or duality theory (DT) to convert the bi-level problem into a single level. Hence, an exact algorithm using the reformulation-and-decomposition technique (RDT) is utilized to attain the optimal solution to this complex mixed-integer bi-level programming (MIBP) problem. The IEEE 118-bus electric power network is used for numerical studies. Results from the numerical studies signify the effectiveness of the presented model showing that a well-designated power system can significantly mitigate market power.

Resilient closed-loop supply chain network design considering quality uncertainty: A case study of stone quarries

According to the important role of the mining industry in the economic growth of developing countries, this industry is taken into consideration significantly. However, few studies have been conducted on developing mining supply chains that take into account the unique conditions of this industry, such as disruptions and product quality. This paper proposes a multi-period, multi-product mixed-integer quadratic programming problem to optimize a closed-loop stone supply chain network design. Compared to previous studies, we consider resilience in the mining supply chain for the first time. Furthermore, the quality characteristics of extracted and final stones are considered in a developed reliable model, and two-stage stochastic programming is applied to handle the quality uncertainty in the mining supply chain. Additionally, a price-dependent demand is considered in this research to investigate the competition between local and imported stone prices. A real-world case study on Iranian stone mining is analyzed to demonstrate the efficiency and applicability of the proposed model. Finally, some managerial insights are presented as guidance to managers of the mentioned supply chain to help them make better decisions. The results show that the transportation costs impact profit more than the operational costs. Moreover, West Azerbaijan and Isfahan have great potential for being the poles of stone in Iran. West Azerbaijan is also appropriate for exporting stones to neighboring countries, geographically.