Non-convex Mixed-integer Programming Research Articles

A new iterative mixed integer linear programming based real time energy efficient management of AC-DC distribution networks

In the smart grid era, AC-DC distribution networks are evolving for integrating massive amounts of distributed energy resources, especially battery associated solar power generation units, into distribution networks in most energy efficient ways. Performing real time energy management for such networks is challenging due to presence of different power electronic converters, grid-edge devices and voltage controlling equipment. Existing studies either focused on developing offline day ahead methods, or shortsighted greedy strategies by neglecting the offline beneficial attributes in real time optimization frameworks. On the contrary, this article proposes a novel real time AC-DC distribution network energy management portfolio by merging load control and conservation voltage reduction techniques to achieve energy efficient operation of the network by regulating the operation of the controllable resources. Initially, the overall optimization problem is developed as a mixed integer non-convex programming by modelling the offline benefits as time coupled stochastic expressions in real time optimization platform. The non-convex expressions are later simplified by adopting different linearization techniques and the entire energy management framework is revised as a simple mixed integer linear programming (MILP). The original problem is decoupled for each time step by simplifying the time coupled expressions using virtual queues and Lyapunov functions. Additionally, a new iterative MILP algorithm is proposed to solve the revised energy management problem with less computation complexity and time. Unlike the previous solution methods, the proposed algorithm initializes the variables by their median values and handles the infeasibilities by adding tangential cutting plane constraints and penalty variable minimization objective. Demonstrating on 33-bus AC-DC distribution network, the superiority of the proposed real time energy management process and iterative MILP algorithm is established after comparing with standard energy management portfolios and existing solution methods.© 2017 Elsevier Inc. All rights reserved.

Bi-objective optimization for supply chain ripple effect management under disruption risks with supplier actions

In practice, supplier actions are often taken to reduce the impact of disruption propagation in the supply chain and ensure continuity of material flows. However, these actions can be very costly. The selection of appropriate supplier actions to reduce the disruption risk is of great interest to both academics and practitioners. However, there is no study on optimally selecting supplier actions to find the best balance between the cost of these actions and the disruption risk. This work investigates a new bi-objective supply chain ripple effect management problem, considering supplier actions. The two objectives are to minimize the manufacturer’s disruption risk and the expected total action cost. To efficiently address the problem, an integrated approach that combines Markov decision process (MDP), dynamic Bayesian network (DBN), and bi-objective nonconvex mixed-integer programming model, along with optimization techniques, is designed. From this study, the following managerial insights can be drawn: (i) for different desired risk reductions, cost-effective supplier actions are different and can be identified by the proposed approach to support decision-making; (ii) the risk decreases with the increase of the total action cost before the risk threshold is achieved, and the disruption risk cannot be smaller than the risk threshold, even if more costly actions are taken; (iii) the costs of supplier actions have no impact on the risk threshold, while the state probability distributions of suppliers and the manufacturer affect the risk threshold.

Energy-Efficient Resource Allocation for Backscatter-Assisted Wireless Powered MEC

In this paper, we study the energy-efficient resource allocation for a backscatter-assisted wireless powered mobile edge computing (MEC) network. Considering the binary offloading mode and the limited computation capacity of the MEC server, we propose to minimize the MEC server's energy consumption by jointly optimizing the binary offloading decision of each IoT node, the computing frequencies and time at the MEC server and IoT nodes, the backscatter time and reflection coefficients of IoT nodes, as well as the MEC server's transmit power and time. It is formulated into a non-convex mixed integer programming problem. To solve this problem, we first obtain the optimal computing time and frequency for the MEC server and the optimal computing time of each IoT node based on the proof by contradiction and the monotonicity of the objective function, then we decouple the resulting simplified problem into two subproblems and transform each subproblem into a convex one. On this basis, we propose a low-complexity iterative algorithm to solve the simplified problem by solving the two convex subproblems alternately. Simulation results verify the fast convergence of the proposed iterative algorithm and its superiority over the baseline schemes in terms of the MEC server's energy consumption.

Rate-Splitting Multiple Access for Uplink Massive MIMO With Electromagnetic Exposure Constraints

Over the past few years, the prevalence of wireless devices has become one of the essential sources of electromagnetic (EM) radiation to the public. Facing with the swift development of wireless communications, people are skeptical about the risks of long-term exposure to EM radiation. As EM exposure is required to be restricted at user terminals, it is inefficient to blindly decrease the transmit power, which leads to limited spectral efficiency and energy efficiency (EE). Recently, rate-splitting multiple access (RSMA) has been proposed as an effective way to provide higher wireless transmission performance, which is a promising technology for future wireless communications. To this end, we propose using RSMA to increase the EE of massive MIMO uplink while limiting the EM exposure of users. In particularly, we investigate the optimization of the transmit covariance matrices and decoding order using statistical channel state information (CSI). The problem is formulated as non-convex mixed integer program, which is in general difficult to handle. We first propose a modified water-filling scheme to obtain the transmit covariance matrices with fixed decoding order. Then, a greedy approach is proposed to obtain the decoding permutation. Numerical results verify the effectiveness of the proposed EM exposure-aware EE maximization scheme for uplink RSMA.

Optimizing fairness in cellular networks with mobile drone relays

Aiding the ground cellular network with aerial base stations carried by drones has experienced an intensive raise of interest in the past years. Reconfigurable air-to-ground channels enable aerial stations to enhance users’ access links by means of seeking good line-of-sight connectivity while hovering in the air. In this article, we propose an analytical framework for the 3D placement of a fleet of coordinated drone relays. This framework optimizes network performance in terms of user throughput fairness, expressed through the α-fairness metric. The optimization problem is formulated as a mixed-integer non-convex program, which is intractable. Hence, we propose an extremal-optimization-based algorithm, Parallelized Alpha-fair Drone Deployment (PADD), which solves the problem online, in low-degree polynomial time. We evaluate our proposal by means of numerical simulations over the real topology of a dense city. We discuss the advantages of integrating drone relay stations in current networks and test several resource scheduling approaches in both static and dynamic scenarios, including with progressively larger and denser crowds.

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.

Deep Reinforcement Learning Based Resource Allocation in Multi-UAV-Aided MEC Networks

Resource allocation for mobile edge computing (MEC) in unmanned aerial vehicle (UAV) networks has been a popular research issue. Different from existing works, this paper considers a multi-UAV-aided uplink communication scenario and investigates a resource allocation problem of minimizing the total system latency and the energy consumption, subject to constraints on transmit power of mobile users (MUs), system latency caused by transmission and computation. The problem is confirmed to be a challenging time-series mixed-integer non-convex programming problem, and we propose a joint UAV Movement control, MU Association and MU Power control (UMAP) algorithm to solve it effectively, where three sub-problems are optimized iteratively. Specifically, UAV movement and MU association are optimized utilizing deep reinforcement learning (DRL) to decrease the energy consumption and system latency. Next, a closed-form solution of the MU transmit power is derived. Finally, simulation results show that the UMAP algorithm can significantly decrease the system latency and energy consumption and increase the coverage rate compared with benchmark algorithms.

Scalability Improvement of IEEE 802.11ah IoT Networks

In this paper, we propose a non-orthogonal multiple access (NOMA) based grouping method for IEEE 802.11ah, a promising platform for the internet of things (IoT). The grouping method improves the scalability of IoT networks, by reducing collisions in the access points (APs). The proposed method puts those IoT devices (IoT-Ds) whose channel gains are far enough from each other, i.e., who satisfy NOMA constraints, in the same group. Therefore, using successive interference cancellation (SIC), the AP is able to decode the simultaneous signal transmissions from IoT-Ds in a group. To assign IoT-Ds into groups and determine their transmission power, we formulate a total throughput maximization problem as a joint optimal grouping and power allocation problem, which is a non-convex mixed-integer programming problem. We convert it to a convex problem using quadratic fractional programming, and then we solve it using augmented Lagrange multiplier (ALM) method. Moreover, to reduce the complexity of the solution, we propose a fast grouping method to allocate power to each group in parallel. Simulation results show that the proposed methods have outstanding performance compared to conventional association identifier (AID)-based grouping method; besides, scalability of the network in terms of throughput, power consumption and channel utilization improves dramatically because of the collision reduction of IoT-Ds, which is achieved by deploying NOMA and SIC. Furthermore, the fast grouping method decreases the computational complexity greatly at the expense of a small reduction in network performance.

Computation bits maximization in backscatter-aided wireless powered MEC using binary offloading

This article considers a backscatter-aided wireless powered mobile edge computing (BC-aided WPMEC) network, in which the tasks data of each Internet of Things (IoT) device can be computed locally or offloaded to the MEC server via backscatter communications, and design a resource allocation scheme regarding the weighted sum computation bits (WSCB) maximization of all the IoT devices. Towards this end, by optimizing the mobile edge computing (MEC) server’s transmit power, IoT devices’ power reflection coefficients, local computing frequencies and time, the time allocation between the energy harvesting and task offloading, as well as the binary offloading decision at each IoT device, we built a WSCB maximization problem, which belongs to a non-convex mixed integer programming problem. For solving this, the proof by contradiction and the objective function’s monotonicity are considered to determine the optimal local computing time of each IoT device and the optimal transmit power of the MEC server, and the time-sharing relaxation (TSR) is adopted to tackle the integer variables, which are used to simplify the original problem. Then, we decouple the simplified problem into two sub-problems by means of the block coordinate decent (BCD) technology, and each of the sub-problems is transformed to a convex one by introducing auxiliary variables. Based on this, we design a two-stage alternative (TSA) optimization algorithm to solve the formulated WSCB problem. Computer simulations validate that the TSA algorithm has a fast convergent rate and also demonstrate that the proposed scheme achieves a higher WSCB than the existing schemes.

Propulsion Energy Minimization for Fixed-Wing-UAV-Assisted Full-Duplex Mobile Relaying via Hybrid Trajectory Design

This paper solved a propulsion energy minimization problem subject to a total data-bit constraint of an unmanned aerial vehicle (UAV)-enabled full-duplex mobile relaying system, where a fixed-wing UAV is dispatched as a full-duplex mobile relay to assist data transfer from a source to a destination. Here, three trajectory flying modes are used, namely, the UAV first flies along a circular path above the source, next flies to the destination along a straight line, and finally flies along a circular path above the destination until all the data-bits have been transferred. Since the propulsion energy minimization problem is a nonconvex mixed integer programming problem, its closed-form solution is not tractable, and hence, it is transformed to three subproblems so as to simplify its solution. After solving the three subproblems, an iterative algorithm is proposed to achieve a suboptimal solution to the propulsion energy minimization problem, leading to a new hybrid circular/straight trajectory (HCST) design. Computer simulations are conducted to validate the effectiveness of the proposed HCST design. It is shown that the proposed HCST design performs well in terms of energy saving for the long distance and big data communication cases compared with the straight or circular flight trajectory design.

Real-Time Advanced Energy-Efficient Management of an Active Radial Distribution Network

This article elucidates a new real-time optimization framework for advanced energy-efficient management of active radial distribution networks. The proposed energy management process leverages the benefits of simultaneous deployment of online direct load control (DLC) and conservation voltage reduction (CVR) for decreasing peak energy demand. Initially the proposed problem is designed as a time-coupled stochastic mixed integer nonconvex programming (MINCP) to accommodate long-term offline beneficial aspects in real-time optimization framework, which is later simplified using merger of Queueing theory and Lyapunov optimization. A successive mixed integer linear programming (s-MILP) solution approach is proposed for accurate and fast convergence of the revised MINCP framework. The efficacy of the developed strategy is evaluated after comparing with two-benchmark energy management models (viz. offline and online greedy algorithm) by demonstrating on modified IEEE 69-bus test system. Further scalability of the proposed approach is validated by testing on large distribution networks.

Resource Allocation and Computation Offloading for Wireless Powered Mobile Edge Computing.

In this paper, we investigate a resource allocation and computation offloading problem in a heterogeneous mobile edge computing (MEC) system. In the considered system, a wireless power transfer (WPT) base station (BS) with an MEC sever is able to deliver wireless energy to the mobile devices (MDs), and the MDs can utilize the harvested energy for local computing or task offloading to the WPT BS or a Macro BS (MBS) with a stronger computing server. In particular, we consider that the WPT BS can utilize full- or half-duplex wireless energy transmission mode to empower the MDs. The aim of this work focuses on optimizing the offloading decision, full/half-duplex energy harvesting mode and energy harvesting (EH) time allocation with the objective of minimizing the energy consumption of the MDs. As the formulate problem has a non-convex mixed integer programming structure, we use the quadratically constrained quadratic program (QCQP) and semi-definite relaxation (SDR) methods to solve it. The simulation results demonstrate the effectiveness of the proposed scheme.

A New Real Time Energy Efficient Management of Radial Unbalance Distribution Networks Through Integration of Load Shedding and CVR

This paper elucidates a new real time energy management framework for radial active unbalance distribution networks (UDNs) by integrating load shedding and conservation voltage reduction (CVR) techniques. In contrast with the shortsighted real time optimization strategies, the proposed technique accounts offline beneficial aspects in real time optimization platform as time coupled stochastic expressions. Those are further simplified to a mixed integer non-convex programming (MINCP) using merger of Queueing theory and Lyapunov optimization process. To solve the complex MINCP portfolio, a consecutive mixed integer linear programming (c-MILP) based solution method is proposed after adopting necessary linear approximations. After demonstrating on modified IEEE 123 bus test network, it is showed that the proposed real time strategy can provide most energy efficient, secure and reliable operation to the UDNs and can accommodate offline advantageous attributes successfully along with the real time load shedding and CVR constraints. Validating the power flow solutions at OpenDSS platform, it is proved that the proposed c-MILP approach possess fast convergence and provide near optimal power flow solutions. Further investigations certify that presence of residential consumers are more beneficial for the networks as they are more sensitive to voltage.

Minimum Overhead Beamforming and Resource Allocation in D2D Edge Networks

Device-to-device (D2D) communications is expected to be a critical enabler of distributed computing in edge networks at scale. A key challenge in providing this capability is the requirement for judicious management of the heterogeneous communication and computation resources that exist at the edge to meet processing needs. In this paper, we develop an optimization methodology that considers the network topology jointly with device and network resource allocation to minimize total D2D overhead, which we quantify in terms of time and energy required for task processing. Variables in our model include task assignment, CPU allocation, subchannel selection, and beamforming design for multiple-input multiple-output (MIMO) wireless devices. We propose two methods to solve the resulting non-convex mixed integer program: semi-exhaustive search optimization, which represents a “best-effort” at obtaining the optimal solution, and efficient alternate optimization, which is more computationally efficient. As a component of these two methods, we develop a novel coordinated beamforming algorithm which we show obtains the optimal beamformer for a common receiver characteristic. Through numerical experiments, we find that our methodology yields substantial improvements in network overhead compared with local computation and partially optimized methods, which validates our joint optimization approach. Further, we find that the efficient alternate optimization scales well with the number of nodes, and thus can be a practical solution for D2D computing in large networks.

Towards balanced three-phase charging: Phase optimization in adaptive charging networks

We study the problem of phase optimization for electric-vehicle (EV) charging. We formulate our problem as a non-convex mixed-integer programming problem whose objective is to minimize the charging loss. Despite the hardness of directly solving this non-convex problem, we solve a relaxation of the original problem by proposing the PXA algorithm where “P”, “X”, and “A” stand for three variable matrices in the formed phase optimization problems. We show that under certain conditions, the solution is given by the PXA precisely converges to the global optimum. In addition, using the idea of model predictive control (MPC), we design the PXA-MPC, which is an online implementation of the PXA. Compared to other empirical phase balancing strategies, the PXA algorithm significantly improves the charging performance by maximizing energy delivery, minimizing charging price, and assisting future energy planning. The efficacy of our algorithm is demonstrated using data collected from a real-world adaptive EV charging network (ACN).

Reconfigurable Intelligent Surface With Energy Harvesting Assisted Cooperative Ambient Backscatter Communications

The performance of cooperative ambient backscatter communications (CABC) can be enhanced by employing reconfigurable intelligent surface (RIS) to assist backscatter transmitters. Since the RIS power consumption is a non-negligible issue, we consider a RIS assisted CABC system where the RIS with energy harvesting circuit can not only reflect signal but also harvest wireless energy. We study a transmission design problem to minimize the RIS power consumption with the quality of service constraints for both active and backscatter transmissions. The optimization problem is a mixed-integer non-convex programming problem which is NP-hard. To tackle it, an algorithm is proposed by employing the block coordinate descent, semidefinite relaxation and alternating direction method of multipliers techniques. Simulation results demonstrate the effectiveness of the proposed algorithm.

Reconfigurable Intelligent Surface Enabled Vehicular Communication: Joint User Scheduling and Passive Beamforming

Given its ability to control and manipulate wireless environments, reconfigurable intelligent surface (RIS), also known as intelligent reflecting surface (IRS), has emerged as a key enabler technology for the six-generation (6G) cellular networks. In the meantime, vehicular environment radio propagation is negatively influenced by a large set of objects that cause transmission distortion such as high buildings. Therefore, this work is devoted to explore the area of RIS technology integration with vehicular communications while considering the dynamic nature of such communication environment. Specifically, we provide a system model where RoadSide Unit (RSU) leverages RIS to provide indirect wireless transmissions to disconnected areas, known as dark zones. Dark zones are spots within RSU coverage where the communication links are blocked due to the existence of blockages. In details, a discrete RIS is utilized to provide communication links between the RSU and the vehicles passing through out-of-service zones. Therefore, the joint problem of RSU resource scheduling and RIS passive beamforming or phase-shift matrix is formulated as an optimization problem with the objective of maximizing the minimum average bit rate. The formulated problem is mixed integer non-convex program which is difficult to be solved and does not account for the uncertain dynamic environment in vehicular networks. Thereby, we resort to alternative methods based on Deep Reinforcement Learning to determine RSU wireless scheduling and Block Coordinate Descent (BCD) to solve for the phase-shift matrix, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> passive beamforming, of the RIS. The Markov Decision Process (MDP) is defined and the complexity of the solution approach is discussed. Our numerical results demonstrate the superiority of our proposed approach over baseline techniques.

On the Energy Efficiency Maximization of NOMA-Aided Downlink Networks With Dynamic User Pairing

This study investigates a combined system comprising non-orthogonal multiple access (NOMA) and beamforming in a downlink network. To fully exploit the advantages of NOMA, user (UE) pairing and beamforming design are jointly optimized via a generalized model for UE association, subject to energy efficiency maximization. Owing to the combination of binary variables and nonconvex constraints, the resulting optimization problem belongs to the class of mixed-integer nonconvex programming. An innovative algorithm, integrating the inner-approximation and Dinkelbach methods, is proposed herein to address a nonconvex fractional function. By introducing a pairing matrix and relaxing the binary variables into continuous ones, our approach is capable of reaching an optimal solution, where two arbitrary UEs are optimally paired regardless of geographical or spatial constraints. For practical scenarios, we further propose a robust design to manage the effect of channel estimation errors under settings involving channel uncertainty. Numerical results show that our proposed designs, even with the presence of the imperfect channel state information at the base station, significantly outperform the conventional beamforming and existing pairing schemes.

Residual Energy Maximization-Based Resource Allocation in Wireless-Powered Edge Computing Industrial IoT

Industrial Internet of Things (IIoT) is a new stage for traditional industry to achieve intelligent development. However, the problems of limited resource, communication congestion, and capacity-constrained batteries have emerged due to massive wireless sensing devices (WSDs). With the recent advent of the wireless power transfer (WPT) technique and the development of edge computing technology, the IIoT pays much attention to the interconnected, instant, and high-intelligent system. In this article, we first consider a three-layer architecture to describe the IIoT environment and we propose a resource allocation strategy aiming at maximizing the residual energy of WSDs. The optimization of residual energy is formulated as a mixed-integer nonconvex programming NP hard problem, by constraining the offloading decision, power allocation, computing resource allocation, and time allocation. In addition, an improved hybrid whale optimization algorithm (IHWOA) is proposed to search for the approximate optimal solution. Rapid convergent and stable efficient solution is obtained through simulation experiments. Finally, numerical results prove that the proposed solution achieves good performance.

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming