Nonconvex Nonlinear Programming Problem Research Articles

Resource Allocation in Backscatter-Assisted Wireless Powered MEC Networks With Limited MEC Computation Capacity

In this paper, we consider a backscatter-assisted wireless powered mobile edge computing (MEC) network, where multiple Internet-of-Things (IoT) nodes harvest energy from the energy signals transmitted by a power beacon (PB) and utilize the harvested energy for local computing and task offloading via hybrid backscatter communication (BackCom) and active transmission (AT). Considering the limited computation capacity of the MEC server and the quality-of-service (QoS) and energy-causality constraints per IoT node, we propose two resource allocation schemes to maximize the total computation bits of all the IoT nodes and the system computation energy efficiency (EE), respectively, by jointly optimizing the computation frequency and time of the MEC server and each IoT node, the transmit power of the PB and each IoT node, and the BackCom power reflection coefficient and the time for energy harvesting (EH), BackCom, and AT of each IoT node. The non-convex computation bits maximization problem is transformed to a convex one by introducing a series of auxiliary variables and proof by contradiction, and then solved by the existing convex tools. The system computation EE maximization is a non-convex nonlinear programming problem. We propose a two-layer iterative algorithm to solve it optimally and devise a reduced-complexity iterative algorithm to solve it sub-optimally by leveraging the block coordinate decent technique. Computer simulations validate the convergence of the proposed iterative algorithms and their superior performance over the benchmark schemes in terms of the computation bits or EE.

Delay-Tolerant UAV-Assisted Communication: Online Trajectory Design and User Association

UAV-assisted communication is a promising paradigm to enhance the performance of wireless networks. In this paper, we consider the network randomness in the delay-tolerant UAV-assisted communication systems. We aim to optimize both the UAV trajectory and user association in an online manner to achieve a finite queueing delay at the users' buffers with the minimum energy consumption of the UAVs. We first formulate our problem as a stochastic dynamic programming problem that integrates the future expected energy consumption and delay into its objective function and constraints, respectively. To deal with the inaccurate knowledge of future user demand and mobility, we apply the Lyapunov optimization technique and convert it into a series of online joint UAV trajectory and user association optimization problems. However, each online problem is a non-convex non-linear integer programming problem, which is very challenging to solve in general. As such, we first eliminate the coupling relationship of user association variables in each online problem. By exploiting the special graph structure of the problem, we can decompose the joint problem into inner optimization and outer optimization problems. Then, we propose the online UAV mobility and user association selection (UMUAS) scheme, which includes two steps to solve the inner and outer problems. Simulation results show that our online UMUAS scheme achieves the near-optimal performance of the energy-delay tradeoff, which also has a 44.2% improvement over the greedy scheme and a 51.3% improvement over the interference-free scheme. Moreover, it achieves the highest energy efficiency among the three benchmark schemes.

Full Life-Cycle Optimal Battery Scheduling for Maximal Lifetime Value Considering Degradation

The dilemma between battery operating revenue and aging has not been addressed appropriately by previous studies. This paper presents a co-optimization method of battery full life-cycle scheduling and lifespan for its maximal lifetime value, involving usage limits, nonlinear aging characteristics, and time-value-of-money effects. The resulting dispatch model consists of numerous large-scale non-convex nonlinear programming (NLP) problems with the nonlinearity appearing in the equality constraint, which cannot be solved efficiently through conventional methods. Thus, we design an exact and fast solution approach including the equivalent problem transformation, a modified pegging algorithm, and a novel acceleration algorithm. The proposed methods are illustrated and validated by numerical tests using real historical data from Pecan St. Project. Test results suggest that it is not the case that the longer service life, the more battery lifetime profits can be generated. The proposed scheduling method can improve the lifetime profits than the conventional methods. For a battery with a 15-year design life, the optimal scheduling and lifespan with a 5-day resolution can be obtained within half an hour.

ESN Reinforcement Learning for Spectrum and Flight Control in THz-Enabled Drone Networks

Terahertz (THz)-band communications have been envisioned as a key technology to support ultra-high-data-rate applications in 5G-beyond (or 6G) wireless networks. Compared to the microwave and mmWave bands, the main challenges with the THz band are in its i) large path loss hence limited network coverage and ii) visible-light-like propagation characteristics hence poor support of mobility in blockage-rich environments. This paper studies quantitatively the applicability of THz-band communications in blockage-rich mobile environments, focusing on a new network scenario called FlyTera. In FlyTera, a set of hotspots mounted on flying drones collaboratively provide data streaming services to ground users, in the microwave, mmWave and THz bands. We first provide a mathematical formulation of the FlyTera control problem, where the objective is to maximize the network spectral efficiency by jointly controlling the flight of the drone hotspots, their association to the ground users, and the spectrum bands used by the users. To solve the resulting problem, which is shown to be a mixed integer nonlinear nonconvex programming (MINLP) problem, we design distributed solution algorithms based on a combination of echo state learning and reinforcement learning. An extensive simulation campaign is then conducted with SimBAG, a newly developed Simulator of Broadband Aerial-Ground wireless networks. It is shown that no single spectrum band can meet the requirements of high data rate and wide coverage simultaneously. Moreover, from the network-level point of view, THz-band communications can significantly benefit from the mobility of the flying drones, and on average 4 - 6 times higher (rather than lower) throughput can be achieved in mobile than in static environments.

Convex Approximation Algorithm for AC/DC Distribution Network With Energy Router

The optimal operation model of AC/DC distribution network with energy router (ER) is essentially a nonconvex nonlinear programming (NLP) problem. In order to improve the feasibility of solving the model, a convex approximation algorithm is proposed in this work. The steady-state model of ER is developed with considering the loss characteristics and multiport coordinated control strategy. It is embedded in the optimization formulations of AC/DC network as basic operating equations. Then, using second-order cone relaxation technology, the power flow equations of AC and DC distribution networks are convexly relaxed. On this basis, the highly nonlinear operating model of ER is linearized by introducing a successive approximation approach. Therefore, the original NLP problem is transformed into the convex programming problem and the solution efficiency is improved. Meanwhile, an iterative solution algorithm is developed to ensure the accuracy of the convex approximation approach. Simulation results verify the feasibility and efficiency of the proposed algorithm.

A risk-sensitive task offloading strategy for edge computing in industrial Internet of Things

Edge computing has become one of the key enablers for ultra-reliable and low-latency communications in the industrial Internet of Things in the fifth generation communication systems and is also a promising technology in the future sixth generation communication systems. In this work, we consider the application of edge computing to smart factories for mission critical task offloading through wireless links. In such scenarios, although high end-to-end delays from the generation to completion of tasks happen with low probability, they may incur severe casualties and property loss and should be seriously treated. Inspired by the risk management theory widely used in finance, we adopt the Conditional Value at Risk to capture the tail of the delay distribution. An upper bound of the Conditional Value at Risk is derived through analysis of the queues both at the devices and the edge computing servers. We aim to find out the optimal offloading policy taking into consideration both the average and the worst-case delay performance of the system. Given that the formulated optimization problem is a non-convex mixed integer nonlinear programming problem, a decomposition into subproblems is performed and a two-stage heuristic algorithm is proposed. The simulation results validate our analysis and indicate that the proposed algorithm can reduce the risk in both the queueing and end-to-end delay.

Energy-Efficient Time-Domain Equilibrium Scheduling and Optimization Scheme for Energy Harvesting-Powered D2D Communication

Energy Harvesting- (EH-) powered Device-to-Device (D2D) Communication underlaying Cellular Network (EH-DCCN) has been deemed as one of the basic building blocks of Internet of Things due to its green energy efficiency and adjacent communication. But available energy will be one of the biggest obstacles when implementing EH-DCCN due to the immaturity of EH technology and the volatility of environmental energy resources. To improve energy utilization, this study investigates an efficient scheduling and power allocation scheme about transmission load equilibrium in the time domain. Accordingly, a short-term Sum Energy Efficiency (stSEE) maximization problem for EH-powered D2D communication is modelled, while ensuring a fundamental transmission rate requirement of cellular users. Consequently, the optimization problem is a nonconvex mixed integer nonlinear programming problem. Thus, we propose a two-layer convex approximation iteration algorithm which can obtain a feasible quasioptimal solution for the stSEE problem. Simultaneously, a two-step heuristic algorithm in a slot-by-slot fashion is also developed to acquire a suboptimal solution without requiring statistical knowledge of channel and energy arrival processes. Simulated analysis indicates that the short-term scheduling strategy can obtain better performances in terms of energy efficiency and transmission rate than conventional real-time scheduling scheme. Besides, the maximum scheduled number of EH-D2D pairs underlaying one cellular user under different EH efficiency is analysed, which can give us a theoretical reference about the deployment of future EH-DCCN.

Distributed Joint Power, Association and Flight Control for Massive-MIMO Self-Organizing Flying Drones

This article studies distributed algorithms to control self-organizing flying drones with massive MIMO networking capabilities - a network scenario referred to as mDroneNet . We attempt to answer the following fundamental question: what is the optimal way to provide spectrally-efficient wireless access to a multitude of ground nodes with mobile hotspots mounted on drones and endowed with a large number of antennas; when we can control the position of the drone hotspots, the association between the ground users and the drone hotspots, as well as the pilot sequence assignment and transmit power for the ground users? To the best of our knowledge, this is the first time that massive MIMO capabilities are considered in self-organizing flying drone networks. We first derive a mathematical formulation of the problem of joint power, association and movement control in mDroneNet, with the objective of maximizing the aggregate spectral efficiency of the ground users. It is shown that the resulting network control problem is a mixed integer nonlinear nonconvex programming (MINLP) problem. Then, a distributed solution algorithm with polynomial time complexity is designed by solving three closely-coupled subproblems: access association, joint pilot sequence assignment and power control, and drone movement control. As a performance benchmark, a globally-optimal but centralized solution algorithm is also designed based on a combination of the branch and bound framework and convex relaxation techniques. Results indicate that the distributed solution algorithm converges fast (within tens of iterations) and achieves a network spectral efficiency very close to the global optimum obtained by the centralized solution algorithm (over 90% in average).

Energy-Efficient Transmission Rate Selection and Power Control for Relay-Assisted Device-to-Device Communications Underlaying Cellular Networks

Device-to-device (D2D) communication underlaying cellular networks is seen as a promising technology for future communication systems, especially when relays are employed to extend the range of D2D links. However, the mutual interference between the spectrum-sharing D2D links and conventional cellular (CC) links is still the dominating performance limiting factor, which enforces those links to adopt higher transmission power. As energy saving is always one of the key concerns, we propose to minimize the total transmission energy consumption of a relay-assisted D2D link and a CC link sharing radio resources by jointly optimizing their transmission rate selection and power control (TRSPC). We formulate the optimization problem as a non-convex non-linear programming (NLP) problem and then develop a game theory based distributed approach to solve it. Simulation results demonstrate that our game theory based TRSPC approach can enormously decrease the total transmission energy consumption compared with existing works.

Two‐parameter Kautz network‐based LTV‐MPC for non‐linear standalone micro‐grid control

This study proposes a novel linear time-variant model predictive controller (LTV-MPC) for the centralised control of non-linear standalone micro-grids. At each sample, within the prediction horizon, LTV-MPC linearises the non-linear micro-grid model around the state and input reference trajectories resulting in a linear time-variant (LTV) model. The LTV model is used for predicting the forced response of the micro-grid. The natural response is predicted by solving the non-linear model along the state and input reference trajectories. An optimal control problem for the LTV-MPC is formulated using the complete predicted response, which is a quadratic programming problem instead of a non-convex non-linear programming problem. The quadratic programming problem is solved online at each sample to generate the optimal control trajectories within the control horizon. The study recommends the use of two-parameter orthonormal Kautz networks in the LTV-MPC design for the control trajectories approximation. The approximation drastically reduces the number of optimising variables in the optimal control problem without compromising LTV-MPC performance. A standalone eight bus micro-grid with one synchronous distributed generator (DG) and one photovoltaic-DG is considered for the analysis. The LTV-MPC performance is assessed for the different load disturbance and source intermittency scenarios. The results are compared with the existing MPC designs.

Optimal Power Flow with Renewable Generation: A Modified NSGA-II-based Probabilistic Solution Approach

The rapid expansion of renewable generation has drastically increased the planning complexity of modern power systems as additional uncertainties, environmental concerns, and technical–economic issues should be accounted for. Within this context, the best operation performance of contemporary power system operators (SOs) depends not just on tractable realistic optimal power flow (OPF) formulations, but also on powerful optimization approaches. In this work, a tractable life-like multi-objective probabilistic OPF-based model for the SO’s medium-term operation considering high penetration of renewable resources is proposed. This model includes an explicit formulation of the operation of dispatchable and non-dispatchable generation, shunt reactive power sources, and under-load tap-changing (ULTC) transformers. The resulting model is a large-scale probabilistic multi-objective non-convex nonlinear mixed-integer programming (NLMIP) problem with continuous, discrete, and binary variables. To ensure tractability, uncertainties are modeled through a fast and efficient 2m probabilistic approach. To handle the nonlinearities and non-continuous variables that characterize the problem, a modified non-dominated sorting genetic algorithm (NSGA)-II solution approach is proposed and effectively tested.

The rate of convergence of proximal method of multipliers for nonlinear programming

We analyze the rate of convergence of the proximal method of multipliers for non-convex nonlinear programming problems. First, we prove, under the strict complementarity condition, that the rate of convergence of the proximal method of multipliers is linear and the ratio constant is proportional to 1/c when the ratio is small enough, which implies that the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to . Second, we prove that, without strict complementarity condition, the rate of convergence of the proximal method of multipliers is proportional to 1/c when c exceeds a threshold.

User Association and Small-Cell Base Station On/Off Strategies for Energy Efficiency of Ultradense Networks

The widespread application of wireless mobile services and requirements of ubiquitous access have resulted in drastic growth of the mobile traffic and huge energy consumption in ultradense networks (UDNs). Therefore, energy-efficient design is very important and is becoming an inevitable trend. To improve the energy efficiency (EE) of UDNs, we present a joint optimization method considering user association and small-cell base station (SBS) on/off strategies in UDNs. The problem is formulated as a nonconvex nonlinear programming problem and is then decomposed into two subproblems: user association and SBS on/off strategies. In the user association strategy, users associate with base stations (BSs) according to their movement speeds and utility function values, under the constraints of the signal-to-interference ratio (SINR) and load balancing. In particular, taking care of user mobility, users are associated if their speed exceeds a certain threshold. The macrocell base station (MBS) considers user mobility, which prevents frequent switching between users and SBSs. In the SBS on/off strategy, SBSs are turned off according to their loads and the amount of time required for mobile users to arrive at a given SBS to further improve network energy efficiency. By turning off SBSs, negative impacts on user associations can be reduced. The simulation results show that relative to conventional algorithms, the proposed scheme achieves energy efficiency performance enhancements.

QOS aware channel and power allocation scheme for D2D enabled cellular networks

Device-to-device (D2D) communication enabled cellular system is capable of enhancing the spectrum utilization and throughput performance of the system. However, D2D users (D2Ds) in close proximity share its radio resources with the cellular users (CUs), thereby adding an additional amount of interferences from D2D transmitters and affecting the performance of cellular networks. To reduce these problems, we propose a novel channel selection and power allocation scheme incorporating quality of service (QOS) parameter for CU and D2D pairs. In order to improve the spectral efficiency, an efficient resource sharing strategy wherein multiple channels of CUs can be reused by each D2D pair is introduced. To cope up with the overloaded traffic at the base station (BS) due to the coexistence of different types of users and to reduce the computational complexity of the network, we divide our problem of resource sharing into two sub-problems. The channel assignment which is a linear programming problem determines the number of channels that can be shared by each D2D pair. Secondly, the power allocation for D2D pairs is a non-convex non-linear programming problem and is difficult to solve. Thus, the problem is transformed into a convex form using the exponential form of transmit power in the Laplace domain. By using Lagrangian method, the optimal power of D2Ds is determined such that it maximizes D2D sum-rate while preserving QOS of CU, thereby not affecting the normal cellular communication. The paper also elaborates on the throughput performances of D2D pairs which is affected by the position of D2Ds and CUs and distance of separation between D2Ds and CUs. Thus, we choose the radius of coverage as a metric for D2D communication. The effectiveness of proposed resource sharing and power allocation scheme is also illustrated through numerical examples.

Optimal Dispatch of Battery Energy Storage System Using Convex Relaxations in Unbalanced Distribution Grids

This paper presents second-order cone programming (SOCP) and semidefinite programming (SDP) models to solve the multiperiod optimal control problem of unbalanced three-phase distribution grids with battery energy storage systems. The decision variables are the active and reactive power of the battery energy storage system. The objective is to minimize the power loss and energy purchase cost from the distribution substation. The optimal dispatch problem requires solution by volt/VAR optimization. The SOCP and SDP models ensure global optimum of original nonconvex nonlinear programming problem. Multiobjective volt/VAR optimization is performed and the benefits of reactive power support from battery energy storage systems are explored. A simulation-based heuristic to extract rank-one solution from the higher rank solution of SDP model is also proposed. Empirical results show the numerical stability and exactness of the proposed three-phase SOCP and SDP models.

Decentralized control for residential energy management of a smart users microgrid with renewable energy exchange

This paper presents a decentralized control strategy for the scheduling of electrical energy activities of a microgrid composed of smart homes connected to a distributor and exchanging renewable energy produced by individually owned distributed energy resources. The scheduling problem is stated and solved with the aim of reducing the overall energy supply from the grid, by allowing users to exchange the surplus renewable energy and by optimally planning users &#x02BC controllable loads. We assume that each smart home can both buy &#x002F sell energy from &#x002F to the grid taking into account time-varying non-linear pricing signals. Simultaneously, smart homes cooperate and may buy &#x002F sell locally harvested renewable energy from &#x002F to other smart homes. The resulting optimization problem is formulated as a non-convex non-linear programming problem with a coupling of decision variables in the constraints. The proposed solution is based on a novel heuristic iterative decentralized scheme algorithm that suitably extends the Alternating Direction Method of Multipliers to a non-convex and decentralized setting. We discuss the conditions that guarantee the convergence of the presented algorithm. Finally, the application of the proposed technique to a case study under several scenarios shows its effectiveness.

An indirect elicitation method for the parameters of the ELECTRE TRI-nB model using genetic algorithms

Indirect approaches for eliciting preference model parameters for multiple criteria decision aiding are of growing interest because they imply relatively less cognitive effort from the decision-maker (DM). Direct approaches are particularly hard in the case of the new ELECTRE TRI-nB method, because the task involves eliciting a number of limiting profiles for each category boundary. However, in ELECTRE methods, the simultaneous inference of the whole set of parameters needs the construction and resolution of a non-linear non-convex programming problem, which is typically very hard to solve. Therefore, an evolutionary-based method to infer the parameters of the ELECTRE TRI-nB model is proposed in this paper. The quality of the solutions is tested by measuring the capacity to restore the assignment examples and the capacity to make consistent assignments of new actions. In extensive computer experiments, using the pseudo-conjunctive assignment procedure, some main conclusions arise: (i) the capacity of the method to restore the training examples reaches high values, mainly with three and five limiting profiles per category; and (ii) the capacity to make appropriate assignments of new actions (not belonging to the training information) can be greatly improved by increasing the number of limiting profiles.

A primal-dual integrated nonlinear rescaling approach applied to the optimal reactive dispatch problem

The objective of this paper is to propose a novel augmented Lagrangian approach for solving the Optimal Reactive Dispatch (ORD) problem in electric power systems, which consists in a large nonconvex Nonlinear Programming (NLP) problem. Given an NLP problem, its associated dual problem is solved by a proximal point method, whose distance between two points is calculated by means of a convex combination involving Bregman’s distance and Csiszar’s entropic φ-divergence distance pondered by a weighting factor, namely Integrated Distance Measure (IDM). Such dual proximal point method with the IDM leads to an equivalent augmented Lagrangian method with a new family of nonquadratic penalty functions for the primal problem, namely Integrated Nonlinear Rescaling (INLR) method. The concepts of integrated logarithmic modified barrier and integrated exponential functions, which are elements of the new family of penalty functions, are defined. A Primal-Dual Integrated Nonlinear Rescaling (PDINLR) method is proposed to solve convex and nonconvex NLPs. A small convex NLP problem is used to depict how such algorithm attains optima, and a small nonconvex NLP problem is used to show how the proposed approach outperforms other known methods in the area when a suitable value for the weighting factor is chosen. The effectiveness, efficiency and the robustness of the proposed PDINLR method with the integrated logarithmic modified barrier function are shown by the resolution of the ORD problem for the IEEE 30 and 300-bus test-systems.

Energy-efficient multi-cell resource allocation in cognitive radio-enabled 5G systems

In this paper, we propose an energy-efficient resource allocation (RA) algorithm in cognitive radio-enabled 5th generation (5G) systems, where the scenario including one primary system and multiple secondary cells is considered. Because of the high spectrum leakage of traditional orthogonal frequency division multiplexing (OFDM), alternative modulation schemes regarded as the potential air interfaces in 5G are analyzed, e.g., filter bank-based multi-carrier (FBMC), generalized frequency division multiplexing (GFDM), and universal filtered multi-carrier (UFMC). Our objective is to maximize the whole energy efficiency of secondary system defined by the ratio of the capacity to the total power consumption subject to some practical constraints. The general formulation leads to a non-convex mixed-integer nonlinear programming problem with fractional structure, which is challenging to solve due to its intractability and significant complexity. Therefore, we resort to an alternate optimization framework to optimize the variables of subcarrier assignment and power allocation, where successive convex approximation (SCA) is employed so that the general formulation is finally transformed into a solvable convex problem. Numerical results validate the effectiveness of the proposed RA algorithm, and the comparison with some existing RA algorithms is conducted. In addition, the performance of using different 5G candidate waveforms in the energy-efficient RA algorithm is also presented and discussed.

A near-optimal cloud offloading under multi-user multi-radio environments

Computation offloading is an effective way to augment computation capabilities of mobile devices for emerging resource-hungry mobile applications. In this paper, we study the computation offloading problem under multi-user multi-radio (MUMR) environments, where users can transmit partial computation tasks to a remote cloud via multiple radio links. We formulate the problem as a maximization of the total number of beneficial users in consideration of time delay and energy consumption simultaneously. Since the proposed optimization problem is a non-convex mixed integer non-linear programming (MINLP) problem that is difficult to tackle using conventional methods. We convert the MINLP problem into a bilinear problem equivalently by introducing additional variables and then relax the problem to a convex optimization problem by McCormic envelopes method. We develop a Branch and Bound algorithm to solve the problem, and numerical results demonstrate that the proposed method can obtain a near-optimal solution.