Mixed-integer Nonlinear Optimization Problem Research Articles

A test instance generator for multiobjective mixed-integer optimization

Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When developing and improving algorithms which hopefully allow to handle those difficulties in the future, good test instances are required. These can then be used to detect the strengths and weaknesses of different algorithmic approaches. In this paper we present a generator for test instances to evaluate solvers for multiobjective mixed-integer linear and nonlinear optimization problems. Based on test instances for purely continuous and purely integer problems with known efficient solutions and known nondominated points, suitable multiobjective mixed-integer test instances can be generated. The special structure allows to construct instances scalable in the number of variables and objective functions. Moreover, it allows to control the resulting efficient and nondominated sets as well as the number of efficient integer assignments.

A flexibility-based multi-objective model for contingency-constrained transmission expansion planning incorporating large-scale hydrogen/compressed-air energy storage systems and wind/solar farms

The remarkable arrival of uncertainties given by the fluctuations in the output of renewable energy sources (RESs) calls for a more flexible power grid. In confronting this issue, large-scale energy storage systems play a vital role in achieving higher flexibility. In this regard, the authors of this study present here a new multi-objective model for contingency-constrained transmission expansion planning that incorporates large-scale hydrogen/compressed-air energy storage systems and wind/solar farms to simultaneously boost both supply-demand-related flexibility (SDFX) and grid-related flexibility (GDFX). The proposed model is formulated as a non-convex mixed-integer nonlinear master-slave optimization problem. The planning objectives, modeled through the master problem, are intended to minimize the investment and operation costs, while maximizing the SDFX enhancement metric minus the GDFX degradation metric. The slave problem, however, aims to maximize the community welfare function (CIWF) and microgrid welfare function (MIWF) under both normal and N-1 operating conditions. To solve the resulting non-convex mixed-integer nonlinear master-slave optimization problem, a potent symphony orchestra search algorithm (SOSA)—empowered with a multi-computational-step, multi-dimensional, multiple-homogeneous structure—is employed to allow better diversification and exploration. Following the determination of optimal solutions, a conservative-based fuzzy satisfying approach is applied to characterize the best trade-off solution that suits cost-effectiveness and flexibility requirements. The newly developed model was implemented on the IEEE 24-bus and IEEE 118-bus test grids, and the simulation results proved its effectiveness and practicality.

Fairness in maximal covering location problems

This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) α-fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

Towards global parameter estimation exploiting reduced data sets

We focus on deterministic global optimization (DGO) for nonconvex parameter estimation problems. Realistic and accurate solutions often require a fitting against very large measurement data sets, resulting in intractable size for DGO. Thus, we aim at accelerating the branch-and-bound algorithm by using reduced data sets for constructing valid bounds. We focus on fitting the equation of state for propane, which is of high interest for the chemical industry. The resulting estimation problem is a challenging nonconvex mixed-integer nonlinear optimization problem. We investigate the validity of using reduced data sets by comparing how the lower and upper bounds change when replacing the full data set with different reduced data sets. We account for regions with high and low quality fits by considering the results for the whole feasible region and 100 different subregions. Our results indicate that both regions containing solution candidates and regions containing only low quality fits can be identified based on reduced data sets. Moreover, we observe that the average CPU time per branch-and-bound iteration typically decreases if reduced data sets are used.

DG-integrated stochastic multiyear distribution expansion planning considering fault current-limiting high-temperature superconducting cables

In this paper, the authors present a new stochastic multiyear framework for distribution expansion planning (DEP) that integrates fault current-limiting high-temperature superconducting cables (FCL-HTSCs) and distributed generations (DGs). The proposed framework, from a new perspective, is capable of analyzing and comparing the efficiency of the FCL-HTSCs with other, more generic cables under different short-circuit conditions. The objective function to be minimized isthe net present value of the total investment costs for reinforcing and/or installing substations, feeders, FCL-HTSCs, and DGs, as well as operation and maintenance costs. The framework also considers Kirchhoff’s current and voltage laws, operational limits on equipment capacities, voltage limits, as well as financial and discrete logical constraints. As a comprehensive overview, the authors have developed: (i) a graph-based bi-conditional scheme to ensure radiality requirements and (ii) a multi-horizon fractional information-gap decision theory (MH-FIGDT) to address the stochastic nature of anticipated load demand, power production of the DGs, and a capital expenditure budget. The resulting mixed-integer nonlinear optimization problem is solved by an integer-coded melody search algorithm (ICMSA) empowered with a multi-computational-stage multi-dimensional multiple-homogeneous structure that offers better performance in diversification and exploration. Case studies using the standard 27-node and realistic, large-scale 104-node distribution grids are provided here in order to show the effectiveness of the proposed framework. Based on simulation results, several conclusions can be drawn: (i) the MH-FIGDT critical cost and/or MH-FIGDT critical deviation coefficient chosen by the distribution grid operator play a key role in achieving robust expansion plans against the given uncertainty set; (ii) the incorporation of the FCL-HTSCs into the DEP problem offers a satisfactory compromise between the required amount and capacity of the equipment and total investment costs; (iii) the functionality of the FCL-HTSCs outperforms the generic cables in mitigating feeder congestion and excessive fault currents under normal and short-circuit conditions, respectively; and, (iv) the variations in fault currents caused by rising DG penetration are keep below the nominal interrupt rating of the circuit breakers, which speaks to the suitability of the proposed framework.

Voltage regulation and power loss mitigation by optimal allocation of energy storage systems in distribution systems considering wind power uncertainty

Due to the ever increasing in the energy demand and the growth of the pollution problem, further interest in renewable energy becomes prominent, especially wind energy. However, the intermittent nature of the wind speed results in the system's insecurity problems. Integrating the energy storage system (ESS) optimally is the best so far solution. In this paper, a probabilistic discretizing method is derived and generalized to consider the uncertainties of the wind generators. Moreover, a mixed integer non-linear optimisation problem is constructed comprises three objective functions to be minimized simultaneously. The objectives comprising the total operation and planning cost of ESSs, the average voltage deviation and average power losses. The solving method is a hybrid algorithm incorporates the non-dominated sorting genetic algorithm (NSGAII), multi-objective particle swarm optimisation (MOPSO) and a decision-making algorithm. The aim is to determine the optimal location and sizing of ESSs considering their reactive power capability. 69 radial bus distribution system is adopted to demonstrate the efficacy of the proposed hybrid algorithm and performing some case studies. The simulation results verified the capability of ESSs to enhance the voltage profile and reduce the power losses, notably when reactive power capability is examined.

A New Decision-Making Strategy for Techno-Economic Assessment of Generation and Transmission Expansion Planning for Modern Power Systems

Planning for the intensive use of renewable energy sources (RESs) has attracted wide attention to limit global warming and meet future load growth. Existing studies have shown that installing projects such as transmission lines, energy storage systems (ESSs), fault current limiters, and FACTs facilitate the integration of RESs into power systems. Different generation and transmission network expansion planning models have been developed in the literature; however, a planning model that manages multiple types of projects while maximizing the hosting capacity (HC) is not widely presented. In this paper, a novel planning framework is proposed to enhance and control the HC level of RESs by comparing various kinds of renewables, ESSs, fault current limiters, and FACTs to choose the right one, economically and technically. The proposed problem is formulated as a challenging mixed-integer non-linear optimization problem. To solve it, a solution methodology based on a developed decision-making approach and an improved meta-heuristic algorithm is developed. The decision-making approach aims to keep the number of decision variables as fixed as possible, regardless of the number of projects planned. While an improved war strategy optimizer that relies on the Runge-Kutta learning strategy is applied to strengthen the global search ability. The proposed decision-making approach depends primarily on grouping candidate projects that directly impact the same system state into four separate planning schemes. The first scheme relies on the impedance of devices installed in any path to optimally identify the location and size of the new circuits and the series-type FACTs. The second scheme is based on optimally determining the suitable types of ESSs. On the other hand, the third scheme optimizes the reactive power dispatched from the ESSs and shunt-type FACTs simultaneously. The fourth scheme is concerned with regulating the power dispatched from different types of RESs. All of the simulations, which were carried out on the Garver network and the 118-bus system, demonstrated the ability of the investigated model to select the appropriate projects precisely. Further, the results proved the robustness and effectiveness of the proposed method in obtaining high-quality solutions in fewer runs compared to the conventional method.

Adaptive Protection for Active Distribution Networks: An Approach Based on Fuses and Relays With Multiple Setting Groups

Protection schemes are essential in active distribution networks and microgrids’ reliable, efficient, and flexible operation. However, the protection of these networks presents significant challenges due to operational changes, such as variations in topology, distributed energy resources connection/disconnection, and microgrid operating modes, among others. This paper proposes an adaptive protection scheme based on overcurrent devices with several setting groups based on artificial intelligence algorithms. The developed strategy is composed of two stages. In the off-line stage, a clustering technique is employed to group the active distribution network operating scenarios exhibiting similarities. The optimal settings for the protection devices are determined for each set of scenarios. On the other hand, in the on-line stage, the protection strategy’s implementation and operation, considering the active distribution network’s existing communication system, are defined. Furthermore, the approach formulates the overcurrent relay coordination as a mixed-integer non-linear optimization problem, and as a result, the optimal setting of the overcurrent protection devices is obtained. It aims to minimize the operating time, considering the transformers’ thermal limits, fuse operating curves, and overcurrent relay settings. The solution is determined by using an Augmented Lagrangian genetic algorithm. The presented protection scheme is validated on the modified IEEE 34 node test feeder, considering the main operating scenarios of the active distribution networks, such as topology changes, distributed energy resource connection/disconnection, and microgrid operating modes (on-grid and off-grid). The results obtained and its easy implementation indicates the high potential for real-life applications.

Machine Learning-Based Uplink Scheduling Approaches for Mixed Traffic in Cellular Systems

The problem of the uplink resource allocation of mixed-traffic types in cellular networks is a challenging problem that has not been addressed sufficiently in the literature. In this paper, we consider the 5G uplink scheduling for Ultra-Reliable and Low Latency Communications and enhanced Mobile Broad-Band (eMBB) traffic types. There are three main scheduling techniques to be considered, namely, the grant-based (GB), the semi-persistent, and the grant-free (GF) techniques. Furthermore, there are three different schemes used in GF scheduling, namely, the reactive, the k-repetitions, and the proactive schemes. We devise a mathematical model for the GF services using the k-repetitions scheme as the first model to define such traffic in a single cell. In addition, the GB scheduling model for eMBB traffic is adapted to fit our problem. We formulate the scheduling problem as a mixed-integer non-linear programming optimization problem. We introduce a complete system model that includes GF and GB subsystems. We introduce a novel mixed scheduler that combines the advantages of two well-known schedulers in the literature. We introduce novel machine-learning-based scheduling algorithms and evaluate them in comparison to well-known algorithms in the literature in addition to the optimal bound that we also derive. The results show that the proposed algorithms produce near-optimal results in real time.

Outer Approximation for Mixed-Integer Nonlinear Robust Optimization

Currently, few approaches are available for mixed-integer nonlinear robust optimization. Those that do exist typically either require restrictive assumptions on the problem structure or do not guarantee robust protection. In this work, we develop an algorithm for convex mixed-integer nonlinear robust optimization problems where a key feature is that the method does not rely on a specific structure of the inner worst-case (adversarial) problem and allows the latter to be non-convex. A major challenge of such a general nonlinear setting is ensuring robust protection, as this calls for a global solution of the non-convex adversarial problem. Our method is able to achieve this up to a tolerance, by requiring worst-case evaluations only up to a certain precision. For example, the necessary assumptions can be met by approximating a non-convex adversarial via piecewise relaxations and solving the resulting problem up to any requested error as a mixed-integer linear problem.In our approach, we model a robust optimization problem as a nonsmooth mixed-integer nonlinear problem and tackle it by an outer approximation method that requires only inexact function values and subgradients. To deal with the arising nonlinear subproblems, we render an adaptive bundle method applicable to this setting and extend it to generate cutting planes, which are valid up to a known precision. Relying on its convergence to approximate critical points, we prove, as a consequence, finite convergence of the outer approximation algorithm.As an application, we study the gas transport problem under uncertainties in demand and physical parameters on realistic instances and provide computational results demonstrating the efficiency of our method.

Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm.

Buffer-Aware User Selection and Resource Allocation for an Opportunistic Cognitive Radio Network: A Cross-Layer Approach

In this paper, we focus on a cross-layer resource allocation problem for an opportunistic cognitive radio network, where secondary users (SUs) share a primary network’s licensed spectrum only when the primary network is sensed to be idle. We consider cooperative spectrum sensing, where SUs participate in sensing only when a benefit from resource allocation is guaranteed. Number of SUs for cooperative spectrum sensing is an important parameter as it defines both sensing and resource allocation performance. The fusion centre captures interaction between physical layer spectrum sensing, channel condition, and higher layer data buffer while selecting SUs for cooperative sensing. We consider heterogeneous data types at SUs’ data buffers during SU selection to make our system model more general. We form a mixed integer non-linear optimization problem, from which we select SUs’ set for sensing and resource allocation, appropriate sensing thresholds, and corresponding resource allocation parameters. Due to it’s combinatorial nature, the optimization problem is non-trivial. We devise an optimal algorithm to solve the optimization problem. Moreover, we also propose a computationally efficient and near-optimal greedy algorithm with suitable performance bounds. We also show advantage of our proposed optimal algorithms compared to other traditional methods through extensive simulations.

Energy‐efficient computation offloading and resource allocation in delay‐constrained vehicular edge network

SummaryCellular vehicular‐to‐everything (C‐V2X), as a key technology of Internet of Vehicles (IoV), is promised to be enhanced and strengthened to improve road traffic safety and achieve intelligent transportation in 6G era. However, computation‐intensive and latency‐sensitive computation tasks of autonomous driving create a great challenge for the computation and storage limited vehicles. Fortunately, mobile edge computing (MEC) architecture offers a possible solution for the challenge. In this paper, a joint computation offloading and resource allocation algorithm is proposed to solve the computation tasks offloading problem in the scenario of vehicular edge computing network. First, the computation offloading and resource allocation are jointly modeled as a mixed integer nonlinear optimization problem. Aiming at minimizing the total system cost (weighted sum of delay and energy consumption), a particle encoding method and a particle refinement algorithm are proposed based on the compression factor particle swarm optimization, and multilevel penalty function is adopted to deal with the constraints of the objective. Finally, experimental performances validate the effectiveness and feasibility of the proposed algorithm.

Simultaneous Optimization of Well Count and Placement: Algorithm, Validation, and Field Testing

SummaryRobust identification of the optimal well count and corresponding well locations/trajectories under the influence of subsurface uncertainty is a very challenging yet crucial element of field development plans. The well-count optimization (WCO) component of the problem involves an integer-valued optimization parameter because of the discrete nature of the well count. On the other hand, the well-location, well-trajectory, and well-opening-time optimization components typically feature real-valued continuous optimization parameters. The combined optimization problem encompasses both integer- and real-valued parameters. This class of problems is referred to as the mixed-integer nonlinear optimization problem in the literature. It is one of the most challenging classes of optimization problems and requires specialized optimizers. We have developed a new optimization protocol and accompanying optimizers to enable the joint optimization of well-count, well-locations (including well-trajectory parameters), and well-opening time within the framework of an industrial-grade subsurface field development optimization (sFDO) platform which encompasses state-of-the-art well-location optimization (WLO) capabilities. We have extended effective fault-tolerant global and local optimizers to solve the mixed-integer nonlinear optimization problem associated with the presence of well count in addition to real-valued parameters and optionally including well-opening-time parameters. We have introduced a novel well-priority-order concept to enumerate the wells subject to WCO. The resulting novel capability is simply coined as the simultaneous well-count optimization (SimWCO) method.The SimWCO method is first validated on a small yet well-known benchmark model. Investigations include assessing the effects of the objective-function type, well-priority order, and robust optimization including the optimization of well-opening-time parameters. SimWCO has been field tested on two real-life field development optimization problems. SimWCO has been compared with computationally intensive concurrent WCO and cumbersome-to-apply reverse- and forward-creaming WCO techniques as part of the field testing work. Reservoir A case involves optimization of well count and locations of up to three vertical production wells. It is a robust optimization application involving multiple subsurface realizations. The optimal well count and locations are sought in a single perforation target zone in this test. Reservoir B case involves the optimization of up to six deviated production wells in addition to eleven active production wells. This case features well-by-well assignment of perforation-target zones, a new development in sFDO. Results of this work demonstrate the viability of simultaneous optimization of well count, well locations, and optionally well-opening times on realistic real-life field development optimization problems using an industry-grade distributed parallel optimization framework. We also quantitatively demonstrate that SimWCO is more than three-fold computationally more efficient compared to alternative techniques in the Reservoir B field test.

Reducing committed emissions of heating towards 2050: Analysis of scenarios for the insulation of buildings and the decarbonisation of electricity generation

Infrastructure for heat provision in the built environment needs to change remarkably to support lowering carbon emissions and achieving climate mitigation targets before 2050. We propose a computational approach for finding a mix of heat options per neighbourhood that minimises cumulative carbon emissions between 2030 and 2050, referred to as committed emissions, while at the same time adhering to technological constraints at both the household and neighbourhood scales. To establish this approach, we integrated bottom-up heat demand modelling at neighbourhood scale with a mixed-integer non-linear optimisation problem. Nine scenarios with different pathways for the insulation of buildings and the decarbonisation in electricity generation were considered and applied to three neighbourhoods in the city of Amsterdam, the Netherlands. The results show that (i) the committed emissions are ten times lower between 2030 and 2050 in scenarios in which ambitious measures are taken for the insulation of buildings and the decarbonisation in electricity generation, (ii) only in these ‘ambitious scenarios’ low temperature heat systems, such as heat pumps and low temperature heat networks, are optimal solutions for minimising committed emissions, (iii) if less ambitious insulation and decarbonisation measures are taken, high temperature heat options can be part of the heat mix with lowest committed emissions, and (iv) the minimum heat density for low temperature heat networks is not always achieved, creating risks for carbon lock-ins when applying these heat networks. Our results clearly indicate that pathways for the retrofitting of buildings and the decarbonisation in electricity generation need to be taken into account jointly when designing renewable and low-carbon heat systems to optimally reduce carbon emissions towards 2050 and reduce future carbon lock-ins.

A seismic-resilient multi-level framework for distribution network reinforcement planning considering renewable-based multi-microgrids

In this paper, a new resilient framework is presented for distribution network reinforcement planning (DNRP) with the consideration of renewable-based multi-microgrids (RMGs) to mitigate seismic risks. For this aim, the proposed framework is formulated as a non-convex mixed-integer nonlinear four-level optimization problem. The first level outlines a short-term corrective measures problem to remedy seismic risks using feeder reconfiguration and distributed energy resources rescheduling. The second level represents an earthquake-related catastrophic failures problem in which peak ground acceleration and distribution component vulnerability are modeled through attenuation functions and fragility curves, respectively. The third and fourth levels, however, describe coordination of a decentralized double-layer multistage microgrid reinforcement planning (MGRP) problem and a centralized cost-effective multistage DNRP problem to characterize seismic-resilient optimal reinforcement plans. Due to its desirable handling of multi-level optimization problems having a non-convex mixed-integer nonlinear nature, the multi-computational-step, multi-dimensional, multiple-homogeneous improved melody search algorithm, referred to as a symphony orchestra search algorithm (SOSA), is used to solve the proposed framework. The performance of the newly developed framework is numerically analyzed through implementing it to the standard 33-, 54-, 119- and 136-node distribution test networks. The numerical results well corroborate the sufficiency and profitableness of the proposed framework in achieving low vulnerability and high resilience to seismic risks.

Intelligent Reflecting Surface-Aided Device-to-Device Communication: A Deep Reinforcement Learning Approach

Recently, the growing demand of various emerging applications in the realms of sixth-generation (6G) wireless networks has made the term internet of Things (IoT) very popular. Device-to-device (D2D) communication has emerged as one of the significant enablers for the 6G-based IoT network. Recently, the intelligent reflecting surface (IRS) has been considered as a hardware-efficient innovative scheme for future wireless networks due to its ability to mitigate propagation-induced impairments and to realize a smart radio environment. Such an IRS-assisted D2D underlay cellular network is investigated in this paper. Our aim is to maximize the network’s spectrum efficiency (SE) by jointly optimizing the transmit power of both the cellular users (CUs) and the D2D pairs, the resource reuse indicators, and the IRS reflection coefficients. Instead of using traditional optimization solution schemes to solve this mixed integer nonlinear optimization problem, a reinforcement learning (RL) approach is used in this paper. The IRS-assisted D2D communication network is structured by the Markov Decision Process (MDP) in the RL framework. First, a Q-learning-based solution is studied. Then, to make a scalable solution with large dimension state and action spaces, a deep Q-learning-based solution scheme using experience replay is proposed. Lastly, an actor-critic framework based on the deep deterministic policy gradient (DDPG) scheme is proposed to learn the optimal policy of the constructed optimization problem considering continuous-valued state and action spaces. Simulation outcomes reveal that the proposed RL-based solution schemes can provide significant SE enhancements compared to the existing optimization schemes.

A Three-Stage Alternative Optimization Promoting Multi-UAV-Assisted Mobile Offloading

A solution using multiple-relay method is presented to provide an efficient solution using UAV-assisted mobile devices to complete computation offloading tasks, which considers the UAVs in the offloading system to help mobile devices to offload tasks in remote areas. Additionally, a mixed integer nonlinear optimization (MINO) problem is constructed to maximize minimum user computational speed, and a three-stage iterative optimization algorithm is proposed to find a solution of the MINO problem. Simulation experiments are setup to verify the effectiveness of the devised methods, which show that our proposed algorithm and solution is superior to the single UAV method.

Reward Factor-Based Multiple Agile Satellites Scheduling With Energy and Memory Constraints

Earth observing satellites (EOS) orbit around the earth to perform observation tasks specified by users. The additional maneuverability resulting from higher degrees of freedom than nonagile EOS (N-AEOS) provides agile EOS (AEOS) a significantly larger visible time window to complete the tasks. As a consequence, the task scheduling for AEOS is much more computationally complex than N-AEOS. In this article, a mixed-integer nonlinear optimization problem is formulated to find a near-optimal task allocation for a realistic AEOS scheduling problem. The satellite resources, such as energy and memory constraints, are considered in this problem. A reward factor is used to address the requirement of multiple scans in order to complete a task. A probability factor is also taken into consideration to incorporate the uncertainty of successful scans due to external factors, such as cloud coverage. An elitist mixed coded genetic algorithm-based satellite scheduling (EMCGA-SS) algorithm is proposed to solve the formulated problem. EMCGA-SS is extended to elitist mixed coded hybrid genetic algorithm-based satellite scheduling by combining a hill-climber mechanism in order to have better initialization. Experimental results to illustrate the performance of the algorithms and a comparison with some widely used methodologies are also presented.

Integrated UAV Trajectory Control and Resource Allocation for UAV-Based Wireless Networks With Co-Channel Interference Management

In this article, we study the trajectory control, subchannel assignment, and user association design for unmanned aerial vehicles (UAVs)-based wireless networks. We propose a method to optimize the max-min average rate subject to data demand constraints of ground users (GUs) where spectrum reuse and co-channel interference management are considered. The mathematical model is a mixed-integer nonlinear optimization problem which we solve by using the alternating optimization approach where we iteratively optimize the user association, subchannel assignment, and UAV trajectory control until convergence. For the subchannel assignment subproblem, we propose an iterative subchannel assignment (ISA) algorithm to obtain an efficient solution. Moreover, the successive convex approximation (SCA) is used to convexify and solve the nonconvex UAV trajectory control subproblem. Via extensive numerical studies, we illustrate the effectiveness of our proposed design considering different UAV flight periods and number of subchannels and GUs as compared with a simple heuristic.