Mixed Integer Nonlinear Programming Problem Research Articles

Assessment of reliability measures and cost optimization of a solar seed sowing machine

PurposeIn this research work, the general form of reliability measures, which include availability, mean time to failure (MTTF), and sensitivity analysis, are investigated with their graphical representation, which would help designers and engineers improve the reliability of the system. Along with reliability assessment, a mathematical model is developed and solved to achieve the minimum cost of the system as well as maximum reliability.Design/methodology/approachIn the proposed work, a general model of a solar seed sowing machine is considered for reliability evaluation using the Markov model process. The proposed system is a series-parallel arrangement of components where three components, namely the solar panel, batteries and direct current (DC) motor, are connected in series while all the operators are connected in parallel. The implemented Markov model approach assesses several parameters of reliability, which opens the scope for improvement in reliability and other measures like mean time to failure (MTTF) and sensitivity of the proposed system. So that the machine can deliver the desired output on the field. Also, the particle swarm optimization (PSO) algorithm is applied to optimize the cost of the system with the desired level of reliability.FindingsImplementation of PSO provides the optimal cost for the proposed system with a predetermined level of reliability, which shows the relationship between reliability and cost of the system. Also, the Markov process approach provides the availability function, reliability function, reliability at different time values, MTTF and sensitivity of the proposed system.Originality/valueThis work evaluates the crucial characteristics of reliability for the proposed solar seed sowing machine using the Markov model which is a stochastic model. The assessment of reliability measures such as MTTF, availability and sensitivity plays a vital role in measuring and improving the performance of the machine in the actual environment. Examining the data obtained in this research is of great importance for the manufactures and system designers. Also, the powerful optimization technique PSO is implemented to solve a non-linear mixed-integer programming problem that provides the optimal cost for the system with desired reliability.

Economic modelling and optimisation of SPRT-based quality control schemes for individual observations

In many industrial processes, it may not be practical to obtain sample sizes larger than one due to various reasons. As a result, practitioners must rely on control charts based on individual observations for statistical process monitoring and control. The sequential probability ratio test (SPRT) chart is an appropriate solution for such situations. Existing literature predominantly delves into the statistical aspects of designing or optimising an SPRT chart, neglecting the economic and associated design aspects. However, past experience suggests that statistical design may not always be optimal from an economic perspective. This paper aims to bridge this research gap by proposing a two-stage Markov chain approach to develop an economic model for the optimal design of the SPRT chart with individual observations. Following the principles of economic-statistical designs, optimal parameters are determined by solving a mixed-integer non-linear programming problem that minimises the long-run cost per item while ensuring compliance with practical constraints. Through an extensive study, we find that the economic performance of the SPRT chart surpasses that of competing individual control charts in many cases. This indicates that the economic-statistical design of the SPRT chart can yield significant economic benefits while maintaining desirable statistical properties. Moreover, enhancements have been introduced to refine the optimal design of the SPRT chart, retaining excellent overall performance across a wide range of shifts. Finally, we provide two industrial examples to illustrate the effectiveness of the proposed SPRT chart.

Collaborative Computation Offloading and Resource Management in Space–Air–Ground Integrated Networking: A Deep Reinforcement Learning Approach

With the increasing dissemination of the Internet of Things and 5G, mobile edge computing has become a novel scheme to assist terminal devices in executing computation tasks. To elevate the coverage and computation capability of edge computing, a collaborative computation offloading and resource management architecture was proposed in space–air–ground integrated networking (SAGIN). In this manuscript, we established a novel model considering the computation offloading cost constraints of the communication, computing and cache model in the SAGIN. To be specific, the joint optimization problem of collaborative computation offloading and resource management was modeled as a mixed integer nonlinear programming problem. To address this issue, this paper proposed a computation offloading and resource allocation strategy based on deep reinforcement learning (DRL). Differing from traditional methods, DRL does not need a well-established formulation or previous information, and it is capable of revising the strategy adaptively according to the environment. The simulation results demonstrate the proposed approach can achieve the optimal reward values in the case of different terminal device numbers. Furthermore, this manuscript provided the analysis with variant parameters of the proposed approach.

NOMA Assisted Two-Tier VR Content Transmission: A Tile-Based Approach for QoE Optimization

Virtual reality (VR) provides users with an immersive and interactive experience through head-mounted devices, which has attracted increasing attention in recent years. Specifically, tile-based VR content transmission provides a promising approach to alleviate the conflict between limited bandwidth and high-performance requirements (e.g., high-resolution and low-delay). However, the tiling pattern affects the encoding efficiency and visual distortion of the VR content. Accounting for this issue, in this paper, a quality of experience (QoE)-aware cost minimization problem is investigated for a tile-based VR content transmission scenario. In particular, an edge server (ES) co-located at a cellular base station (BS) separates its generated VR content into several tiles according to the tiling pattern selection, and a weighted-to-spherically-uniform quality model is used to evaluate the effect of different tiling patterns on QoE. Moreover, to improve the transmission performance between the edge server and VR users (VRUs), unmanned aerial vehicles (UAVs) are leveraged as relay points to provide line of sight channels. Then, we formulate an optimization problem to minimize the sum of weighted total energy consumption and VR content distortion (i.e., QoE-aware cost) by jointly optimizing the tiling pattern selections, the VRUs-UAV grouping, partial computing decisions, and resource allocation. The formulated problem is a mixed integer non-linear programming problem, which is challenging to solve. To address this difficulty, we equivalently decompose the formulated problem into three subproblems and propose corresponding algorithms to solve them, respectively. Numerical results demonstrate that our proposed solution can effectively reduce the QoE-aware cost for VR content transmission in comparison with other baseline algorithms.

An online integrated satellite–terrestrial IoT task offloading and service deployment strategy

As a core component of 6G networking, low earth orbit (LEO) satellite networks are considered a promising solution for providing network services in remote areas and have received considerable attention in recent years. Meanwhile, with the rapid development of IoT terminals and applications, an increasing emphasis has been placed on task offloading for real-time tasks. However, most existing works on task offloading for integrated satellite–terrestrial IoT (IST-IoT) applications are based on the assumption that the global task and network information is known, an assumption that is obviously not met in online real-time task offloading. In addition, current studies rarely consider the tradeoff among the task offloading volume, satellite endurance and wholesale cost of terrestrial resources, which are precisely the holistic issues that satellite network operators must confront. To address such issues, this study considers task offloading, service deployment and resource allocation in highly dynamic online task offloading scenarios with the goal of maximizing the average task offloading volume. Moreover, virtual queues are constructed in this study to account for the impacts of long-term satellite endurance and terrestrial network resource costs on task offloading. We first decouple the original problem to obtain a single-time-slot optimization problem within the Lyapunov optimization framework, and we then propose a 2-stage optimization approach based on deep reinforcement learning (DRL) to solve the complex single-time-slot mixed integer nonlinear programming (MINLP) problem. Simulation experiments demonstrate that our proposed algorithm can yield near-optimal solutions that show superior performance compared to existing results.

SMITS: Social and Mobility aware Intelligent Task Scheduling in Vehicular Fog Computing — A Federated DRL Approach

Vehicular fog computing (VFC) has become an enticing research hot spot to provide resources for the Internet of Vehicles (IoV) application requests. Moreover, with the massive expansion of services in vehicular fog networks such as augmented reality, 3-D gaming, and autonomous driving, the allocation of fog computing resources to IoV applications constraining the deadline and energy consumption of the vehicles is becoming challenging. In this paper, we investigate a task scheduling problem in vehicular fog networks to jointly optimize the success rate of vehicular tasks and energy consumption of vehicles by considering the moving paths of the vehicles and the social relationships among the vehicles. In this problem, we model the social relationship among the vehicles based on their communication patterns and social characteristics to improve the success rate of the tasks. We also incorporate the mobility of vehicles using the Markov renewal process (MRP) technique. Initially, we formulate a mixed integer nonlinear programming (MINLP) problem for the proposed problem and further prove it to be an NP-hard problem. To solve the proposed problem, we design a federated deep reinforcement learning (FDRL) mechanism by converting the problem into a Markov decision process (MDP) problem. We compare our proposed algorithm with existing scheduling approaches, and simulation results show that the proposed algorithm performs efficiently for task scheduling problems. The proposed algorithm achieved a substantial improvement of 12% in the maximization of the success rate and 36% in the minimization of the energy consumption compared to the existing algorithms.

Simultaneous Minimization of Water Age and Pressure in Water Distribution Systems by Pressure Reducing Valves

AbstractPressure reducing valves (PRVs) are essentially used to reduce operational pressures in water distribution systems (WDSs) to minimize water leakage. However, water age in a WDS is an important variable describing the water quality and should be kept as low as possible. Therefore, the aim of this study is to investigate the possibility and potential of simultaneously minimizing both pressure and water age by using PRVs. To determine the optimal location and setting of PRVs, a mixed-integer nonlinear programming (MINLP) problem is formulated with minimization of the sum of the weighted total water age and pressure as the objective function, where the weighting factor can be defined by the user’s preference. The equality constraints consist of the hydraulic equations and water age functions to describe pressure and water age in the distribution network, while the inequality constraints ensure them in the defined operating ranges, respectively. Applying the proposed approach to two case studies, the results show that both water age and pressure can indeed be significantly reduced by the optimized position and setting of the PRVs.

Transmission Expansion Planning Considering Storage, Flexible AC Transmission System, Losses, and Contingencies to Integrate Wind Power

To meet future load projection with the integration of renewable sources, the transmission system must be planned optimally. Thus, this paper introduces a comparative analysis and comprehensive methodology for transmission expansion planning (TEP), incorporating the combined effects of wind power, losses, N-1 contingency, a FACTS, and storage in a flexible environment. Specifically, the optimal placement of the FACTS, known as series capacitive compensation (SCC) devices, is used. The intraday constraints associated with wind power and energy storage are represented by the methodology of typical days jointly with the load scenarios light, heavy, and medium. The TEP problem is formulated as a mixed-integer nonlinear programming (MINLP) problem through a DC model and is solved using a specialized genetic algorithm. This algorithm is also used to determine the optimal placement of SCC devices and storage systems in expansion planning. The proposed methodology is then used to perform a comparison of the effect of the different technologies on the robustness and cost of the final solution of the TEP problem. Three test systems were used to perform the comparative analyses, namely the Garver system, the IEEE-24 system, and a real-world Colombian power system of 93 buses. The results indicate that energy storage and SCC devices lead to a decrease in transmission requirements and overall investment, enabling the effective integration of wind farms.

Tradeoff Between Age of Information and Operation Time for UAV Sensing Over Multi-Cell Cellular Networks

Unmanned aerial vehicles (UAVs) have a significant potential for sensing applications in further cellular networks due to their extensive coverage and flexible deployment. In this paper, we consider a multi-cell cellular network with a cellular-connected UAV, which senses data with onboard sensors and uploads sensory data to the ground base stations (BSs). To evaluate the freshness of sensory data, we employ the concept of age of information (AoI), which is defined as the time elapsed since the latest successful transmission of sensory data. A lower AoI implies fresher sensory data, which may lead to the increase of UAV operation time. To balance such tradeoff, we aim to minimize the weighted sum of operation time and total AoI for the UAV by jointly optimizing transmission scheduling, BS association, as well as UAV trajectory. The problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve due to the time-varying propagation channels. To this end, we first characterize the average communication performance with statistic channel information, and then develop a search algorithm to obtain the optimal solution via employing the optimal structure as well as convex optimization techniques, while a low-complexity Double Graph based Algorithm (DGA) is developed to obtain a suboptimal solution. Then, by taking into account the site-specific performance and making fast decisions online, we propose a Deep reinforcement Learning Algorithm (DLA). Compared to DGA, DLA can adapt to the specific local environment and obtain a solution more rapidly once the training process is completed. Simulation results show that the proposed algorithms outperform the benchmarks about 30%, and achieve flexible tradeoff between operation time and AoI of UAV sensing, which is not available by considering just one objective.

Joint Service Caching, Resource Allocation and Task Offloading for MEC-Based Networks: A Multi-Layer Optimization Approach

To provide reliable and elastic Multi-access edge computing services, one feasible solution is to federate geographically proximate edge servers to form a logically centralized resource pool. Optimization of such systems, however, becomes challenging. In this paper, we study the problem of maximizing users' QoE in a MEC-based network, through jointly optimizing service caching, resource allocation and task offloading decisions. We formulate a mixed-integer nonlinear programming (MINLP) problem for the task and establish its NP-hardness. To tackle it efficiently, we propose a novel two-stage algorithmic solution based on approximation and decomposition theory. The proposed algorithm achieves high system performance while at the same time, ensures all constraints from different layers are satisfied. Meanwhile, the structure of the algorithm also fits the multi-layer optimizing feature, making it suitable to be implemented at different layers. In addition, we propose a distributed and online version of our mechanism with very limited information exchange between MEC servers, and further demonstrate how the cost of service switches from real MEC systems can be incorporated into our framework. We evaluate our mechanisms through simulations with both synthetic and real-world traces, and results indicate they are effective as compared to representative baseline algorithms.

Multi-User Computation Offloading and Resource Allocation Algorithm in a Vehicular Edge Network.

In Vehicular Edge Computing Network (VECN) scenarios, the mobility of vehicles causes the uncertainty of channel state information, which makes it difficult to guarantee the Quality of Service (QoS) in the process of computation offloading and the resource allocation of a Vehicular Edge Computing Server (VECS). A multi-user computation offloading and resource allocation optimization model and a computation offloading and resource allocation algorithm based on the Deep Deterministic Policy Gradient (DDPG) are proposed to address this problem. Firstly, the problem is modeled as a Mixed Integer Nonlinear Programming (MINLP) problem according to the optimization objective of minimizing the total system delay. Then, in response to the large state space and the coexistence of discrete and continuous variables in the action space, a reinforcement learning algorithm based on DDPG is proposed. Finally, the proposed method is used to solve the problem and compared with the other three benchmark schemes. Compared with the baseline algorithms, the proposed scheme can effectively select the task offloading mode and reasonably allocate VECS computing resources, ensure the QoS of task execution, and have a certain stability and scalability. Simulation results show that the total completion time of the proposed scheme can be reduced by 24-29% compared with the existing state-of-the-art techniques.

Biogas upgrading—Computer-aided ionic liquid absorbent design and process evaluation

Biogas is a renewable energy source and needs to be upgraded to biomethane for injection into the natural gas grid or use as fuel. To design ionic liquid (IL) solvents for biogas upgrading, a computer-aided ionic liquid design (CAILD) method and the corresponding process simulation are presented. The UNIFAC-IL model is employed to calculate the solubility of gases in ILs, while group contribution (GC) based models are used to predict the physicochemical properties of ILs. By using the performance index (PI) as the objective function and the structural feasibility and physicochemical properties as constraints, a mixed-integer nonlinear programming (MINLP) problem is formulated and solved by the generate-and-test method. Two IL solvents, [MMPY][Tf2N] (1,3-dimethylpyridinium bis(trifluoromethylsulfonyl)imide) and [MMPY][eFAP] (1,3-dimethylpyridinium tris(pentafluoroethyl) trifluorophosphate), are found to be the optimal IL solvents from 880 IL candidates. To perform the process simulation by using the designed ILs, the parameters for the equations of calculation of required properties are regressed. A sensitivity analysis is performed to find the optimal conditions for the process. Finally, the developed process is compared with the water-scrubbing process for biogas upgrading.

Establishing a hierarchical local market structure using multi-cut Benders decomposition

Local electricity markets (LEMs) such as peer-to-peer (P2P) and community-based markets allow prosumers and consumers to exchange electricity products and services locally. In order to coordinate electricity trading and flexibility services, this paper proposes a hierarchical prosumer-centric market framework with a hybrid LEM and a local flexibility market (LFM). Multi-cut Benders decomposition (MCBD) is employed to decompose the integrated hybrid LEM into a centralized P2P market and multiple community-based markets. The aggregators coordinate energy sources and demands of households in low voltage (LV) distribution networks (DN) as virtual power plants (VPPs) and engage in trading through a P2P market over the medium voltage (MV) DN. In addition, a modified MCBD (M-MCBD) approach is proposed to accelerate the convergence process. The LFM is operated by the distribution system operator (DSO) and is formulated as a mixed-integer nonlinear programming (MINLP) problem which is further relaxed to a mixed-integer second-order cone programming (MI-SOCP) problem. The case study demonstrates that aggregators were able to collaborate on trading within the hybrid LEM to minimize the costs incurred by prosumers within the network. Furthermore, the proposed M-MCBD method improves the scalability of the MCBD by enhancing its convergence speed and accuracy, as demonstrated by testing on problems of varying scales.

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. The code and data are available at https://github.com/cassiebuhler/conservation-dfo.

Dynamic microgrid formation for resilient distribution systems considering large-scale deployment of mobile energy resources

Microgrids (MGs) are promising solutions to improve power distribution system (PDS) resilience against natural disasters. However, the existing MG formation approaches based on the linearized Distflow (LinDistflow) model always demand MG roots and their corresponding topologies. This can result in an increased number of variables and constraints in the optimization problem, and deteriorate their computational performance. To this end, an adaptive LinDistflow model is proposed based on the single commodity flow model in graph theory in this paper. Specifically, we show that active and reactive powers can be represented as commodities, which are sent from one node to each of its adjacent nodes in the graph. Then, the power flow and nodal voltage calculation based on the commodity flow only requires adjacent node information of the original topology rather than various MG topologies caused by the dynamic deployment of mobile energy resources (MERs). Furthermore, by incorporating the adaptive LinDistflow model as constraints, a dynamic MG formation approach is proposed for resilient load restoration considering large-scale MER deployment. The problem is formulated as a mixed-integer nonlinear programming problem (MINLP). A linearization technique is proposed based on the propositional logic constraints. It employs the propositional logic that partitions the solution space into two separated regions. Accordingly, the region that the solution lies in can be selected linearly. The effectiveness of the proposed approach is demonstrated based on the IEEE 37-Node, 123-Node and 8500-Node Test Feeders.

Ionic liquid-ethanol mixed solvent design exemplified for the decarbonization of shale gas and biogas

Shale gas and biogas, recognized as “clean” energy sources, hold the potential to replace fossil fuels, necessitating efficient decarbonization processes. This study proposes a mixed solvent, combining ionic liquid (IL) and ethanol, for a cost- and energy-effective decarbonization approach. Initially, a computer-aided molecular method optimizes the IL molecule structure, identifying 1-hydroxy-3-methyl-pyridinium trifluoroacetate ([OHMPY][CF3COO]) through solving a formulated mixed-integer nonlinear programming (MINLP) problem. The [OHMPY][CF3COO]-ethanol mixed solvent's performance is validated in shale gas and biogas decarbonization across diverse gas compositions and feed conditions. A comprehensive comparison with the traditional MDEA-based CO2 removal process is conducted, evaluating energy, economic, and environmental aspects. Results indicate that the [OHMPY][CF3COO]-ethanol decarbonization process offers 30.65%-41.48% power savings, a 3.68%-17.18% reduction in investment costs, and an 18.08%–22.45% decrease in CO2 emissions. These findings underscore the significant potential of the proposed IL-ethanol binary mixed solvent in decarbonization processes.

Online Joint Optimization of Virtual Network Function Deployment and Trajectory Planning for Virtualized Service Provision in Multiple-Unmanned-Aerial-Vehicle Mobile-Edge Networks

The multiple-unmanned-aerial-vehicle (multi-UAV) mobile edge network is a promising networking paradigm that uses multiple resource-limited and trajectory-planned unmanned aerial vehicles (UAVs) as edge servers, upon which on-demand virtual network functions (VNFs) are deployed to provide low-delay virtualized network services for the requests of ground users (GUs), who often move randomly and have difficulty accessing the Internet. However, VNF deployment and UAV trajectory planning are both typical NP-complete problems, and the two operations have a strong coupling effect: they affect each other. Achieving optimal virtualized service provision (i.e., maximizing the number of accepted GU requests under a given period T while minimizing the energy consumption and the cost of accepting the requests in all UAVs) is a challenging issue. In this paper, we propose an improved online deep reinforcement learning (DRL) scheme to tackle this issue. First, we formulate the joint optimization of the two operations as a nonconvex mixed-integer nonlinear programming problem, which can be viewed as a sequence of one-frame joint VNF deployment and UAV-trajectory-planning optimization subproblems. Second, we propose an online DRL based on jointly optimizing discrete (VNF deployment) and continuous (UAV trajectory planning) actions to solve each subproblem, whose key idea is establishing and achieving the coupled influence of discrete and continuous actions. Finally, we evaluate the proposed scheme through extensive simulations, and the results demonstrate its effectiveness.

Particle Swarm Optimization for Directional Overcurrent Relay Coordination with Distributed Generation

The Directional Overcurrent Relays (DOCRs) Coordination with Distributed Generation (DG) optimization problem is addressed in this study using the optimization method Particle Swarm Optimization (PSO). Changes in fault current, bus voltages, power flow, and reliability may result from DG integration. Thus, it might have an impact on the current protection coordination system. The formulation is built on a Mixed Integer Non-Linear Programming (MINLP) problem to address this DOCR issue. MATLAB was used to validate the technique on the IEEE-14 bus system, and Electrical Test Transient Analyzer Programming (ETAP) version 2021 software was used to model the test system. According to the simulation results, the suggested PSO with DG for Case 2 has reduced power loss by 6.24% and relay operating time by 46.79% when compared to PSO without the presence of DG.

Saving Energy and High-Efficient Inspection to Offshore Wind Farm by the Comprehensive-Assisted Drone

Facing the method’s limitations of the existing drone inspection on offshore wind farms, we adopt a new comprehensive-assisted drone automated inspection scheme under the comprehensive assistance. Our objectives are saving energy and high-efficient inspection. The such inspection is used to formulating the two mixed-integer nonlinear programming problems based on two new drone basic models: the mobile edge computing driven drone computation system model and the drone flight model. To solve the problems, we split them into four subproblems, and a new improved heuristic algorithm is created to address. In turns, the waypoints, total inspection time, inspection energy consumption, and traveling distance of unmanned aircraft vehicle (UAV) and the traveling distance of boat are obtained by K-means algorithm and the smallest enclosing circle (SEC) algorithm, the Lin-Kernighan Heuristic 3 (LKH-3) algorithm, and the LKH. Finally, conducting the comprehensive optimization and simulation, the simulation numeric results are gotten. The simulation results demonstrate that as for the two aspects of the total energy consumption and inspection efficiency under different data amount and average wind speed, the scheme improves at most 44% and 23.5% than the current other three; the scheme achieves the objective of saving energy and high-efficient inspection.

Joint Dataset Reconstruction and Power Control for Distributed Training in D2D Edge Network

The intrinsic nature of non-independent and identically distributed datasets on heterogeneous devices slows down the distributed model training process and reduces the training accuracy. To settle this problem, we propose a dataset reconstruction scheme to transform the data distribution of training device’s dataset into independent and identically distributed dataset via data exchange among trusted devices. For energy efficiency, we further consider power control for the devices. We then formulate an optimization problem, which is a mixed integer non-linear programming problem, to minimize the total energy consumption for each round of distributed training. Due to the NP-hardness and coupling property of the optimization problem, we decompose it into two subproblems for dataset reconstruction and power control, respectively. An approximation algorithm is designed to obtain a near-optimal auxiliary devices set for dataset reconstruction with minimum energy consumption, while meeting the variance constraint of the optimization problem. We prove that approximation algorithm has a worst-case approximation ratio of 1+ln|Ωi(t)|, where |Ωi(t)| is the required data samples for dataset reconstruction of each training device. For power control, we design a dynamic programming algorithm to further reduce the energy consumption. For comparison, we propose three benchmark schemes that adopt either one of the algorithms or neither. We also customize three baseline algorithms based on the state-of-the-arts to compare with our proposed algorithm. Numerical results show that, our proposed algorithm outperforms three benchmarks on the average energy consumption for one round for different cases. When varying the labels that each device owns, our proposed algorithm outperforms the other three baseline algorithms on training accuracy. Besides, when setting a target accuracy, our proposed algorithm always has the lowest energy consumption.