Optimal distribution of reliability for a large network based on connectivity

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms （GA）. Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

Multi-Period Optimal Distribution Model of Energy Medium and Its Application

A mathematical model of optimal energy medium distribution in steelmaking process is formulated. In this model, three kinds of important energy mediums including byproduct gases, steam and electricity are considered, and the objective function accounts for both the change of generation and consumption of the byproduct gases and the demand of low （or middle） pressure steam and electricity for each period to maximize the benefit of products cost and minimize the consumption of energy. The results indicate that the optimal distribution scheme of byproduct gases, middle pressure steam, low pressure steam and electricity is achieved and case study shows that 6% of operation cost is reduced by using the proposed model comparing with the previous model.

OPTIMAL DYNAMIC LOAD DISTRIBUTION OF MULTIPLE COOPERATING ROBOT MANIPULATORS

For the situation of multiple cooperating manipulators handling a single object,an equilibrium equation is presented in which the manipulator dynamics and control forces/torques are taken into account,and a expression is derived to allow the optimal dynamic load distribution of the combined system can be made.

An Optimal Control-Based Distributed Reinforcement Learning Framework for A Class of Non-Convex Objective Functionals of the Multi-Agent Network

This paper studies a novel distributed optimization problem that aims to minimize the sum of the non-convex objective functionals of the multi-agent network under privacy protection, which means that the local objective of each agent is unknown to others. The above problem involves complexity simultaneously in the time and space aspects. Yet existing works about distributed optimization mainly consider privacy protection in the space aspect where the decision variable is a vector with finite dimensions. In contrast, when the time aspect is considered in this paper, the decision variable is a continuous function concerning time. Hence, the minimization of the overall functional belongs to the calculus of variations. Traditional works usually aim to seek the optimal decision function. Due to privacy protection and non-convexity, the Euler-Lagrange equation of the proposed problem is a complicated partial differential equation.Hence, we seek the optimal decision derivative function rather than the decision function. This manner can be regarded as seeking the control input for an optimal control problem, for which we propose a centralized reinforcement learning(RL) framework. In the space aspect, we further present a distributed reinforcement learning framework to deal with the impact of privacy protection. Finally, rigorous theoretical analysis and simulation validate the effectiveness of our framework.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.

THE OPTIMAL ACTIVITY DISTRIBUTION IN NONISOTHERMAL PELLETS

The nonisothermal effectiveness fcator for reaction with kinetics r=kc^m/(l+Kc)~a can be improved bycatalysts with nonuniform activity distribution.The optimal distribution function in one-dimensional modelwith which the effectiveness factor can be maximized is a δ-function which means that the activity of thecatalyst should be concentrated on a layer with negligible thickness in a precise locationfrom the centerof pellets.The general equations for predicting the value ofand maximum effectiveness factor as a functionof thermodynamic,kinetic and transport parameters are derived and they can be given explicitly in the case ofa=O,m=a or isothermal reaction.An active layer with definite thickness and a deviation from the optimal locationboth decrease thevalue of the effectiveness factor.It has been shown numerically that the effectiveness factor decreases slightlywith an active layer at the inner side of x but seriously at outer side.

A Cooperative Security Monitoring Mechanism Aided by Optimal Multiple Slave Cluster Heads for UASNs

As each cluster head(CH)sensor node is used to aggregate,fuse,and forward data from different sensor nodes in an underwater acoustic sensor network(UASN),guaranteeing the data security in a CH is very critical.In this paper,a cooperative security monitoring mechanism aided by multiple slave cluster heads(SCHs)is proposed to keep track of the data security of a CH.By designing a low complexity“equilateral triangle algorithm(ETA)”,the optimal SCHs(named as ETA-based multiple SCHs)are selected from the candidate SCHs so as to improve the dispersion and coverage of SCHs and achieve largescale data security monitoring.In addition,by analyzing the entire monitoring process,the close form expression of the probability of the failure attack identification for the SCHs with respect to the probability of attack launched by ordinary nodes is deduced.The simulation results show that the proposed optimal ETA-based multiple SCH cooperation scheme has lower probability of the failure attack identification than that of the existing schemes.In addition,the numerical simulation results are consistent with the theoretical analysis results,thus verifying the effectiveness of the proposed scheme.

Distributionally robust optimization based chance-constrained energy management for hybrid energy powered cellular networks

Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.

Distributionally Robust Newsvendor Model for Fresh Products under Cap-and-Offset Regulation

The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.

Distributed Robust Optimal Dispatch for the Microgrid Considering Output Correlation between Wind and Photovoltaic

As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids.This paper proposes an optimization scheme based on the distributionally robust optimization(DRO)model for a microgrid considering solar-wind correlation.Firstly,scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function;then the generated scenario results are reduced by K-means clustering;finally,the probability confidence interval of scenario distribution is constrained by 1-norm and∞-norm.The model is solved by a column-and-constraint generation algorithm.Experimental studies are conducted on a microgrid system in Jiangsu,China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties,which verifies the effectiveness of the proposed DRO model.

Leader-follower Optimal Selection Method for Distributed Control System in Active Distribution Networks

Aiming at the shortcomings of a traditional centralized control in an active distribution network(AND),this paper proposes a leader-follower distributed group cooperative control strategy to realize multiple operation and control tasks for an ADN.The distributed information exchange protocols of the distributed generation(DG)group devoted to node voltage regulation or exchange power control are developed using a DG power utilization ratio as the consensus variable.On these bases,this study further investigates the leader optimal selection method for a DG group to improve the response speed of the distributed control system.Furthermore,a single or multiple leader selection model is established to minimize the constraints of the one-step convergence factor and the number of leaders to improve the response speed of the distributed control system.The simulation results of the IEEE 33 bus standard test system show the effectiveness of the proposed distributed control strategy.In addition,the response speed of a DG control group can be improved effectively when the single or multiple leaders are selected optimally.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Distributed Periodic Event-Triggered Optimal Control of DC Microgrids Based on Virtual Incremental Cost

This article presents a distributed periodic eventtriggered(PET)optimal control scheme to achieve generation cost minimization and average bus voltage regulation in DC microgrids.In order to accommodate the generation constraints of the distributed generators(DGs),a virtual incremental cost is firstly designed,based on which an optimality condition is derived to facilitate the control design.To meet the discrete-time(DT)nature of modern control systems,the optimal controller is directly developed in the DT domain.Afterward,to reduce the communication requirement among the controllers,a distributed event-triggered mechanism is introduced for the DT optimal controller.The event-triggered condition is detected periodically and therefore naturally avoids the Zeno phenomenon.The closed-loop system stability is proved by the Lyapunov synthesis for switched systems.The generation cost minimization and average bus voltage regulation are obtained at the equilibrium point.Finally,switch-level microgrid simulations validate the performance of the proposed optimal controller.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.

DISTRIBUTED OPTIMAL LOCAL DOUBLE LOOP NETWORK

A distibuted optimal local double loop(DOLDL) network is presented. Emphasis is laid on the topology and distributed routing algorithms for the DOLDL. On the basis of building an abstract model, a set of definitions and theorems are described and proved. An algorithm which can optimize the double loop networks is presented. The optimal values of the topologic parameters for the DOLDL have been obtained by the algorithm, and these numerical results are analyzed. The study shows that the bounds of the optimal diameter (d) and average hop distance (a) for this class of networks are [square-root 3N -2] less-than-or-equal-to d less-than-or-equal-to [square-root 3N+1] and (5N/9(N-1)) (square-root 3N-1.8) < a < (5N/9 (N-1)). (square-root 3N - 0.23), respectively (N is the number of nodes in the network. (3 less-than-or-equal-to N less-than-or-equal-to 10(4)). A class of the distributed routing algorithms for the DOLDL and the implementation procedure of an adaptive fault-tolerant algorithm are proposed. The correctness of the algorithm has been also verified by simulating.

Medical Feature Selection Approach Based on Generalized Normal Distribution Algorithm

This paper proposes a new pre-processing technique to separate the most effective features from those that might deteriorate the performance of the machine learning classifiers in terms of computational costs and classification accuracy because of their irrelevance,redundancy,or less information;this pre-processing process is often known as feature selection.This technique is based on adopting a new optimization algorithm known as generalized normal distribution optimization(GNDO)supported by the conversion of the normal distribution to a binary one using the arctangent transfer function to convert the continuous values into binary values.Further,a novel restarting strategy(RS)is proposed to preserve the diversity among the solutions within the population by identifying the solutions that exceed a specific distance from the best-so-far and replace them with the others created using an effective updating scheme.This strategy is integrated with GNDO to propose another binary variant having a high ability to preserve the diversity of the solutions for avoiding becoming stuck in local minima and accelerating convergence,namely improved GNDO(IGNDO).The proposed GNDO and IGNDO algorithms are extensively compared with seven state-of-the-art algorithms to verify their performance on thirteen medical instances taken from the UCI repository.IGNDO is shown to be superior in terms of fitness value and classification accuracy and competitive with the others in terms of the selected features.Since the principal goal in solving the FS problem is to find the appropriate subset of features that maximize classification accuracy,IGNDO is considered the best.

Optimizing Domain Distribution of Grain Oriented Silicon Steel by Using Antimony as the Laser Surface Alloying Element

For reducing the core loss of grain oriented silicon steel and improving its aging property, a new method, the LLSA by using Sb as the laser surface alloying element, was investigated, and at proper technique conditions rather good result was obtained.

Distributionally Robust Optimal Dispatch of Offshore Wind Farm Cluster Connected by VSC-MTDC Considering Wind Speed Correlation

Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.