Optimizing communication network geodiversity for disaster resilience through shielding approach

The article analyzes the existing legal mechanisms for managing critical information infrastructure in Ukraine. The instruments for their improvement are proposing in this article. An important component of critical infrastructure is its information component – a critical information infrastructure. The sphere of protection of critical information infrastructure in Ukraine is at the initial stage of formation. The current legislation defines only certain objects of socio-economic sphere, in which extraordinary events can lead to socially dangerous consequences. In view of the fact, that the term “critical information infrastructure” does not having a consistent interpretation in different countries, we propose our opinion. “Critical information infrastructure is a system of information management of critical facilities and information and communication networks that provide defense capabilities and security of public and private institutions, whose operation may flow to the national security of Ukraine” (KII). In the KII we can identified information and network components. Information environment of KII is a system for information management of critical objects, including computing and information resources that form automated control systems (ACS). The network component of KII consists of a set of telecommunication devices, communication lines and network equipment, systems of open protocols for the exchange of information between elecommunication devices, global system of digital addresses and digital identifiers, software. The Internet network can be considered as a technological add-on over a telecommunication network that provides the provision of data transmission and processing services (e-mail, teleconferencing, file transfer, access to computing and information systems in local area networks). The main threat to the safety of ACS of critical information infrastructure objects is targeted actions on information systems, information and telecommunication networks by software and hardware. KII legal security include two main components – national and international. The national component may be forming by a set of principles, legal institutions and norms, which are enshrined in the national legislation regulating public relations in Ukraine in the area of counteracting the security threats of the ACS of critical objects. In order to protect the most important objects of KII, it is necessary to identify these objects. The current legislation defines such categories of objects, for which special conditions for ensuring their protection and functioning are established. Some of them, in whole or in part, may be classifying as objects of critical infrastructure. The specificity of providing information security was reflecting in such Ukraine laws like “On the Fundamentals of National Security of Ukraine”, “On the Concept of the National Program of Informatization”, “On the National Program of Informatization”. As well as the Concept of Development of the Security and Defense Sector of Ukraine, the National Security Strategy of Ukraine, the Strategy of Cybersecurity Of Ukraine. The National Security Strategy identifies actual threats to national security and sets priorities for information security, cyber security and security of information resources and critical infrastructure. At the same time, the implementation of the state policy in the field of security of KII requires the further development of legal principles and norms governing the relevant social relations, that is, the national component of the legal security of KII. Ukraine should ensure the establishment of a nationwide system for assessing risks and threats to critical infrastructure, and after the legislative definition of the main terms, the implementation of the Identification of Critical Information Infrastructure objects. Identification of objects of critical information infrastructure can be accomplishing by introducing the certification of objects of critical information infrastructure. Such passports must contain general data about the facility, data on the main sources of danger, data on hazardous natural conditions, technological processes and response to threats. The international component of the legal security of KII provides for the regulation of a set of principles and norms defined by international treaties and recognized by the state, regulating issues of international cooperation in this area. Ukraine has signed the Convention on Cybercrime together with the member states of the Council of Europe and other States. It is aiming at stopping actions against the confidentiality, integrity and availability of computer systems, networks and computer data, as well as abusing such systems, networks and data by installing the criminal responsibility for such behavior, the provision of powers sufficient to combat criminal offenses, and the conclusion of agreements on rapid and reliable international cooperation. In addition, the plan of measures for 2017 on implementation of the Cybersecurity Strategy of Ukraine provides for the implementation of Directive 2008/114/EC on the protection of critical infrastructure, in particular on cybersecurity and cyber defense of critical infrastructure objects. Development of the system of international information security, the following main groups of international relations that requirenormative legal regulation within the framework of the legal security of KII: definition of the boundaries of the national KII in the global information and communication infrastructure and fixing signs of computer incidents in the control system of critical objects information infrastructure. The absence of generally recognized borders of state sovereignty of States in this space is a significant obstacle to the application of international law to the actions of other states. In particular, this impedes the establishment of limits of responsibility of states for violating the security of the KII and organizing international cooperation in the field of countering computer crime. The urgency of the legislative consolidation of signs of computer incidents in the automated control system of critical information infrastructure objects suggests the widespread use of the concept of “incident” in international law. An incident in cyberspace usually associated with a violation of the functioning of the components of cyberspace – an electronic collection environment and automated processing of information that determines the processes of the implementation of these operations, as well as information systems and automated control systems. The essence of the general definition of the “international incident” in the field of KII will be determining, firstly, by the nature of international relations between states that are violating by the “incident”. This event may be the result of unforeseen actions of the state, including actions that harm the interests of public bodies of one or more states, or, conversely, be one of many intentional but minor provocations carried out by agents of one state against another state. Given that international relations in the field of incidents in the field of KII are not regulating by international treaties, the main and, in fact, the only source of international law in this case serves as an international custom, however, its application to the sphere of KII is accompanying by considerable difficulties. For Ukraine, it is possible to introduce the positive experience of other states in the security of the KII. In particular, the problem of security of information technologies has been enshrined in the international standard ISO / IEC 15408 “General criteria for assessing the safety of information technology”.

Network function virtualization (NFV) brings the potential to provide the flexible implementation of network functions and reduce overall hardware cost by running service function chains (SFCs) on commercial off-the-shelf servers with many-core processors. Towards this direction, both academia and industry have spent vast amounts of effort to address the optimal placement challenges of NFV middleboxes. Most of the servers usually are equipped with Intel X86 processors, which adopt Non-Uniform Memory Access (NUMA) architecture. However, existing solutions for placing SFCs in one server either ignore the impact of hardware architecture or overlook the dependency between middleboxes. Our empirical analysis shows that the placement of virtual network functions (VNFs) with interdependency in a server needs more particular consideration. In this paper, we first manage the optimal placement of VNFs by jointly considering the discrepancy of cores in different NUMA nodes and interdependency between network functions (NFs), and formulate the optimization problem as a Non-Linear Integer Programming (NLIP) model. Then we find a reasonable metric to describe the dependency relation formally. Finally, we propose a heuristic-based backtracking placement algorithm (BPA) to find the near-optimal placement solution. The evaluation shows that, compared with two state-of-art placement strategies, our algorithm can improve the aggregate performance by an average of 20% or 45% within an acceptable time range.

Network Function Virtualization (NFV) offers service delivery flexibility and reduces overall costs by running service function chains (SFCs) on commodity servers with many cores. Existing solutions for placing SFCs in one server treat all CPU cores as equal and allocate isolated CPU cores to network functions (NFs). However, advanced servers often adopt Non-Uniform Memory Access (NUMA) architecture to improve the scalability of many-core systems. CPU cores are grouped into nodes, incurring performance degradation due to cross-node memory access and intra-node resource contention. Our evaluation shows that randomly selecting cores to place NFs in an SFC could suffer from 39.2 percent lower throughput comparing to an optimal placement solution. In this article, we propose Octans, an NFV orchestrator to achieve maximum aggregate throughput of all SFCs in many-core systems. Octans first formulates the optimization problem as a Non-Linear Integer Programming (NLIP) Model. Then we identify the key factor for problem solving as evaluating the throughput drop of an NF caused by other NFs in the same SFC or different SFCs, i.e., performance drop index, and propose a formal and accurate prediction model based on system level performance metrics. Finally, we propose two online algorithms to quickly find near-optimal placement solutions for one-time and incremental deployment. Extensive evaluation on a prototype implementation shows that Octans significantly improves the aggregate throughput comparing to two state-of-the-art placement solutions by 27.1 ~ 45.2 percent for one-time deployment and by 20.9 ~ 38.1 percent for incremental deployment, with very low prediction errors. Moreover, Octans could quickly find a near-optimal placement solution with tiny optimality gap.

This study focuses on a real-world case that is defined as an extension of the container loading problem (CLP) with weakly heterogeneous types of boxes. A company producing plastic cups wants to increase its efficiency in container loading operations. To solve the problem, a hybrid approach including a static rule to rank orders and integer nonlinear programming (INLP) models is developed. INLP models form box sizes according to the properties of the cups, and determine the position of the boxes in layers while simultaneously minimizing the layer-depth. The presented approach is tested on real-world cases and benchmark data sets. The results show that simultaneously forming boxes and solving the CLP increases the effectiveness of container loading operations.

Critical Infrastructures (CIs) are vital backbones of modern societies and are increasingly depending on Information Technology (IT) and communication networks. Due to the increasing IT penetration, CIs are more and more connected with each other, with advantages and disadvantages. Due to this interconnection, CIs can provide their services more cost-efficiently. On the other hand, in case of disturbances, their behaviour cannot ever be mastered, as the large blackouts in the USA and Europe have shown. The increasing complexity and manifold conventional and emerging threats jeopardise the system of mutually dependent CIs. Critical Infrastructure Protection (CIP) attracts notice more and more from the public. Modelling and Simulation (M&S) expand now into the analysis and planning of processes and procedures of infrastructures. This paper gives an overview of the recent research in the field of CIP, where the EU project Integrated Risk Reduction of Information-based Infrastructure Systems (IRRIIS) is used as a role model.

Current and planned solutions used in the ICT infrastructure are largely based on Photonic and RF Communications Systems. Rapid advances in photonic and RF photonic technologies have significantly accelerated the introduction of these new technologies in access storage, backbone and grid networks, defining and building the rules to ensure transfer of multi Tera-bit volumes of data. The purpose of this volume is to provide a vehicle for directing research in this area from multiple lenses in the selected areas of investigation. Following an introduction by the editors, reviews of research will be clustered into two sections. The first part of this Special Issue focuses on the Photonic and RF Communications systems technologies and this Section comprises 7 articles. Recent solutions in wideband and multi-band RF circuits are presented in the articles 7 through 9 in the second part of the Special Issue. The first article, by Arash Bahrami , et al., present an experimental evaluation of a radio-over-fiber system. In the paper, the authors proposed an optical microwave radio-over-fiber system in which an integrated dual-parallel Mach-Zehnder modulator is biased at the maximum transmission biasing point. The authors consider the two following modulation schemes: binary phase shift keying (BSK) and quadrature phase shift keying (QPSK) over fiber spans of 10 and 25 km of standard single mode fiber. The obtained results show that the second order sideband of optical microwave has the potential to provide error-free transmission for BPSK and QPSK. John S. Vardakas , et al. in the next article, analyse the delay of converged Wavelength Division Multiplexing Ethernet Passive Optical Network and WiMax networks. In such access networks, the provision of Quality of Service (QoS) support is a challenging issue, mainly due to the different bandwidth allocation mechanisms of the two access technologies. In the paper, the authors analyse the delay performance by considering multiple service-classes with different priorities. The proposed analytical model allows the calculation of the average end-to-end packet delay of each service-class as the sum of the queuing delay in both domains. The accuracy of the analysis was verified by simulation. Ioannis Mamounakis , et al., propose a novel traffic prediction method to minimize packet delay in Ethernet Passive Optical Networks. The authors utilise traffic information to predict the accumulated burst size of each respective optical network unit in the following cycle. The paper demonstrates and proves that a significant delay enhancement can be accomplished by reporting the predicted burst size, rather than the current one, to the Optical Line Terminal (OLT). The simulation experiments carried out by the authors show that a significant decrease in the delay can be obtained without any changes to the dynamic bandwidth assignment scheme at the OLT. The paper by Mariusz Głąbowski , et al. proposes an analytical model of a multi-service switching network with overflow links with finite capacity in the first stage of the network. This model can be used to evaluate the QoS parameters which are closely interrelated with the method of operation of the large capacity optical nodes. The proposed method allows their traffic capacity to be increased through a significant decrease in the phenomenon of internal blocking in switching networks which is the basic element of the node. The proposed calculation method is validated by the authors via simulation. Aboagela Dogman , et al. present an integrated QoS management process for multimedia traffic in wire and wireless networks. In the proposed process, the statistics of traffic are determined and then used as an input to a fuzzy interface system (FIZ). FIZ allows the traffic to be accurately sampled and this traffic is in the next step pre-processed using a fuzzy c-means (FCM). FIZ identifies clusters representing poor, average and good QoS. This information is then used in a multilayer perceptron neural network to assess the overall QoS for multimedia traffic. The authors showed that the developed adaptive statistical sampling represents traffic more correctly than systematic, stratified and random non-adaptive sampling methods. The article by Adam Kaliszan , et al. provides a generalised convolution algorithm for modelling state-dependent systems. This model corresponds to the system that uses one or many physical resources, e.g. one or a set of lambda channels in DWDM optical networks. The proposed calculation method can be used for the analysis and dimensioning of optical networks and systems. This method is also useful for an optical system in which advanced traffic management mechanism have been applied, e.g. bandwidth reservation or threshold mechanism. The accuracy of the proposed model is validated by simulation experiments. From their onset RF Communications Systems have been critical to the development of ICT infrastructure. In mobile and satellite communication systems, wideband and multi-band RF circuits are important for achieving high-date wireless transmission and supporting a large number of standards (e.g. UMTS, WiFi, WiMAX, or LTE). A wideband or multi-band RF circuit can replace a number of single-band RF circuits, leading to a significant reduction of size, weight and cost of modern wireless systems. There have been a great number of recent developments in the above areas over the past years. The articles that outline these solutions are in the latter part of this Special Issue, i.e. comprise articles from Article 7 through Article 9. The article by Bingo Wing-Kuen Ling , et al. discusses the frequency spectrum of a pulse for ultra wideband impulse radio systems as the frequency response of a real valued causal rational infinite impulse response filter. The pulse design problem is formulated as a functional inequality constrained optimization problem that can be solved by the method proposed by the authors. This pulse can be generated via an excitation of a simple circuit. Numerical simulation results confirm that the energy compaction performance defined in the frequency domain of the proposed pulse outperforms that of existing pulses. It is worth emphasizing that the pulse can be generated via an excitation of a simple circuit. In their article, Xue Li and , et al. present the WiFi leakage problem that appears in the users' equipment that simultaneously use both LTE and WiFi technologies. The authors propose WiFi leakage detection algorithms for successful detection of the weak WiFi leakage in the presence of both LTE signal and Gaussian noise. The algorithms include energy ratio detection, entropy ratio detection and cyclostationary detection based on spectral correlation function. The effectiveness and efficiency of the proposed WiFi leakage detection techniques have been confirmed by simulations performed for different scenarios. The article by Piotr Remlein discusses the performance of Intelligent Transportation Systems (ITS) that consists of satellite mesh networks. In the paper the author analyses a new power-limited and energy-efficient systems employing coded continuous phase modulation signals and with multiuser Frequency Division Multiplexed transmission. The results obtained by the author show that good performance of the proposed solution can be achieved by reducing the inter-carrier frequency spacing and using simple iterative ICI cancellation algorithm at the receiver. Based on the results, it can be concluded that this system might constitute a desirable option in ITS satellite mesh, ad-hoc networks. The objective of this Special Issue is to bring together the state-of-the-art research contributions that address challenges in emerging devices and architecture for photonic systems and RF circuits for wideband and multi-band communications systems. Due to the complexity and scope of the subject area, the set of articles presented attempts to address only some selected relevant issues. The Guest Editors believe though that the contributions included in the Special Issue will inspire the research activities of leading authors and scholars worldwide. The Guest Editors also expect this Special Issue to provide insight into the questions that they address as the presented articles expose important contributions to each of the relevant subject areas. Piotr Zwierzykowski received MSc and PhD (Hons) degrees in telecommunications from Poznan University of Technology, Poland, in 1995 and 2002, respectively. Since 1995 he has been working at the Poznan University of Technology, where he is currently an Assistant Professor. Piotr Zwierzykowski is the author, or co-author, of over 200 journals and conference publications and three books in the area of computer and communication networks. His research covers modelling and dimensioning of optical networks, teletraffic engineering and routing. He is a Senior Member of IEEE and the Secretary in the IEICE Europe Section. Steven Gao received a PhD degree from Shanghai University, P.R. China. He is a Professor and Chair in RF and Microwave Engineering at University of Kent, UK. His research covers smart antennas, satellite antennas, phased arrays, RF and microwave circuits (power amplifiers), satellite communications, UWB radars, synthetic-aperture radars and mobile communications. From 2007 to 2012, he was a Senior Lecturer and Head of Space Antennas and Microwave System Group at Surrey Space Centre, University of Surrey, UK. He has two books including “Space Antenna Handbook” (Wiley, 2012) and “Circularly Polarized Antennas” (IEEE-Wiley, 2014), published over 200 papers and holds several patents in smart antennas and RF. He is an IEEE AP-S Distinguished Lecturer and a Chair of LAPC 2013. He is an Invited Speaker at IWAT'2014 (Sydney), SOMIRES'2013 (Japan), APCAP'2014 (China), etc. He is an Associate Editor of Radio Science and the Editor-in-Chief for Wiley Book Series on "Microwave and Wireless Technologies". He is a Fellow of the IET. Wai Pang Ng received his BEng (Hons) Communication and Electronic Engineering and IEE Prize from Northumbria University, UK and PhD in Electronic Engineering from University of Wales Swansea, UK in 1997 and 2001, respectively. He is a Reader of Optical Communications at Northumbria University. From 2001 to 2004, he was a Senior Networking Software Engineer at Intel Corporation, before starting his academic career at Northumbria University. He has published over 80 journals and conference publications in the area of optical switching, optical signal processing and radio-over-fiber. He is a Chartered Engineer of the Engineering Council UK and a Senior Member of the IEEE. Currently he serves as the Chair of the IEEE UK&RI Communication Chapter. He was also the Co-Chair of the Signal Processing for Communications Symposium in IEEE International Conference on Communications (ICC) 2009 (Dresden, Germany) and now serves as the Publicity Chair of ICC 2015 in London. Zuqing Zhu received a PhD degree from the Department of Electrical and Computer Engineering, University of California, Davis, in 2007. From July 2007 to January 2011, he worked in the Service Provider Technology Group of Cisco Systems, San Jose, as a senior R&D engineer. In January 2011, he joined the University of Science and Technology of China (USTC), where he is currently an Associate Professor. He has published more than 100 papers in peer-reviewed journals and conferences. He has been in the technical program committees (TPC) of INFOCOM, ICC, GLOBECOM, ICCCN and etc. He is also an editorial board member of Elsevier Journal of Optical Switching and Networking, Springer Telecommunication Systems Journal, Springer Photonic Network Communications Journal and Wiley European Transactions on Emerging Telecommunications Technologies amongst others. He has received the Best Paper Awards from the IEEE International Conference on Communications (ICC) 2013, the IEEE Global Communications Conference (GLOBECOM) 2013, and the IEEE International Conference on Networking and Communications (ICNC) 2014. He is a Senior Member of IEEE and OSA.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

In general, it is difficult to directly solve an optimization problem of systems reliability formulated as a nonlinear integer programming (NIP) model. In this paper, we propose a method for solving the NIP problem for the best compromise solution while holding a nonlinear property by using the genetic algorithm. We also report that the optimization problem of systems reliability as a case study is solved using the proposed method. The numerical comparison experiments between the 0-1 LP/0-1 NP formulations are demonstrated and, from the quantitative evaluation, the efficiency of the proposed method is demonstrated. >

The development of the Internet of Vehicle (IoV) is overgrowing toward driving comfort, safety, and efficiency. Autopilot or a car without a driver is one implementation of IoT. To run the full function of IoV, a reliable communication network is needed because the risk will be substantial due to the low quality of network infrastructure services. In this research, we will analyze the quality of network infrastructure services. The analysis can be done through two approaches: direct measurement in the field using a GPS Tracker-based system and modeling using the mathematical function of transmit power of mobile communication transmitting devices. The test is carried out in a specific area with a sample of high traffic and low-density areas. This method was chosen to find the right pattern in measuring the quality of communication network services. The tests carried out produce dynamic data on service quality in certain areas. For areas of low density, the service quality tends to be below as well, and many areas without signal are found, while for areas with high density, the quality of service is found to be good, but network overload conditions often occur.

Network communication is crucial in the Energy Grid of Things (EGoT). Without a network connection, the energy grid becomes just a power grid where the energy resources are available to the customer uni-directionally. A mechanism to analyze and optimize the energy usage of the grid can only happen through a medium, a communications network, that enables information exchange between the grid participants and the service provider. Security implementers of EGoT network communication take extraordinary measures to ensure the safety of the energy grid, a critical infrastructure, as well as the safety and privacy of the grid participants. With the dynamic nature of network communication of the EGoT, the information provided by the customer or the service provider can be falsified by a malicious attacker. Therefore, a trust model is necessary to monitor any abnormal activities. This paper describes a distributed trust model system that meets the need of the EGoT. This paper describes methods for evaluating and improving the distributed trust model using standard hypothesis testing metrics such as true positive, false positive, true negative, false negative, equal error rate, and F1 score. Example calculations are shown based on generated sample data.

Providing effective Through Train Services (TTSs) faces challenges due to complex infrastructure conditions, train performances and passenger demands. To enhance TTSs between two different classes of urban rail transit lines with variations in train speed and capacity, we propose a multi-objective Integer Non-Linear Programming (INLP) model. This model maximizes passenger travel time savings and average train load utilization, and develops an integrated approach to simultaneously optimize the frequencies of through express trains and local trains, as well as the operation zones, stopping patterns and type selection of through trains. Additionally, a Non-Dominated Sorting Genetic Algorithm II is designed to solve the INLP model based on a simple test network and a real-world case from the Nanjing Subway. The unique benefits of our proposed method are demonstrated by a comprehensive compared with the Single Line Operation Mode and the all-stop plans under Through Operation Mode.

Relevance. Holography is becoming one of the most promising areas of visualization of three-dimensional objects, which justifies the emergence of a certain scientific interest in this area of research. There is a general global trend of intensifying the work of specialists on the problem of using holographic technologies in various areas of human activity. Trends in the implementation of holographic services and holographic communication today already require a revision of the principles of planning, designing and building existing communication networks, as well as approaches to the implementation of sixth-generation networks 6G, which are based on the integration of various technologies and communication networks into a single network. A separate issue is the assessment of the quality of service and the quality of perception of holographic services by both objective and subjective assessment methods. There are practically no criteria for assessing the quality of a holographic image, including scales and methods for subjective assessment of the quality of holographic services. Moreover, the properties of the holographic flow are poorly understood, and even less so its influence on communication networks and requirements for network parameters, which makes the tasks of studying traffic characteristics and assessing the quality of service of holographic services very relevant.The aim of the work is to evaluate the quality of perception of holographic conference calls using a subjective evaluation method on a model network. The work uses methods of subjective assessment of the quality of perception. The materials presented in the article reflect the results of the authors' experimental research work on studying the problem of the quality of perception of holographic copies. A description of the developed scheme of a full-scale experiment is given.Results. The data obtained as a result of the work of an expert group on assessing the quality of perception are presented. The subjective assessment of the quality of perception of a holographic image begins to deteriorate with 8 connections and becomes unsatisfactory with 12 connections, which must be taken into account when planning experimental studies of work on assessing the quality of perception. Novelty. For the first time, an assessment of the quality of perception of the provision of a holographic conferencing service was carried out using a subjective assessment method. Theoretical significance. The influence of increasing the number of holographic traffic flows on the quality of perception of the received content is analyzed. Practical significance. Expanding the possibilities for assessing the degree of user satisfaction with holographic services.

We studied a joint inventory location problem assuming a periodic review for inventory control. A single plant supplies a set of products to multiple warehouses and they serve a set of customers or retailers. The problem consists in determining which potential warehouses should be opened and which retailers should be served by the selected warehouses as well as their reorder points and order sizes while minimizing the total costs. The problem is a Mixed Integer Nonlinear Programming (MINLP) model, which is nonconvex in terms of stochastic capacity constraints and the objective function. We propose a solution approach based on a Lagrangian relaxation and the subgradient method. The decomposition approach considers the relaxation of different sets of constraints, including customer assignment, warehouse demand, and variance constraints. In addition, we develop a Lagrangian heuristic to determine a feasible solution at each iteration of the subgradient method. The proposed Lagrangian relaxation algorithm provides low duality gaps and near-optimal solutions with competitive computational times. It also shows significant impacts of the selected inventory control policy into total system costs and network configuration, when it is compared with different review period values.

This paper investigates the voltage regulation problems in DC microgrids (DC-MGs) with nonlinear ZIP loads under malicious cyber-physical attacks, proposing an adaptive decentralized fully-actuated two-step control strategy rooted in the fully actuated system (FAS) approach. At first, a unified fully actuated distributed generation unit (FA-DGU) model is developed, integrating nonlinear load dynamics, renewable energy intermittency, attack-induced disturbances, and power line coupling into a lumped uncertainty framework. Then, a decentralized controller is designed using Radial Basis Function neural networks (RBFNNs) to adaptively approximate unknown ZIP load characteristics and attack-generated perturbations, eliminating dependence on communication networks while enabling plug-and-play (PnP) operations through purely local measurements. Following this, Lyapunov stability analysis rigorously proves the asymptotic convergence of voltage regulation errors at the point-of-common-coupling (PCC) under heterogeneous uncertainties. Finally, various uncertain scenarios in DC-MGs are simulated using MATLAB/Simulink, thereby verifying the feasibility and effectiveness of the proposed control method.

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.