Network Optimization Problem Research Articles

A collective neurodynamic approach for solving distributed system optimum dynamic traffic assignment problems

In this paper, the traditional system optimum dynamic traffic assignment (SO-DTA) problem is solved by distributed multi-agent dynamics. The goal of SO-DTA is to optimally control the route choice of each user to minimize the total travel time by all users over the assignment time period. It is beneficial for reducing the congestion of the traffic network with time-varying demand. Different from the traditional SO-DTA which is formulated and solved in a centralized scheme, we aim at solving it from a multi-agent perspective in a communication network. Based on the cell transmission model, two connector-based relaxed SO-DTA models are provided in a multi-agent system framework for the traffic network with a single destination and multiple destinations, respectively. In the provided models, each cell connector is treated as an agent, which could exchange information with its adjacent connectors to accomplish the system optimization objective. Then, a collective neurodynamic system equipped with the proposed distributed protocol is used to solve general network optimization problems including the above SO-DTA models as special cases. The convergence analysis is further given for the proposed algorithm. Numerical studies over various traffic networks are presented to show the effectiveness of the proposed method.

Guest Editorial: Interplay between Machine Learning and Networking Systems

Recently, the advancement of machine learning (ML) techniques, especially deep learning, reinforcement learning, and federated learning, has led to remarkable breakthroughs in a variety of application domains. The success of ML benefits from the advancement of the Internet, mobile networks, data center networks, and the Internet of Things (IoT) that facilitate data creation and sharing. On the other hand, we have also witnessed a fast growing trend in the networking community toward using ML to tackle challenging problems in network design, management, and optimization, which are traditionally addressed using mathematical optimization theory or human-generated heuristics. ML is also an essential ingredient in the realization of autonomous or self-driving networks.

A Two-Level ADMM Algorithm for AC OPF With Global Convergence Guarantees

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems like AC OPF. In order to overcome this difficulty, we propose a new distributed reformulation for AC OPF and a two-level ADMM algorithm that goes beyond the standard framework of ADMM. We establish the global convergence and iteration complexity of the proposed algorithm under mild assumptions. Extensive numerical experiments over some largest test cases from NESTA and PGLib-OPF (up to 30 000-bus systems) demonstrate advantages of the proposed algorithm over existing ADMM variants in terms of convergence, scalability, and robustness. Moreover, under appropriate parallel implementation, the proposed algorithm exhibits fast convergence comparable to or even better than the state-of-the-art centralized solver.

LTHS: A heuristic algorithm based on local two-hop search strategy for influence maximization in social networks

Influence maximization is a classic network optimization problem, which has been widely used in the field of viral marketing. The influence maximization problem aims to find a fixed number of active nodes. After a specific propagation model, the number of active nodes reaches the maximum. However, the existing influence maximization algorithms are overly pursuing certain indicators of efficiency or accuracy, which cannot be well accepted by some researchers. This paper proposes an effective algorithm to balance the accuracy and efficiency of the influence maximization problem called local two-hop search algorithm (LTHS). The core of the proposed algorithm is a node not only be affected by one-hop neighbor nodes, but also by two-hop neighbor nodes. Firstly, this paper selects initial seed nodes according to the characteristics of the node degree. Generally, the high degree of nodes regards as influential nodes. Secondly, this paper proposes a node two-hop influence evaluate function called two-hop diffusion value (THDV), which can evaluate node influence more accurately. Furthermore, in order to seek higher efficiency, this paper proposes a method to reduce the network scale. This paper conducted full experiments on five real-world social network datasets, and compared with other four well-known algorithms. The experimental results show that the LTHS algorithm is better than the comparison algorithms in terms of efficiency and accuracy.

An overview of quantum computing and quantum communication systems

An overview of quantum computing and quantum communication systems

Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty

In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second-stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network optimization and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.

NetXplain: Real-time explainability of graph neural networks applied to networking

Recent advancements in Deep Learning (DL) have revolutionized the way we can efficiently tackle complex optimization problems. However, existing DL-based solutions are often considered as black boxes with high inner complexity. As a result, there is still certain skepticism among the networking industry about their practical viability to operate data networks. In this context, explainability techniques have recently emerged to unveil why DL models make each decision. This paper focuses on the explainability of Graph Neural Networks (GNNs) applied to networking. GNNs are a novel DL family with unique properties to generalize over graphs. As a result, they have shown unprecedented performance to solve complex network optimization problems. This paper presents NetXplain, a novel real-time explainability solution that uses a GNN to interpret the output produced by another GNN. In the evaluation, we apply the proposed explainability method to RouteNet, a GNN model that predicts end-to-end QoS metrics in networks. We show that NetXplain operates more than 3 orders of magnitude faster than state-of-the-art explainability solutions when applied to networks up to 24 nodes, which makes it compatible with real-time applications; while demonstrating strong capabilities to generalize to network scenarios not seen during training.

Search Space Reduction for Genetic Algorithms Applied to Drainage Network Optimization Problems

In recent years, a significant increase in the number of extreme rains around the world has been observed, which has caused an overpressure of urban drainage networks. The lack of capacity to evacuate this excess water generates the need to rehabilitate drainage systems. There are different rehabilitation methodologies that have proven their validity; one of the most used is the heuristic approach. Within this approach, the use of genetic algorithms has stood out for its robustness and effectiveness. However, the problem to be overcome by this approach is the large space of solutions that algorithms must explore, affecting their efficiency. This work presents a method of search space reduction applied to the rehabilitation of drainage networks. The method is based on reducing the initially large search space to a smaller one that contains the optimal solution. Through iterative processes, the search space is gradually reduced to define the final region. The rehabilitation methodology contemplates the optimization of networks using the joint work of the installation of storm tanks, replacement of pipes, and implementation of hydraulic control elements. The optimization model presented uses a pseudo genetic algorithm connected to the SWMM model through a toolkit. Optimization problems consider a large number of decision variables, and could require a huge computational effort. For this reason, this work focuses on identifying the most promising region of the search space to contain the optimal solution and to improve the efficiency of the process. Finally, this method is applied in real networks to show its validity.

Quickest Flow Algorithms with Time-Varying Attributes

In many real-world situations, there are numerous network optimization problems where the network attributes depend on time. In this paper, we consider single-source single-sink discrete-time dynamic network flow problems. We review some algorithms for the quickest flow problems in two environments (to the network attributes): time-invariant and time-variant. This paper mainly focuses on the existing algorithms for a later one. In literature, most of the authors have made their objectives to determine the earliest arrival time paths along which a given amount of flow can be sent in the minimum time. Evacuation is the most recent research area of network optimization, where quickest flow models allow the estimation of the minimum time required to bring a given number of evacuees to safety.

Efficient Truthful Scheduling and Resource Allocation through Monitoring

We study the power and limitations of the Vickrey-Clarke-Groves mechanism with monitoring (VCGmon) for cost minimization problems with objective functions that are more general than the social cost. We identify a simple and natural sufficient condition for VCGmon to be truthful for general objectives. As a consequence, we obtain that for any cost minimization problem with non-decreasing objective μ, VCGmon is truthful, if the allocation is Maximal-in-Range and μ is 1-Lipschitz (e.g., μ can be the Lp-norm of the agents’ costs, for any p ≥ 1 or p = ∞). We apply VCGmon to scheduling on restricted-related machines and obtain a polynomial-time truthful-in-expectation 2-approximate (resp. O(1)-approximate) mechanism for makespan (resp. Lp- norm) minimization. Moreover, applying VCGmon, we obtain polynomial-time truthful O(1)-approximate mechanisms for some fundamental bottleneck network optimization problems with single-parameter agents. On the negative side, we provide strong evidence that VCGmon could not lead to computationally efficient truthful mechanisms with reasonable approximation ratios for binary covering social cost minimization problems. However, we show that VCGmon results in computationally efficient approximately truthful mechanisms for binary covering problems.

GmFace: An explicit function for face image representation

Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to the complex physiological structures and dynamic behaviors, the mathematical representation of the human face is an especially challenging task. In this paper, an explicit function called GmFace is proposed for face image representation in the form of a multi-Gaussian function. The model utilizes the advantages of two-dimensional Gaussian function which provides a symmetric bell surface with a controllable shape. The GmNet is then designed using Gaussian functions as neurons, with parameters that correspond to each of the parameters of GmFace in order to transform the problem of GmFace parameter solving into a network optimization problem of GmNet. Furthermore, using GmFace, several face image transformation operations can be realized mathematically through simple parameter computation. Experimental results demonstrate that GmFace has a superior representation ability for face images compared to convolutional autoencoder (CAE), principal component analysis (PCA) and discrete cosine transform (DCT) method.

Optimization of stochastic chinese postman networks problem using priorities

The postman problem is concern with the choice of root to follow in order that he or she pass each streets at least once and return at starting point with least traveling distance. The Chinese postman problem is transformed as network optimization problem under certain constraint. Stochastic networks are networks of non-binary vertices that differ over time, reflecting the probability of a connection of two nodes. This paper deals with theoretical and mathematical foundation of stochastic networks related to an additional feature of the Chinese postman Problem (CPP) is that postman visited with first priority node as soon as possible. Fleury’s and Dijkstra’s algorithm have been used with respect to Eulerian path. Finally, this paper also illustrates and justify the implementation of the methodology and algorithms. Consideration of cost factors in the ever network problems gives another scope of research.

Throughput Enhancement of Full-Duplex CSMA Networks Using Multiplayer Bandits

This article studies the network-level throughput of a full-duplex (FD)-enabled CSMA network, considering the link's transmit power (TP) control, carrier-sensing threshold (CST) adjustment, and logarithm access intensity (LAI) adaptation. With the FD technique, a transmitter-receiver pair can transmit and receive simultaneously in the same frequency band. We aim to find the best combination of TP, CST, and LAI for each link to maximize the FD-CSMA network throughput. However, adjusting each link's TP and CST will change the network's carrier-sensing relation or contention graph, consequently leading to a computationally intractable network optimization problem. On the other hand, it is difficult to jointly optimize these three parameters in a fully distributed network. To overcome these, we first decompose this network optimization problem into two subproblems: 1) a joint control and scheduling problem in the transport- and media access control (MAC)-layer and 2) a parameter selection problem in the PHY-layer. Then, the multiplayer multiarmed bandit (MPMAB) framework has been introduced to address this problem by solving the two subproblems alternately. We put forth a fully distributed algorithm, named the stochastic and adversarial optimal FD-CSMA (SAO-FD-CSMA) algorithm, to solve the MPMAB problem by taking advantage of the optimization tool and the bandit theory. The numerical results show that the proposed algorithm outperforms the state-of-the-art bandit algorithms and can improve the network throughput by 43% compared with the random selection method.

Dynamic power control for time-critical networking with heterogeneous traffic

Future wireless networks will be characterized by heterogeneous traffic requirements. Examples can be low-latency or minimum-througput requirements. Therefore, the network has to adjust to different needs. Usually, users with low-latency requirements have to deliver their demand within a specific time frame, i.e., before a deadline, and they coexist with throughput oriented users. In addition, mobile devices have a limited-power budget and therefore, a power-efficient scheduling scheme is required by the network. In this work, we cast a stochastic network optimization problem for minimizing the packet drop rate while guaranteeing a minimum throughput and taking into account the limited-power capabilities of the users. We apply tools from Lyapunov optimization theory in order to provide an algorithm, named Dynamic Power Control (DPC) algorithm, that solves the formulated problem in real time. It is proved that the DPC algorithm gives a solution arbitrarily close to the optimal one. Simulation results show that our algorithm outperforms the baseline Largest-Debt-First (LDF) algorithm for short deadlines and multiple users.

Distributed Stochastic Optimization in Networks With Low Informational Exchange

We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes. While Gradient descent method is a common technique to solve such optimization problem, the computation of the gradient may require much information exchange. In this paper, we consider that each node can only have a noisy numerical observation of its local utility, of which the closed-form expression is not available. This assumption is quite realistic, especially when the system is either too complex or constantly changing. Nodes may exchange partially the observation of their local utilities to estimate the global utility at each timeslot. We propose a distributed algorithm based on stochastic perturbation, under the assumption that each node has only part of the local utilities of the other nodes. We use stochastic approximation tools to prove that our algorithm converges almost surely to the optimum, given that the objective function is smooth and strictly concave. The convergence rate is also derived, under the additional assumption of strongly concave objective function. It is shown that the convergence rate scales as $O\left ({K^{-0.5}}\right )$ after a sufficient number of iterations $K>K_{0}$ , which is the optimal rate order in terms of $K$ for our problem. Although the proposed algorithm can be applied to general optimization problems, we perform simulations for a typical power control problem in wireless networks and present numerical results to corroborate our claims.

Radio Network Planning and Optimization for 5G Telecommunication System Based on Physical Constraints

The paper mainly focuses on the network planning and optimization problem in the 5G telecommunication system based on the numerical investigation. There have been two portions of this work, such as network planning for efficient network models and optimization of power allocation in the 5G network. The radio network planning process has been completed based on a specific area. The data rate requirement can be solved by allowing the densification of the system by deploying small cells. The radio network planning scheme is the indispensable platform in arranging a wireless network that encounters convinced coverage method, capacity, and Quality of Service necessities. In this study, the eighty micro base stations and two-hundred mobile stations are deployed in the -15km×15km wide selected area in the Yangon downtown area. The optimization processes were also analyzed based on the source and destination nodes in the 5G network. The base stations’ location is minimized and optimized in a selected geographical area with the linear programming technique and analyzed in this study.

Design of Trustworthy Cyber–Physical–Social Systems With Discrete Bayesian Optimization

Abstract Cyber–physical–social systems (CPSS) with highly integrated functions of sensing, actuation, computation, and communication are becoming the mainstream consumer and commercial products. The performance of CPSS heavily relies on the information sharing between devices. Given the extensive data collection and sharing, security and privacy are of major concerns. Thus, one major challenge of designing those CPSS is how to incorporate the perception of trust in product and systems design. Recently, a trust quantification method was proposed to measure the trustworthiness of CPSS by quantitative metrics of ability, benevolence, and integrity. The CPSS network architecture can be optimized by choosing a subnet such that the trust metrics are maximized. The combinatorial network optimization problem, however, is computationally challenging. Most of the available global optimization algorithms for solving such problems are heuristic methods. In this paper, a surrogate-based discrete Bayesian optimization method is developed to perform network design, where the most trustworthy CPSS network with respect to a reference node is formed to collaborate and share information with. The applications of ability and benevolence metrics in design optimization of CPSS architecture are demonstrated.

Learning to Schedule Network Resources Throughput and Delay Optimally Using Q+-Learning

As network architecture becomes complex and the user requirement gets diverse, the role of efficient network resource management becomes more important. However, existing throughput-optimal scheduling algorithms such as the max-weight algorithm suffer from poor delay performance. In this paper, we present reinforcement learning-based network scheduling algorithms for a single-hop downlink scenario which achieve throughput-optimality and converge to minimal delay. To this end, we first formulate the network optimization problem as a Markov decision process (MDP) problem. Then, we introduce a new state-action value function called Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -function and develop a reinforcement learning algorithm called Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -learning with UCB (Upper Confidence Bound) exploration which guarantees small performance loss during a learning process. We also derive an upper bound of the sample complexity in our algorithm, which is more efficient than the best known bound from Q-learning with UCB exploration by a factor of γ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> where γ is the discount factor of the MDP problem. Finally, via simulation, we verify that our algorithm shows a delay reduction of up to 40.8% compared to the max-weight algorithm over various scenarios. We also show that the Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -learning with UCB exploration converges to an ε-optimal policy 10 times faster than Q-learning with UCB.

Self-organization scheme for balanced routing in large-scale multi-hop networks

We propose a self-organization scheme for cost-effective and load-balanced routing in multi-hop networks. To avoid overloading nodes that provide favourable routing conditions, we assign each node with a cost function that penalizes high loads. Thus, finding routes to sink nodes is formulated as an optimization problem in which the global objective function strikes a balance between route costs and node loads. We apply belief propagation (its min-sum version) to solve the network optimization problem and obtain a distributed algorithm whereby the nodes collectively discover globally optimal routes by performing low-complexity computations and exchanging messages with their neighbours. We prove that the proposed method converges to the global optimum after a finite number of local exchanges of messages. Finally, we demonstrate numerically our framework’s efficacy in balancing the node loads and study the trade-off between load reduction and total cost minimization.

Traffic optimization in IoT networks

Since the 2000s, the idea that the Internet could be used for machine-to-machine communication and process automation has emerged. Together with the development of electronic objects capable of communicating with IP protocols, this idea led to the concept of the Internet of Things (IoT Internet of Things). Nowadays, the evolution of networks is very intense. New networks are appearing, “all-optical” solutions in the heart of networks, “wireless” solutions to facilitate access to users or to implant sensors / actors in places difficult to access, or finally the Internet of communicating objects. In this evolution, new scientific issues and challenges are emerging. Some of the problems are related to the optimization of generated traffic as well as the improvement of the performance of tools and techniques. Often, these optimization problems lead to models using graphs. The analysis of optimization problems in networks is an important activity. IOT networks create more data traffic that is difficult to control within the operator’s network. The method given in this paper will help network operators optimize their networks and assist developers in improving hardware and software interactions to reduce data traffic in the network.