Routing Problem In Networks Research Articles

Routing Algorithms for SDM Flexible Optical Networks

This paper considers the online routing, modulation, spectrum, and core allocation problem in elastic optical networks. Three algorithms are proposed to minimize the bandwidth blocking probability while taking into account the impact of interference from established lightpaths. These algorithms are based on a sequence of alternative paths, ordered in terms of increasing lengths, determined by Yen’s algorithm. Each of the algorithms for the selected single or dual lightpath enforces the constraints of spectrum continuity, contiguity of the slots, and non-overlapping of the spectra with the established lightpaths, maximizes the number of bits per symbol, and selects a specific core on each link of the path. Simulation studies performed for two sample networks showed that the crosstalk has a significant impact on the bandwidth blocking probability. The best results were obtained by iterating over all paths and all slots, selecting the lightpath with the lowest average crosstalk per slot, consisting of the most loaded cores.

Fixed Automated stations location and UAVs routing problems in urban road Networks: A tailored Branch-&-price algorithm

Unmanned aerial vehicles (UAVs) serve as vital tools for collecting real-time traffic data, enabling rapid responses to events, and optimizing traffic management based on their cost-effectiveness, high flexibility, and wide coverage range advantages. The urban UAV cruising problem primarily focuses on selecting the locations of fixed automated station (FAS) and optimizing UAVs’ cruising routes. This paper introduces a strategy where UAVs can take off and land on different FASs to enhance urban UAVs’ cruising efficiency. Firstly, the problem is formulated as an integrated linear integer model (FU-ILP) which simultaneously determines the locations of FASs and the routes of UAVs. The objective is to minimize redundant cruising distance and cruising cycle time. The FU-ILP model takes into account UAV‘s flight capabilities, FAS’s signal coverage range, power requirements, and battery charging. Moreover, we design a tailored branch-and-price (TB&P) algorithm to decompose the FU-ILP model, which can reduce the variable scale for solving larger-scale cases. Finally, we test the model and the algorithm on the Sioux Falls Test Network. The TB&P algorithm improves computational efficiency by nearly 80%. Moreover, our strategy yields superior results compared to the strategy where UAVs must return to their take-off FASs for recharging. We also demonstrate that increasing the number of UAVs does not reduce redundant cruising distance in the whole network, but it can shorten the cruising cycle. These policy conclusions also apply to the case of Xiongan. This provides a basis for managers to calculate the minimum UAV’s configuration based on the cities’ actual cruising frequency requirements.

On non-superperfection of edge intersection graphs of paths

The routing and spectrum assignment problem in modern flexgrid elastic optical networks asks for assigning to given demands a route in an optical network and a channel within an optical frequency spectrum so that the channels of two demands are disjoint whenever their routes share a link in the optical network. This problem can be modeled in two phases: firstly, a selection of paths in the network and, secondly, an interval coloring problem in the edge intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all possible non-negative integral weights are called superperfect. Therefore, the occurrence of non-superperfect edge intersection graphs of routing paths can provoke the need of larger spectral resources. In this work, we examine the question which minimal non-superperfect graphs can occur in the edge intersection graphs of routing paths in different underlying networks: when the network is a path, a tree, a cycle, or a sparse planar graph with small maximum degree. We show that for any possible network (even if it is restricted to a path) the resulting edge intersection graphs are not necessarily superperfect. We close with a discussion of possible consequences and of some lines of future research.

CIBORG: CIrcuit-Based and ORiented Graph theory permutation routing protocol for single-hop IoT networks

The Internet of Things (IoT) has emerged as a promising paradigm which facilitates the seamless integration of physical devices and digital systems, thereby transforming multiple sectors such as healthcare, transportation, and urban planning. This paradigm is also known as ad-hoc networks. IoT is characterized by several pieces of equipment called objects. These objects have different and limited capacities such as battery, memory, and computing power. These limited capabilities make it difficult to design routing protocols for IoT networks because of the high number of objects in a network. In IoT, objects often have data which does not belong to them and which should be sent to other objects, then leading to a problem known as permutation routing problems. The solution to that problem is found when each object receives its items. In this paper, we propose a new approach to addressing the permutation routing problem in single-hop IoT networks. To this end, we start by representing an IoT network as an oriented graph, and then, based on a reservation channel protocol, we first define a permutation routing protocol for an IoT in a single channel. Secondly, we generalize the previous protocol to make it work in multiple channels. Routing is done using graph theory approaches. The obtained results show that the wake-up times and activities of IoT objects are greatly reduced, thus optimizing network lifetime. This is an effective solution for the permutation routing problem in IoT networks. The proposed approach considerably reduces energy consumption and computation time. It saves 5.2 to 32.04% residual energy depending on the number of items and channels used. Low energy and low computational cost demonstrate that the performance of circuit-based and oriented graph theory is better than the state-of-the-art protocol and therefore is a better candidate for the resolution of the permutation routing problem in single-hop environment.

Optimization of the Colony Size Parameter in the Ant Algorithm for Solving the Routing Problem in Communication Networks

With the increasing amount of information and complexity of communication networks, the issue of routing remains relevant. The routing problem is a classic problem of building a logical structure of a communication network. To solve this problem, many methods are used, such as: genetic algorithms, ant algorithm, swarm intelligence, artificial bee colony algorithm, firefly algorithm, bacterial food search optimization algorithm, etc. Despite the fact that the effectiveness of using the ant algorithm is widely known and described, however, there is no single approach to finding the optimal use case for the algorithm. There is a need to determine the optimal size of the colony when solving the routing problem. The article describes the results of the simulation process of modeling the behavior of ant colonies of different sizes to find the optimal route through the AnyLogic environment. It is determined that by means of simulation it is possible to reproduce the use of the ant algorithm to solve the routing problem in communication networks. To find the optimal ratio of the colony size to the complexity of the task, you can use the grid search methodology. The results clearly demonstrate that with increasing complexity of the task (the number of communication nodes), the same number of ants cope worse with the task. The problem associated with the need to accurately determine the optimal size of a colony is of great practical importance, because an increase in the size of a colony has generally decreasing utility. It was found that for many, an increase in the number of ants from 100 to 500 had a relatively greater effect than an increase in the size of the colony from 1000 to 10000. It is proved that by means of simulation it is possible to reproduce the use of the ant algorithm to solve the routing problem in communication networks.

Research on AdHoc network routing algorithm for link stability prediction

Abstract This study aims to improve network communication efficiency and reliability by researching routing algorithms for predicting link stability in AdHo networks. AdHoc network is a self-organizing, decentralized network structure in which nodes establish temporary connections through wireless communication, making the network resilient and flexible. However, due to the continuous changes in network topology and the instability of wireless links, routing problems in AdHoc networks have become particularly complex. This article proposes a backup path routing algorithm LS-BPR based on link stability prediction. This mechanism takes the path with the minimum delay as the main path, uses the cost function as the standard for selecting backup paths, and then uses the ARIMA model to predict links with good link stability as backup paths. We simulate and compare LS-BPRAODV and AODV protocols using the QualNet simulation platform. The simulation results show that the LS-BPRAODV, with the addition of a prediction mechanism, improves network performance, reduces the number of source node routing discoveries, reduces the number of route breaks, significantly reduces the packet loss rate and information reception delay in the network, and improves the average throughput of the network. This study provides new theoretical and empirical support for the routing algorithm for link stability prediction in AdHo networks, which is of great significance for promoting the development of wireless self-organizing networks.

Innovative Ways of Developing and Using Specific Purpose Alternatives for Solving Hard Combinatorial Network Routing and Ordered Optimisation Problems

This paper reviews some recent contributions by the authors and their associates and highlights a few innovative ideas, which led them to address some hard combinatorial network routing and ordered optimisation problems. The travelling salesman, which is in the NP hard category, has been reviewed and solved as an index-restricted shortest connected graph, and therefore, it opens a question about its ‘NP Hard’ category. The routing problem through ‘K’ specified nodes and ordered optimum solutions are computationally demanding but have been made computationally feasible. All these approaches are based on the strategic creation and use of an alternative solution in that situation. The efficiency of these methods requires further investigation.

An exact method for vehicle routing problem with backhaul discounts in urban express delivery network

The surge in e-commerce has led to an increased demand for urban express services, requiring the strategic development of delivery networks that are both efficient and cost-effective. This study addresses a practical vehicle routing problem (VRP) in an urban express delivery network to minimize transportation costs. Specifically, it considers the implementation of backhaul discounts, a factor disregarded in the existing literature. This VRP is further complicated by various realistic constraints, including pickup and delivery, time windows, multiple trips, heterogeneous fleets, and docking capacity limitations, which make most general VRP solvers inapplicable. This study proposes a trip-based formulation to overcome this challenge and develop a tailored branch-and-price algorithm. Feasible trips are classified into four types to simplify the computation of backhaul discounts, thereby enhancing solution efficiency. Validation with real-world data from SF Express substantiates the efficacy of our method and yields insights for sustainable city logistics management. Moreover, our simplified column generation algorithm exhibits competitive performance, achieving optimal solutions expeditiously for the tested instances.

Optimal control of linear cost networks

We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the Bellman equation giving the optimal cost function and resulting sparse state feedback for these systems can be stated explicitly, with the solution given by a linear program. Our framework admits a range of network routing problems with underlying linear dynamics. These dynamics can be used to model traditional graph-theoretical problems like shortest path as a special case, but can also capture more complex behaviors. We provide an asynchronous and distributed value iteration algorithm for obtaining the optimal cost function and control law.

First train timetabling and passenger transfer routing problems in urban rail transit networks

This paper incorporates the shortest passenger travel paths into the first train timetabling problem in urban rail transit networks. We first propose a path-based first train timetabling problem, which is formulated as a mixed-integer nonlinear programming model to reduce the travel time for passengers. To solve this model, we present a tailored branch-and-bound combined with the timetable-based Dijkstra algorithm. To further enhance the efficiency of the exact algorithm, we design a rolling time heuristic algorithm as a substitute for the branch-and-bound algorithm. Then, we proved that the rolling time heuristic combined with the timetable-based Dijkstra algorithm achieves 97.86% and 99.39% reductions in CPU time while sacrificing only 0.007% and 0.057% of optimality gap by two numerical experiments. Finally, the results based on two test networks with different structures demonstrate that the path-based first train timetabling model effectively improves passenger travel efficiency. Specifically, the travel times are reduced by 744 mins and 761 mins, while the transfer waiting times are reduced by 37.87% and 58.91% compared to the existing timetables. Moreover, the results also demonstrate that loop line networks will increase the difficulty of timetabling and lead to many passengers taking detours. To further enhance the efficiency of commuting for passengers who take the first train, URT operators may consider relaxing the limitations on the departure time of the depot stations.

Computing Bipath Multicommodity Flows with Constraint Programming–Based Branch-and-Price-and-Cut

We propose a constraint programming (CP)–based branch-and-price-and-cut framework to exactly solve bipath multicommodity flow (MCF): an MCF problem with two paths for each demand. The goal is to route demands in a capacitated network under the minimum cost. The two paths must have disjoint arcs, and the delays accumulated along the two paths must be within a small deviation of each other. CP is used at multiple points in this framework: for solving pricing problems, for cut generation, and for primal and branching node heuristics. These modules use a CP solver designed for network routing problems and can be adapted to other combinatorial optimization problems. We also develop a novel, complete, two-level branching scheme. On a set of diverse bipath MCF instances, experimental results show that our algorithm significantly outperforms monolithic CP and mixed integer linear programming models and demonstrate the efficiency and flexibility brought by the tailored integration of linear programming and CP methodologies. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada; Huawei Technologies. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0128 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0128 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Approximate Distance Oracle for Fault-Tolerant Geometric Spanners

In this paper, we present approximate distance and shortest-path oracles for fault-tolerant Euclidean spanners motivated by the routing problem in real-world road networks. A fault-tolerant Euclidean spanner for a set of points in Euclidean space is a graph in which, despite the deletion of small number of any points, the distance between any two points in the damaged graph is an approximation of their Euclidean distance. Given a fault-tolerant Euclidean spanner and a small approximation factor, our data structure allows us to compute an approximate distance between two points in the damaged spanner in constant time when a query involves any two points and a small set of failed points. Additionally, by incorporating additional data structures, we can return a path itself in time almost linear in the length of the returned path. Both data structures require near-linear space.

Solution of the Simultaneous Routing and Bandwidth Allocation Problem in Energy-Aware Networks Using Augmented Lagrangian-Based Algorithms and Decomposition

We discuss several algorithms for solving a network optimization problem of simultaneous routing and bandwidth allocation in green networks in a decomposed way, based on the augmented Lagrangian. The problem is difficult due to the nonconvexity caused by binary routing variables. The chosen algorithms, which are several versions of the Multiplier Method, including the Alternating Direction Method of Multipliers (ADMM), have been implemented in Python and tested on several networks’ data. We derive theoretical formulations for the inequality constraints of the Bertsekas, Tatjewski and SALA methods, formulated originally for problems with equality constraints. We also introduce some modifications to the Bertsekas and Tatjewski methods, without which they do not work for an MINLP problem. The final comparison of the performance of these algorithms shows a significant advantage of the augmented Lagrangian algorithms, using decomposition for big problems. In our particular case of the simultaneous routing and bandwidth allocation problem, these algorithms seem to be the best choice.

Dynamic routing optimization in software-defined networking based on a metaheuristic algorithm

Optimizing resource allocation and routing to satisfy service needs is paramount in large-scale networks. Software-defined networking (SDN) is a new network paradigm that decouples forwarding and control, enabling dynamic management and configuration through programming, which provides the possibility for deploying intelligent control algorithms (such as deep reinforcement learning algorithms) to solve network routing optimization problems in the network. Although these intelligent-based network routing optimization schemes can capture network state characteristics, they are prone to falling into local optima, resulting in poor convergence performance. In order to address this issue, this paper proposes an African Vulture Routing Optimization (AVRO) algorithm for achieving SDN routing optimization. AVRO is based on the African Vulture Optimization Algorithm (AVOA), a population-based metaheuristic intelligent optimization algorithm with global optimization ability and fast convergence speed advantages. First, we improve the population initialization method of the AVOA algorithm according to the characteristics of the network routing problem to enhance the algorithm’s perception capability towards network topology. Subsequently, we add an optimization phase to strengthen the development of the AVOA algorithm and achieve stable convergence effects. Finally, we model the network environment, define the network optimization objective, and perform comparative experiments with the baseline algorithms. The experimental results demonstrate that the routing algorithm has better network awareness, with a performance improvement of 16.9% compared to deep reinforcement learning algorithms and 71.8% compared to traditional routing schemes.

DeepLS: Local Search for Network Optimization Based on Lightweight Deep Reinforcement Learning

Deep Reinforcement Learning (DRL) is being investigated as a competitive alternative to traditional techniques for solving network optimization problems. A promising research direction lies in enhancing traditional optimization algorithms by offloading low-level decisions to a DRL agent. In this study, we consider how to effectively employ DRL to improve the performance of Local Search algorithms, i.e., algorithms that, starting from a candidate solution, explore the solution space by iteratively applying local changes (i.e., moves), yielding the best solution found in the process. We propose a Local Search algorithm based on lightweight Deep Reinforcement Learning (DeepLS) that, given a neighborhood, queries a DRL agent for choosing a move, with the goal of achieving the best objective value in the long term. Our DRL agent, based on permutation-equivariant neural networks, is composed by less than a hundred parameters, requiring only up to ten minutes of training and can evaluate problem instances of arbitrary size, generalizing to networks and traffic distributions unseen during training. We evaluate DeepLS on two illustrative NP-Hard network routing problems, namely OSPF Weight Setting and Routing and Wavelength Assignment, training on a single small network only and evaluating on instances 2x-10x larger than training. Experimental results show that DeepLS outperforms existing DRL-based approaches from literature and attains competitive results with state-of-the-art metaheuristics, with computing times up to 8x smaller than the strongest algorithmic baselines.

Subswarm-guided ant colony optimization with enhanced pheromone update mechanism and beam search for VNF placement and routing

Network Function Virtualization (NFV) is a novel technology that enables flexible and cost-effective networks by replacing the hardware-based middleboxes with software run on virtual machines called virtual network function (VNF). In NFV, each Service Function Chain (SFC) is required to be a set of ordered VNF from that must be optimally located across servers/distributed data centers. This paper studies the multi-objective virtual network function placement and routing problem (MO-VNFPR), which involves placing VNFs optimally in servers nodes and assigning server resources efficiently to these VNFs to satisfy user’s requests in the networks. Most existing methods for this problem only handled one requests or considered VNF placement and SFC routing separately. In this paper, we consider MO-VNFPR with two objectives: (i) minimize the overall cost by deploying servers and installing VNFs; (ii) reduce the network delay. A metaheuristic called subswarm-guided ant colony optimization (named SgACO) is introduced to efficiently solve MO-VNFPR. In SgACO, a subswarm-guided mechanism is adopted to satisfy requests at once by reorganizing the ant colony into subswarms. Moreover, an enhanced pheromone update mechanism and beam search are developed to investigate the search space efficiently. Experimental simulations on COGENT, CONUS, and NSF network topologies demonstrate that our algorithm achieves competitive results and performs better against other existing algorithms.

Exact and heuristic approaches for maximizing flows in UAV-enabled wireless cellular networks with multi-hop backhauls

This paper investigates the problem of data routing in backhaul networks using Unmanned Aerial Vehicles (UAVs) to relay data from Small Cells (SCs) to the core network. The objective is to maximize the total fulfilled demand of data to be routed, while ensuring technical requirements such as hop constraints and edge capacity. The problem is formulated using a compact mixed-integer programming model, which can solve small- and medium-sized topologies. In addition, a fast constructive heuristic based on a maximal tree is developed to solve large-scale topologies, resulting in a significant reduction in CPU time. The quality of the heuristic is evaluated by using column generation for solving the linear programming relaxation of an exponential formulation. The computational study shows the effectiveness and value of the proposed compact model and constructive heuristic for various topology sizes. Furthermore, experiments demonstrate that by keeping the network setup constant and updating the demand vector only, the computational time of the compact model can be drastically reduced for all topology sizes.

SOHO-FL: A Fast Reconvergent Intra-Domain Routing Scheme Using Federated Learning

The development of machine learning provides a new paradigm for network optimizations, e.g., reinforcement learning (RL) has brought great improvements in many fields, such as adaptive video streaming, congestion control of TCP. The fundamental mechanism of such RL-based architectures is that the neural network decision model converges to a stable state by continuously interacting with network environment. However, for network routing problem, such RL-based strategies do not work well due to topology change. This is because topological changes would require the existing RL models to be retrained, while these models may stop making routing decisions or provide non-optimal decisions during the slow reconverging process of retraining, seriously affected transmission performance. To solve this problem, we proposed a fast convergent RL-model (SOHOFL), which can alleviate the performance degradation caused by the slow retraining process by federated learning. The experimental results based on real-world network topologies demonstrate that SOHO-FL outperforms the state-of-the-art algorithms in reconvergence time by 22.3% on average.

Solving the routing and spectrum assignment problem, driven by combinatorial properties

AbstractThe routing and spectrum assignment problem in modern optical networks is an NP‐hard problem that has received increasing attention during the last years. The majority of existing integer linear programming models for the problem uses edge‐path formulations where variables are associated with all possible routing paths so that the number of variables grows exponentially with the size of the instance. To bypass this difficulty, precomputed subsets of all possible paths per demand are typically used, which cannot guarantee optimality of the solutions in general. Our contribution is to provide a framework for the use of edge‐path formulations to minimize the spectrum width of a solution. For that, we select an appropriate subset of paths to operate on with the help of combinatorial properties in such a way that optimality of the solution can be guaranteed. Computational results indicate that our approach is indeed promising to solve the routing and spectrum assignment problem.

A crossover-based multi-objective discrete particle swarm optimization model for solving multi-modal routing problems

Passengers must use a set of modes and vehicles to reach their destination in complicated urban structures. Choosing an optimal route is a complicated optimization problem for these passengers. This study proposes a multi-objective optimization algorithm to solve the routing problem in the urban multi-modal network. The multi-modal network problem considered in this study is a transportation network with subway, Bus Rapid Transit (BRT), taxi, and walking modes. The objective functions determine the optimized route by considering route length, traffic, comfort, and safety. We develop a Crossover-Based Multi-Objective Discrete Particle Swarm Optimization (CBMODPSO) to solve the problem. CBMODPSO has been improved using mutation and crossover operators. Multi-Objective Artificial Bee Colony (MOABC), Multi-Objective Ant Colony Optimization (MOACO), Multi-Objective Biogeography-Based Optimization (MOBBO), Multi-Objective Gray Wolf Optimization (MOGWO), and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithms are used to evaluate and compare the results from the CBMODPSO algorithm. In addition, CBMODPSO results are compared with previous research results. We show the improved algorithm is more repeatable than other algorithms. The CBMODPSO algorithm has a faster convergence rate and is able to get to an optimal solution in a smaller generation number and much less time. The CBMODPSO algorithm is implemented in about one-thirties of the MOBBO duration. Meanwhile, it has a reproducibility of almost twice the MOGWO algorithm.