AUT Journal of Mathematics and Computing
Volume:3 Issue: 2, Oct 2022

Traffic forecasting plays a crucial role in the effective operation of managed lanes, as traffic demand and revenue are relatively volatile given parallel competition from adjacent, toll-free general-purpose lanes. This paper proposes a deep learning framework to forecast short-term traffic volumes and speeds on managed lanes. A network of convolutional neural networks (CNN) was used to detect spatial features. Volume and speed were converted into heatmaps feeding into the CNN layers and temporal relationships were detected by a recurrent neural network (RNN) layer. A dense layer was used for the final prediction. Six months of historical volume and speed data on the I-580 Express Lanes in California, United States were utilized in this case study. Computational results confirm the effectiveness of the proposed data-driven deep learning framework in forecasting short-term traffic volumes and speeds on managed lanes.

Traditionally, the minimax circle location problems concern finding a circle C in the plane such that the maximum distance from the given points to the circumference of the circle is minimized. The radius of the circle can be fixed or variable. In this paper we consider the inverse case, that is: a circle C with radius r0 is given and we want to modify the coordinate of existing points with the minimum cost such that the given circle becomes optimal. Mathematical models and some properties of the cases that circle C becomes optimal with comparing to all other circles, and circle C becomes the best circle with comparing to the circles with radius r0 are presented.

In this paper we pursue a logical approach to prove that the optimisation problem of finding a spanning caterpillar tree in a graph has polynomial algorithm for bounded tree width graphs. A caterpillar (tree) is a tree with the property that if one removes all its leaves only a path is left. To this end we use Courcelle's theorem and we show how one can present the spanning caterpillar tree problem by using monadic-second order logical expression. The value of this approach reflected better by the fact that finding a spanning caterpillar in a graph is an NP-complete problem [9].

Influence maximization (IM) is a challenging problem in social networks to identify initial spreaders with the best influence on other nodes. It is a need to solve this problem with the minimum diffusion time and the most coverage on the communities. However, the spreaders are rarely dependent on diffusion models. A recent research [N. Binesh, M. Ghatee, Distance-Aware Optimization Model for Influential Nodes Identification in Social Networks with Independent Cascade Diffusion, Information Sciences, 581 (2021) 88-105] proposed DASF algorithm for spreaders selection by the Independent Cascade (IC) diffusion model. Here, we present a new optimization model to find spreaders under Linear Threshold (LT) diffusion model. LT is one of the most important models to imitate the behavior of influence propagation in social networks. Our model is a quadratic programming problem based on Laplacian-Plus matrix. We derive its solution by some principal eigenvectors of Laplacian-Plus matrix. We organize the solution process as DALT algorithm. Without community detection, it can identify the spreaders with maximum inter-communities distance, minimum intra-communities distance, and the most significant degrees. By considering various well-known social networks, we show that DALT provides brilliant results and overcomes other local and global spreader finders, especially in social networks with community structures.

The concept of graph burning and burning number (bn(G)) of a graph G was introduced recently [4]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. bn(G) is the minimum time needed to burn a graph G. The problem is NP-complete. In this paper, we develop first heuristics to solve the problem in general (connected) graphs. In order to test the performance of our algorithms, we applied them on some graph classes with known burning number such as θ-graphs, we tested our algorithms on DIMACS and BHOSLIB that are known benchmarks for NP-hard problems in graph theory. We also improved the upper bound for burning number on general graphs in terms of their distance to cluster. Then we generated a data set of 1000 random graphs with known distance to cluster and tested our heuristics on them.

Vertices in a real-world social network can be grouped into densely connected communities that are sparsely connected to other groups, and these communities can be partitioned into successively more cohesive communities. Given the ever-growing pile of research on community detection, various researchers have surveyed the evolution of various community detection methods such as flat community detection, overlapping community detection, dynamic community detection and community search. Yet, the problem of hierarchical community detection, despite being well studied, has not been surveyed and the evolution of methods to identify hierarchies of communities in large-scale complex networks has not been documented. In this survey, we study the hierarchical community detection problem and formally define this problem. We then classify the existing works on hierarchical community detection and discuss some of the flat community detection approaches that are capable of producing hierarchies. We then introduce a set of empirical analysis tools, such as benchmark datasets and accuracy measures to evaluate the performance of a hierarchical community detection method.

One of the problems raised in software defined networks is to determine the number and installation location of controllers so that the cost of implementation reduced and survivability of the network against link or node failure increased. Current investigation in SDN imposes full mesh topology in order to connect controllers. This approach while incurring a huge installation cost, dose not carefully incorporate network survivability requirements. In this paper, we improve an existing integer programming approach to a novel model so as to effectively address user defined survivability requirements. Computational results reported also reveals that our models could be solved by state-of-the-art MIP solvers like CPLEX within a reasonable time limit.

We consider a family of problems that combine network design and facility location. Such problems arise in many practical applications in different fields such as telecommunications, transportation networks, logistic, and energy supply networks. In facility location problems, we want to decide which facilities to open and how to assign clients to the open facilities so as to minimize the sum of the facility opening costs and client connection costs. These problems typically do not involve decisions concerning the routing of the clients’ demands to the open facilities; once we decided on the set of open facilities, each client is served by the closest open facility. In network design problems, on the other hand, we generally want to design and dimension a minimum-cost routing network providing sufficient capacities to route all clients’ demands to their destinations. These problems involve deciding on the routing of each client’s demand. But, in contrast to facility location problems, demands’ destinations are predetermined. In many modern day applications, however, all these decisions are interdependent and affect each other. Hence, they should be taken simultaneously. The aim of this work is to survey models, algorithmic approaches and methodologies concerning such combined network design facility location problems.

Vehicle scheduling problem is an important combinatorial optimization problem arising in the management of transportation companies. The problem consists of assigning a set of timetabled trips to a set of vehicles to minimize a given objective function. In this paper, vehicle scheduling problem under undeterministic conditions is considered. The paper states the necessity of considering the uncertain condition in the problem and reviews the different solution approaches to deal with the conditions of uncertainty. The main objective of this paper is to discuss the importance of considering uncertainty in vehicle scheduling problem, review the relevant literature and present some directions for future work.

Deep convolutional neural networks have been widely and successfully used for various computer vision tasks. The main bottleneck for developing these models has been the lack of large datasets labeled by human experts. Self-supervised learning approaches have been used to deal with this challenge and allow developing models for domains with small labeled datasets. Another challenge for developing deep learning models is that their performance decreases when deployed on a target domain different from the source domain used for model training. Given a model trained on a source domain, domain adaptation refers to the methods used for adjusting a model or its output such that when the model is applied to a target domain, it achieves higher performance. This paper reviews the most commonly used self-supervised learning approaches and highlights their utility for domain adaptation.

This paper proposes an integrated system to control ramps and adjust variable speed limits. It includes three essential modules to predict the starting time of congestion and a fuzzy controller to determine the parameters and a model predictive control. An Apriori algorithm that is a powerful tool for frequent pattern mining is used in the first module. The proposed system is neither sensitive to the traffic distribution nor computationally intensive. Two traffic simulators of Aimsun and CTMSIM are applied to validate the results. Compared with the most recent algorithms, including Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM), this system improves prediction accuracy up to 2.63%. The results of ramp metering and variable speed limit subsystems are also promising. The embedded controller shows 0.6% and 4% overall and rush hour improvement in the total travel time.

Considering the stochastic traffic networks one can follow an assignment procedure to estimate flows. However, the interdependent bi-modal assignment problems are solved just for deterministic status. To this gap, this paper extends a traffic assignment problem for an interdependent bi-modal network under Stochastic User Equilibrium (SUE) conditions. To solve this problem, a new algorithm is presented by combining a user equilibrium algorithm namely Streamline algorithm with a Logit model. In our algorithm, the interaction between private and public traffic flows is explicitly modeled and travel time for each mode is considered as a function of two-mode flows. Also, the origin-destination matrix was split between two modes based on the binomial Logit function. Some networks were considered to illustrate the performance and the accuracy of the proposed stochastic user equilibrium algorithm on the interdependent bi-modal networks. Numerical results showed that this algorithm provided reasonable solutions with high accuracy in a small computation time compared with the other user equilibrium (UE) algorithms.