Network Flow Optimization Research Articles

AI-Driven Neural Networks for Real-Time Passenger Flow Optimization in High-Speed Rail Networks

AI-Driven Neural Networks for Real-Time Passenger Flow Optimization in High-Speed Rail Networks

Legal fuzzy incidence blocks and legal flow reduction sets with application to water distribution networks

Directed fuzzy incidence graphs (DFIGs) are fuzzy incidence structures where each edge and incidence pair has a specific direction. In these graphs, the relationships are not symmetric, making it easier to identify the extent of interaction between nodes and arcs. The comprehensive investigation of connectivity in directed fuzzy incidence graphs holds the potential to provide solutions for a wide range of real-world problems including traffic flow optimization in one-way traffic networks and migration analysis of refugees across various countries. The main objective of this paper is to extend the connectivity concepts of directed fuzzy incidence graphs, which help to analyze various stochastic networks influenced by external factors. The major concepts discussed in this article are legal fuzzy incidence blocks, legal flow reduction sets, and the DFIG-version of Menger's theorem. Directed fuzzy incidence graphs having no legal flow reduction nodes are defined as legal fuzzy incidence blocks (LFI-blocks). Legal flow reduction nodes (LFR-nodes) are distinct elements, the elimination of which results in a reduction of the directed incidence connectivity between some other pair of nodes. Since LFI-blocks lack these elements, the removal of none of the nodes reduce the legal flow between other pair of nodes. Consequently, for each node under consideration, any other pair of nodes connected by at least one di-path must possess a widest legal di-path which avoids that specific node. LFI-blocks exhibit differing attributes in contrast to their counterparts in fuzzy graphs and fuzzy incidence graphs. This viewpoint motivated the authors to investigate these distinctions and assess the possibility of defining equivalent conditions for LFI-blocks, similar to the equivalent conditions established for fuzzy blocks and fuzzy incidence blocks. A key characteristic of legal fuzzy incidence blocks is their capacity to incorporate legal flow reduction links, even allowing for the presence of shared nodes among two legal flow reduction links. This contrasts with fuzzy graphs and fuzzy incidence graphs, where if two fuzzy bridges happen to share a common node, it results in that node being a fuzzy cutnode. Two equivalent conditions are proposed for a directed fuzzy incidence graph to become a legal fuzzy incidence block. It is shown that any two nodes in a legal fuzzy incidence block which are connected by at least one di-path, but not by a legal flow reduction link will have at least two internally disjoint widest legal di-paths joining them. To identify the maximum number of such internally disjoint widest legal di-paths, the notion of legal flow reduction set of nodes and arcs is introduced. These sets are characterized using widest legal di-paths. Moreover, the DFIG-version of Menger's theorem for nodes is established, which explains the relation between number of internally disjoint widest legal di-paths and cardinality of legal flow reduction sets in a directed fuzzy incidence graph. Also, an illustration of Menger's theorem is proposed for water distribution networks.

Electric vehicle battery chemistry affects supply chain disruption vulnerabilities

We examine the relationship between electric vehicle battery chemistry and supply chain disruption vulnerability for four critical minerals: lithium, cobalt, nickel, and manganese. We compare the nickel manganese cobalt (NMC) and lithium iron phosphate (LFP) cathode chemistries by (1) mapping the supply chains for these four materials, (2) calculating a vulnerability index for each cathode chemistry for various focal countries and (3) using network flow optimization to bound uncertainties. World supply is currently vulnerable to disruptions in China for both chemistries: 80% [71% to 100%] of NMC cathodes and 92% [90% to 93%] of LFP cathodes include minerals that pass through China. NMC has additional risks due to concentrations of nickel, cobalt, and manganese in other countries. The combined vulnerability of multiple supply chain stages is substantially larger than at individual steps alone. Our results suggest that reducing risk requires addressing vulnerabilities across the entire battery supply chain.

Research on Piano Curriculum Education and Its Performance Ecosystem Based on Network Flow Optimization

Abstract This paper investigates music education, where an efficient and accurate performance evaluation system in the piano teaching and performance ecosystem is increasingly becoming an essential tool for improving teaching quality and performance level. The objective evaluation of students’ performance skills can be achieved by carefully analyzing piano performances using the network flow optimization technique. This technique optimizes the performance evaluation system’s audio recognition ability by analyzing the piano audio signal and solving the multi-constraint nonlinear optimization problem in a limited time domain. This paper establishes a network flow optimization model, applies the multi-constraint nonlinear optimization technique, and combines the non-negative matrix decomposition and dynamic time regularization algorithm to analyze the piano performance for experiments. After optimization processing, hundreds of piano audio samples were collected, and the audio recognition accuracy was improved by 20%. By optimizing and processing the audio signals from the network stream, the evaluation system could detect polyphony more accurately and track the musical score effectively, improving accuracy and efficiency. Using the non-negative matrix decomposition algorithm, the accuracy of detecting polyphony can reach 85%, while the dynamic temporal regularization algorithm can match the position of the musical score with 95% accuracy. The accuracy of piano performance evaluation is optimized by this network flow optimization method, providing new technical means for music education, and promoting the quality of teaching and performance.

Optimization of network flows for rural extension of fruit and vegetable agricultural technologies

Abstract This paper focuses on the rural promotion of fruit and vegetable agricultural technology and proposes a network flow optimization model based on linear programming for the diffusion of fruit and vegetable agricultural technology. Based on the Bass model, it describes the process of natural growth of network users and the word-of-mouth effect among them. Fruit and vegetable agricultural technology diffusion in real social networks is fitted and predicted by the social network information dissemination model, and the network flow problem of fruit and vegetable agricultural technology promotion is optimized using linear programming equations. Based on this basis, the algorithm designed in this paper and the effect of rural promotion of fruit and vegetable agricultural technology are analyzed with relevant data. The results show that the coefficient of the variable of the number of promotion times in the behavior of agrotechnology promotion is 0.064, which has a significant positive effect on the evaluation of the rural promotion performance of fruit and vegetable agricultural technology, indicating that increasing the number of agricultural technology training and enriching the content of agricultural technology promotion will help to improve the evaluation of the rural promotion performance of fruit and vegetable agricultural technology by farmers. The network flow optimization model constructed in this paper can enable farmers to master more modern fruit and vegetable agricultural technology to meet the needs of modern production of fruit and vegetable agriculture so as to improve the level of local fruit and vegetable agricultural development.

Teaching Integration of Piano and Traditional Music Elements in Colleges and Universities Based on Network Flow Optimization

Abstract In this paper, from the basis of piano music theory, pitch and twelve equal temperaments are studied, and due to the characteristics of the piano’s construction, there are different timbres and harmonic structures. In order to realize the digitization of music signals for piano teaching, the collected analog signals are converted into digital signals by Fourier transform, the samples are inputted into the neural network model to get the output results, and the loss function based on Markov’s music language model in piano teaching is used to find the partial derivatives of the parameters to realize the maximization of the efficiency of the piano pitch and note recognition. According to the multi-task learning in neural networks and the envelope curve of notes, we construct the automatic music transcription model in piano teaching based on CNN-HMM and use the simulation experiment analysis to empirically analyze the piano teaching based on CNNHMM. The results show that the dual-channel audio results are improved by 2.68% in F1 value, 3.18% in accuracy and 2.61% in recall than the mono audio results. That is, dual-channel audio has richer information than mono audio, which enables the CNN-HNN network to learn richer features and thus improve the pitch and note recognition results. In this paper, the reliability of the teaching quality evaluation results of the CNN-HMM-based quantitative assessment model for facilitating the combination of electronic organ and piano teaching concepts ranges from 78.1% to 85.4%. This study provides guiding value for the development of digital piano teaching, which is of great significance for the innovative reform of piano teaching in colleges and universities.

A fuzzy multiobjective linear programming approach for green multiechelon distribution network design

PurposeDistribution network design involves a set of strategic decisions in supply chains because of their long-term impacts on the total logistics cost and environment. To incorporate a trade-off between financial and environmental aspects of these decisions, this paper aims to determine an optimal location, among candidate locations, of a new logistics center, its capacity, as well as optimal network flows for an existing distribution network, while concurrently minimizing the total logistics cost and gas emission. In addition, uncertainty in transportation and warehousing costs are considered.Design/methodology/approachThe problem is formulated as a fuzzy multiobjective mathematical model. The effectiveness of this model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network with 22 products and a planning horizon of 20 periods. The model is solved by using the min–max and augmented ε-constraint methods with CPLEX as the solver. In addition to illustrating model’s applicability, the effect of choosing a new warehouse in the model is investigated through a scenario analysis.FindingsFor the applicability of the model, the results indicate that the augmented ε-constraint approach provides a set of Pareto solutions, which represents the ideal trade-off between the total logistics cost and gas emission. Through a case study problem instance, the augmented ε-constraint approach is recommended for similar network design problems. From a scenario analysis, when the operational cost of the new warehouse is within a specific fraction of the warehousing cost of third-party warehouses, the solution with the new warehouse outperforms that without the new warehouse with respective to financial and environmental objectives.Originality/valueThe proposed model is an effective decision support tool for management, who would like to assess the impact of network planning decisions on the performance of their supply chains with respect to both financial and environmental aspects under uncertainty.

Traffic safety performance evaluation in a connected vehicle environment with queue warning and speed harmonization applications

With the increased adoption of connected vehicle (CV) technologies, safety information is becoming increasingly available to drivers. This study investigates three main questions (1) Do CV-based traffic management applications improve safety on roadways with existing infrastructure-based traffic management systems? (2) Can combining two CV technologies have a greater impact on safety than a single CV technology? and (3) Do geometric and traffic composition factors impact the efficiency of CV technologies? We applied a rarely-used CV dataset and conducted a comprehensive simulation analysis of varying conditions and CV penetration rates that studies have not considered. Two CV applications (queue warning and speed harmonization) implemented in the Intelligent Network Flow Optimization experiment in Seattle, WA were evaluated. Results showed that driver safety performance, based on speed metrics (standard deviation and percentage of extreme values) improved under the CV driving conditions. Combining conventional variable speed limit systems with queue warnings also improved safety for CV drivers. Furthermore, the implementation of a single CV application (queue warning) showed positive changes in the aforementioned speed metrics, congestion mitigation, and reduced conflicts. With the two CV applications combined, no significant differences were observed. Additional tests investigated the impacts of lane changes and roadway attributes on safety in the CV environment.

Applying network flow optimisation techniques to minimise cost associated with flood disaster.

The estimated amount of $1016673.37 becomes a benchmark for the government, research agencies and other developmental agencies for the purpose of planning. By using the air and road transport modes, and allowing direct and indirect transportation to the PODs, it saved time, resulting in many lives being saved.

Implementasi Algoritma A* (A-Star) dan Greedy Dalam Penentuan Routing Pada Wide Area Network (WAN)

The continuous development of the internet has led to changes in routing complexity. In the context of a wide area network (WAN), network flow optimization becomes a major issue in the selection of the fastest route, which involves routing protocols. Algorithms in routing protocols are designed to determine the shortest path. Therefore, studies are needed regarding how to build a routing algorithm that can be used to get the shortest path in each process. This study aims to reduce network workload and compare the computation involved in determining the shortest path using the Greedy algorithm and the A* algorithm. The simulation results show that the A* algorithm is superior to greedy. The measurement results show that the final cost of the Greedy algorithm is 44 and the A* algorithm is 38. Taking into account the heuristic value for each node, the A* algorithm is superior to the Greedy algorithm in determining the shortest path.

Risk-based inventory scheduling framework to fulfill multi-product orders within a production network

Production facilities are critical components of the global economy and supply chain. Firms are forced to balance several competing objectives—from reducing operating costs by managing inventory to increasing profits by satisfying customer demand. The act of scheduling material through an interconnected production network is analytically challenging; therefore, stakeholders require statistical insights to strengthen the decision-making process. This inventory scheduling application allows decision-makers to monitor the status and impact of numerous production parameters while aiming to mitigate the propagation of schedule risk through the system. This work presents a material planning framework that (i) jointly represents work center and material relationships and (ii) integrates stochastic methods to assess potential risk. Using network flow optimization and Monte Carlo simulation, this work accommodates three primary considerations: (i) safety stock, and other inventory restrictions, (ii) multi-product order satisfaction, and (iii) costs derived from holding inventory and delaying orders. An illustrative example examines the impact of twelve experimental scenarios on order fulfillment, work center utilization, and material inventory and production.

Effect of demand uncertainty on omnichannel distribution network design strategies

AbstractTo investigate the effect of uncertain demand on various omnichannel distribution network strategies and analyze the impacts of various online order fulfillment policies, a two‐staged network optimization model is built. The two stages are a deterministic model to define the optimal distribution network and a simulation model to determine the optimal network flow to maximize the total profit for a given distribution network and online order fulfillment policy. This study shows the importance of taking demand uncertainty, requested delivery time, and customer service level (CSL) into account in designing an omnichannel distribution network. The results of the simulation model indicate that shipments from warehouse (SFW) and hybrid strategies more successfully cope with variation because there is a greater profit decline in shipments from store (SFS) strategies. The results also show that applying a dynamic assignment policy plays an important role in handling variation in demand. The study shows that, as demand uncertainty and CSL increase, having products available in central repositories becomes even more important to cope with demand variation. The study also indicates SFS strategies that seem more profitable in the assumed‐to‐be deterministic model might be misleading because SFS strategies become less profitable (compared to SFW strategies) when demand uncertainty is taken into account.

Neural network flow optimization using an oscillating cylinder

Flow behaviors of a downstream object can be affected significantly by an upstream object in close proximity. Combined with the neural network algorithms, this concept is used for flow control in this study to optimize the aerodynamic performance of a downstream object. Flow with an oscillating cylinder placed upstream is systematically studied because there are multiple control parameters that influence the flow dynamics around the downstream object. These control parameters are used as the input factors of a back-propagation neural network, and then a revised genetic algorithm is applied to find the optimal set of control parameters. In the current study, we use an airfoil in a low-Reynolds-number flow as an example to investigate the proposed neural network flow optimization concept. The datasets used to train the neural network are from the computational simulation with a previously validated immerse-boundary method to accommodate the motion of the cylinder. The results show that by optimally placing an upstream moving cylinder, it is possible to enhance the aerodynamic performance of the downstream object. Compared to the reference case, the optimized lift/drag ratio of the downstream airfoil can be achieved 2.4 times of its reference value, while maintaining a relatively high lift coefficient.

A Trade-off between User-Equilibrium and System Optimal Traffic Assignments for Congestion Mitigation in City Networks

Major cities worldwide are plagued by severe traffic congestion during peak periods. Traffic routing to utilise unused link capacities is a good strategy to reduce congestion and increase network performance. A multi-objective optimization model that seeks a via-media solution between System Optimal (SO) and User Equilibrium (UE) network flows while ensuring better utilization of the excess capacities available in the network is proposed. The number of paths between the O-D pairs is restricted to eliminate paths with long travel times and a constraint on Total System Travel Time (TSTT) is introduced. The proposed problem is solved using the weighted average method to determine Pareto optimal solutions. It is found that restricting the flow to only four paths resulted in a TSTT value that is only marginally higher (1.4%) than the SO model. When evaluated against the UE and SO models, the proposed model significantly improved the link capacity utilization (up to 73%) on some of the links. Additionally, the travel times improved by up to 30% on some paths, compared to the UE model. Although certain paths have longer travel times, the TSTT of Pareto front points is less than or equivalent to the UE model. Thus, the model yields a better distribution of flow in the network and is found to be superior to the existing models. Such a model can potentially contribute to sustainability, safety, and better management of transportation infrastructure.

Shuttle Bus Rerouting and Rescheduling Problem considering Daily Demand Fluctuation

In an urban shuttle system, shuttle buses need to pick up passengers waiting at predetermined stops according to their planned schedules (routes and timetables). However, in practice, passenger demand is unstable and has fluctuations, which means that passenger demand at a specific stop is likely to increase or decrease, causing low service quality, long passenger waiting times, and imbalanced utilization of bus capacity. Therefore, we introduce the shuttle bus rerouting and rescheduling strategy, based on which the operator can change the visited stops and arrival times of the shuttle buses and can operate backup buses to handle the passenger demand fluctuations. A three-dimensional space-time-state network is formulated to depict shuttle routes, timetables, and passenger-loading states, and the proposed problem can be formulated as a multicommodity network-flow optimization problem. To solve the model efficiently, we adopt the alternating direction method of multipliers (ADMM) decomposition method to decompose the original problem into several single shuttle routing subproblems. We test the model and algorithm in the 9-node network with three stops, and a larger scale Chicago sketch network is also adopted to demonstrate the effectiveness and efficiency of the proposed model and algorithm. The rerouting and rescheduling results for the Chicago case represent a 5.7% improvement relative to the results with the planned schedules.

A Decision Support System to Enhance Electricity Grid Resilience against Flooding Disasters

In different areas across the U.S., there are utility poles and other critical infrastructure that are vulnerable to flooding damage. The goal of this multidisciplinary research is to assess and minimize the probability of utility pole failure through conventional hydrological, hydrostatic, and geotechnical calculations embedded to a unique mixed integer linear programming (MILP) optimization framework. Once the flow rates that cause utility pole overturn are determined, the most cost-efficient subterranean pipe network configuration can be created that will allow for flood waters to be redirected from vulnerable infrastructure elements. The optimization framework was simulated using the Julia scientific programming language, for which the JuMP interface and Gurobi solver package were employed to solve a minimum cost network flow objective function given the numerous decision variables and constraints across the network. We implemented our optimization framework in three different watersheds across the U.S. These watersheds are located near Whittier, NC; Leadville, CO; and London, AR. The implementation of a minimum cost network flow optimization model within these watersheds produced results demonstrating that the necessary amount of flood waters could be conveyed away from utility poles to prevent failure by flooding.

Drawing the Highways in the Sky for Urban Air Mobility Operations

Urban air mobility (UAM) is a new mode of intracity transportation that promises to free commuters of ground congestion by providing air-taxi services within dense metropolitan environments. The introduction of UAM operations into the airspace, however, brings challenges related to the efficient and equitable management of UAM air traffic, particularly with regard to trajectory assignment and optimization. Near-term UAM missions are anticipated to operate within structured airspace corridors, leading to the interesting problem of corridor formation. In this paper, we describe a minimum-cost, network flow optimization framework that provides global optimal corridors for a given set of origin-destination pairs, subject to airspace metrics such as airspace density, complexity, and flexibility. The framework is applied to both small-scale scenarios that demonstrate the behavior of the framework and a full-scale scenario representative of the Atlanta metropolitan area. This work contributes to understanding how to effectively integrate UAM into the airspace.

Customized bus scheme design of large transport terminals with jointly optimization of departure time, vehicle allocation and routing

The customized bus (CB) service of large transport terminals can provide passengers with convenient transfers and door-to-door services, which has the potential to help ease the pressure of arriving passenger flow in large transport terminals. Considering the costs of operators and passengers, this paper establishes a multi-commodity network flow optimization model to simultaneously obtain departure schedule, passenger-to-vehicle assignment and routing under the condition of multiple vehicle types. It provides more passengers with high-quality CB service and obtains higher vehicle capacity utilization. Accordingly, the solution is proposed that combines a branch-and-cut algorithm with grid-density-based clustering. An illustrative example verifies the effectiveness and tests the impact of the departure time-window. The case study of Chengdu city compares the results under different types of vehicle schemes and conducts the sensitivity analysis of penalty and minimum load ratio. The experiments conclude: (i) The proposed algorithm stably improves computation speed (76.38%) without affecting the optimal results; (ii) a loose time-window can serve more people, but the excessively loose one no longer has impacts on the results. (iii) The multi-type of vehicle scheme performs best compared to the single type of vehicle schemes.

A dynamic scheduling process and methodology using route deviations and synchronized passenger transfers for flexible feeder transit services

The general lack of first/last mile connectivity is one of the main challenges encountered by intercity transport systems. New transportation alternatives called flexible transit systems, which combine on-demand service adjustment capabilities to the regular route and master schedule characteristics of the conventional transit, are therefore increasingly proposed. Feeder transit services can run as one type of flexible transit services, connecting a service area to a major intercity transport network through a transfer hub. Considering the unstable and constantly changing characteristics of daily passenger demand, a dynamic scheduling methodology for feeder transit services is proposed to minimize passenger crowding in vehicles. Deviations in the base route are allowed for accommodating optional requests or visiting potential transfer locations, which further offer a new type of flexible scheduling operation called synchronized passenger transfer. Operators can dynamically expand the spatial coverage of vehicles out of their regular routes to meet each other at appointed locations and times. Then, passengers can transfer between vehicles to minimize or even avoid passenger crowding. In this study, a multi-commodity network flow optimization model with side constraints in a three-dimensional space–time–state network is proposed for this type of dynamic scheduling problem. Additionally, a coordinate descent-based solution framework consisting of three steps (augmentation, decomposition, and linearization) is developed. The proposed model and solution approach are investigated using an eight-node simple network and the Sioux-Falls network, and the Chicago sketch network was adopted to demonstrate the practicability of the proposed model.

Integrated electric logistics vehicle recharging station location–routing problem with mixed backhauls and recharging strategies

The widespread application of electric vehicles for city last-mile logistics has been enhanced by the emerging trend of urban sustainable mobility, which intends to reduce vehicle emissions and the dependence on fossil fuels. The recharging facility location is critical for electric logistics network planning, because it significantly affects future operation costs and efficiency. This study proposes an integrated electric logistics vehicle recharging station location–routing problem with mixed backhauls and recharging strategies, which is formulated as a time-discretized multicommodity network flow optimization model based on a space–time–state–energy representation network. This study aims to optimize the selection of the recharging station location considering route planning with complicated constraints of recharging capacity, facility construction budget, vehicle loading capacity, battery remaining capacity, spatial structure of real road networks, mixed pickup and delivery requests, and service time windows. A hybrid Lagrangian relaxation and alternating direction method of multipliers (LR-ADMM) decomposition solution framework is constructed to decouple the proposed integrated problem into a recharging station location problem for strategic planning and an electric vehicle routing problem with mixed backhauls, time windows, and recharging strategies for operational decisions. These two subproblems are solved alternately by time-dependent forward dynamic programming algorithms embedded into the LR-ADMM framework. The solution quality is guaranteed by calculating the optimality gap between the best lower and upper bounds for each iteration. The experimental results based on the Sioux-Falls network and real-world West Jordan network prove the computational effectiveness and optimization quality of the proposed solution approach.