Network Flow Approach Research Articles

A network flow approach to a common generalization of Clar and Fries numbers

Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. First, we introduce a common generalization of these two concepts for bipartite plane graphs, and then we extend it further to the notion of source-sink pairs of subsets of nodes in a general (not necessarily planar) directed graph. The main result is a min-max formula for the maximum weight of a source-sink pair. The proof is based on the recognition that the convex hull of source-sink pairs can be obtained as the projection of a network tension polyhedron. The construction makes it possible to apply any standard cheapest network flow algorithm to compute both a maximum weight source-sink pair and a minimizer of the dual optimization problem formulated in the min-max theorem. As a consequence, our approach gives rise to the first purely combinatorial, strongly polynomial algorithm to compute a largest (or even a maximum weight) Fries-set of a perfectly matchable plane bipartite graph and an optimal solution to the dual minimization problem.

Towards efficient waste management: identification of waste flow chains in micro-regional detail through monitored data

AbstractCountries around the world are gradually implementing the transition to a circular economy in waste management. This effort should be initiated already at the waste producers. It is necessary to plan and monitor waste management in as much detail as possible, i.e. at the level of micro-regions. At present, only indicators at the national level are analysed, as more detailed data at the micro-regional level are often not available or are burdened with significant errors and inconsistencies. The calculation of waste management indicators for micro-regions will allow to identify the potential for increasing material or energy recovery and to plan the necessary infrastructure directly to these locations instead of blanket and often ineffective legislative actions. This paper presents an approach for determining the producer-treatment linkage, i.e., provides information about each produced waste, where it was treated, and in what way. Such information is often not available based on historical waste management data as there are repeated waste transfers and often aggregated within a micro-region. The network flow approach is based on an iterative procedure combining a simulation with multi-criteria optimization. The chosen criteria replicate expert estimates in investigated issue such as minimum flow splitting, and minimum transfer micro-regions. A data reconciliation is performed where the deviation from all simulations is minimized, given that the capacity constraints of nodes and arcs resulting from the database must be satisfied. The approach is tested on a generated sample task to evaluate the precision and time complexity of the developed tool. Finally, the presented approach is applied to address a case study in the Czech Republic, within which it is possible to identify treatment location and methods for waste from individual regions.

Optimizing fire emergency evacuation routes in underground coal mines: A lightweight network flow approach

In underground mine fires, the presence of smoke, toxic gasses, and high heat can significantly hinder the evacuees from identifying the optimal path to safety. This study presents a framework that couples a mine fire simulator software with a Ford-Fulkerson algorithm to model fire evacuations as a minimum-cost flow problem. The fire-induced risks are quantified based on the MSHA safety standards and a user-friendly FFA computes the evacuation routes. By accumulating the quantified effect of the risk exposure and updating the network depending on the mine conditions, different safe evacuation routes are identified. The algorithm is demonstrated through fire simulation data acquired from a model of the VentSim™ DESIGN software. Airflow quantity, air quality, heat, carbon monoxide concentration, and visibility obstruction are acquired from the simulations and processed through the proposed algorithm. Based on the distribution of the quantified hazards and the MSHA safety standards, the algorithm outputs optimal evacuation paths. The computed evacuation routes minimize the exposure to the fire-induced hazards while at the same time prioritize the shortest routes. The presented framework can be used for evaluating ventilation designs and emergency plans as well as in real-time self-evacuation in mine emergencies.

Truthful and Optimal Data Preservation in Base Station-less Sensor Networks: An Integrated Game Theory and Network Flow Approach

We aim to preserve a large amount of data generated inside base station-less sensor networks (BSNs) while considering that sensor nodes are selfish. BSNs refer to emerging sensing applications deployed in challenging and inhospitable environments (e.g., underwater exploration); as such, there do not exist data-collecting base stations in the BSN to collect the data. Consequently, the generated data has to be stored inside the BSN before uploading opportunities become available. Our goal is to preserve the data inside the BSN with minimum energy cost by incentivizing the storage- and energy-constrained sensor nodes to participate in the data preservation process. We refer to the problem as DPP: d ata p reservation p roblem in the BSN. Previous research assumes that all the sensor nodes are cooperative and that sensors have infinite battery power and design a minimum-cost flow-based data preservation solution. However, in a distributed setting and under different control, the resource-constrained sensor nodes could behave selfishly only to conserve their resources and maximize their benefit. In this article, we first solve DPP by designing an integer linear programming (ILP)-based optimal solution without considering selfishness. We then establish a game-theoretical framework that achieves provably truthful and optimal data preservation in BSNs. For a special case of DPP wherein nodes are not energy-constrained, referred to as DPP-W, we design a data preservation game DPG-1 that integrates algorithmic mechanism design (AMD) and a more efficient minimum cost flow-based data preservation solution. We show that DPG-1 yields dominant strategies for sensor nodes and delivers truthful and optimal data preservation. For the general case of DPP (wherein nodes are energy-constrained), however, DPG-1 fails to achieve truthful and optimal data preservation. Utilizing packet-level flow observation of sensor node behaviors computed by minimum cost flow and ILP, we uncover the cause of the failure of the DPG-1. It is due to the packet dropping by the selfish nodes that manipulate the AMD technique. We then design a data preservation game DPG-2 for DPP that traces and punishes manipulative nodes in the BSN. We show that DPG-2 delivers dominant strategies for truth-telling nodes and achieves provably optimal data preservation with cheat-proof guarantees. Via extensive simulations under different network parameters and dynamics, we show that our games achieve system-wide data preservation solutions with optimal energy cost while enforcing truth-telling of sensor nodes about their private cost types. One salient feature of our work is its integrated game theory and network flows approach. With the observation of flow level sensor node behaviors provided by the network flows, our proposed games can synthesize “microscopic” (i.e., selfish and local) behaviors of sensor nodes and yield targeted “macroscopic” (i.e., optimal and global) network performance of data preservation in the BSN.

A Network Flow Approach to Battery Electric Bus Scheduling

A major challenge to adopting battery electric buses into bus fleets is the scheduling of the battery charging while considering route timing constraints and battery charge. This work develops a scheduling framework to balance the use of slow and fast chargers assuming the bus routes and charger locations are fixed. Slow chargers are utilized when possible to lower the cost of charging and fast chargers are used when needed to meet timing constraints and to ensure a sufficient charge for route execution. A directed graph is used to model the available charge times for buses that periodically return to the station to pick up passengers and to recharge its battery. A constrained network flow Mixed-Integer Linear Program (MILP) problem is formulated to optimize the scheduling of chargers as well as to determine the number of chargers required to meet battery state of charge thresholds. Using a randomly generated route schedule for thirty buses, results are presented that demonstrate the ability of the proposed method to find optimal charging plans while considering time-of-use (TOU) costs and allowing for fixed and variable numbers of chargers. These optimal charging plans reduce costs up to 20.9% compared to a thresholding-based plan and up to 12.3% compared to an optimal strategy that does not consider the TOU costs.

Feasible joint posterior beliefs with binary signals

We extend a quantitative Aumann’s agreement theorem in Arieli et al. (2021) from binary states to arbitrary finite states and provide a complete characterization of feasible joint posteriors beliefs when beliefs supports are binary. Using a network flow approach, we show that the martingale condition and the cut condition for a feasible flow are necessary and sufficient for feasible joint posterior beliefs. For symmetric supports, we show that the cut condition implies that the posteriors beliefs must be positively dependent. We also relate the cut condition to various characterization conditions in the literature.

Network flow and flood routing model for water resources optimization

Real-time management of hydraulic systems composed of multi-reservoir involves conflicting objectives. Its representation requires complex variables to consider all the systems dynamics. Interfacing simulation model with optimization algorithm permits to integrate flow routing into reservoir operation decisions and consists in solving separately hydraulic and operational constraints, but it requires that the water resource management model is based on an evolutionary algorithm. Considering channel routing in optimization algorithm can be done using conceptual models such as the Muskingum model. However, the structure of algorithms based on a network flow approach, inhibits the integration of the Muskingum model in the approach formulation. In this work, a flood routing model, corresponding to a singular form of the Muskingum model, constructed as a network flow is proposed and integrated into the water management optimization. A genetic algorithm is involved for the calibration of the model. The proposed flood routing model was applied on the standard Wilson test and on a 40 km reach of the Arrats river (southwest of France). The results were compared with the results of the Muskingum model. Finally, operational results for a water resource management system including this model are illustrated on a rainfall event.

Dynamic group formation in an online social network

• Recommendations for forming small online groups must balance the needs of the host and potential members. • We present a framework of algorithms for making group recommendations in constantly changing problem sets. • We evaluate the framework using a simulated production environment. • We compare our framework’s approximations to an absolute optimal using network flow optimization. For those seeking to recruit teammates for a specific purpose, like a project or study group, challenges quickly arise once they have exhausted their social circle. In the wake of the current pandemic, meeting new people that are right for a specific team is even more difficult than before due to the lack of in-person events. On social media platforms, users often have large networks of connections but have very few close personal relationships within them. This makes it difficult to find compatible people that share the same goal, and are interested in niche groups on those platforms. We present a scalable framework for establishing small online groups that balance two objectives, making the best group recommendations to users and guiding group hosts to the best users for their group. We illustrate this framework using three use cases. Lastly, we evaluate a serverless implementation using a large social media dataset to simulate a production environment and compare our framework to a network flow approach to solving the problem.

A network flow approach for constellation planning

A graph-based network flow approach to constellation planning is presented that respects spacecraft resources and mission constraints to arrive at a preliminary operational schedule. The method discretizes task fulfillment opportunity windows into graph nodes and then adds edges based on feasibility of transition between these opportunities, either by slew maneuvers or extended-time task fulfillment during downlink operations. Intelligent graph pruning is applied to improve computation performance and provide a versatile planning capability with a minimal impact on the resulting solution. A network flow formulation allows for a simultaneous search for spacecraft plans using a Mixed Integer Linear Program (MILP). The framework enables the definition of appropriate mission constraints to ensure viability and mission efficiency among the constellation of satellites. The planning technique is demonstrated for a mission of 100 satellites to illustrate its capability and performance within this proliferated regime.

Competitive Equilibrium and Trading Networks: A Network Flow Approach

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

A parcel network flow approach for joint delivery networks using parcel lockers

Current courier networks in metropolitan areas are characterised by utilising fleets of vans that perform collection and distribution routes independently. This results in long stem distances, low load factors and high environmental costs. Joint delivery systems have the potential to reduce the distances of pick-up and drop-off routes. In this context, parcel lockers can be utilised to transfer goods between vans, electrical vehicles and bikes to improve the efficiency and sustainability of courier networks. This paper presents a model for designing joint delivery networks in urban areas by utilising parcel lockers. This model has a two-level structure: the lower level dealing with multi-depot capacitated vehicle routing problems (MDCVRP) for a set of depots and lockers whilst the upper level being a (minimum-cost) parcel network flow problem (PNFP) considering goods delivered between depots and lockers and the selection of lockers’ positions and sizes. A hybrid algorithm integrating a Genetic Algorithm with the Lin-Kernighan Heuristic has been developed. The GA focuses on finding solutions for the PNFP. Once the paths of parcel flow are determined, the LKH optimises vehicle flow. This paper is the first to consider the use of parcel lockers for business-to-business networks in the form of MDCVRP.

Design of level of service on facilities for crowd evacuation using genetic algorithm optimization

This paper introduces a novel technique to design the level of service (LOS) for facilities or sub spaces of buildings for the purpose of evacuation planning. LOS is a standard qualitative indicator used to describe flow characteristics in a pedestrian environment. Some evacuation planners use LOS to help determine the network parameters when solving evacuation planning problems by the network flow approach. However, there is currently limited research into the optimization of the LOS parameters themselves to construct more efficient evacuation networks. In this paper the authors used a genetic algorithm optimization approach to determine LOS for facilities to improve the evacuation performance of building networks. Each individual chromosome containing a LOS design represents a fully defined evacuation network that can be solved. The fitness of each network is measured by minimum clearance time, which is calculated by the Capacity Constrained Route Planner (CCRP) approach. A comparative computational test in a hypothetical three-story building shows that the evacuation network under the optimized LOS design has a roughly 11% less minimum clearance time compared to the network under the original LOS design. Sensitivity analysis is also included, focusing on how the population size and the building layout influence the LOS design. In addition, an additional computational test for a twelve-deck cruise ship shows that the approach is scalable to solve more complex evacuation networks. The proposed approach has the potential to provide better LOS assignments for facilities for the government officials to develop effective emergency management strategies.

An information network flow approach for measuring functional connectivity and predicting behavior.

IntroductionConnectome‐based predictive modeling (CPM) is a recently developed machine‐learning‐based framework to predict individual differences in behavior from functional brain connectivity (FC). In these models, FC was operationalized as Pearson's correlation between brain regions’ fMRI time courses. However, Pearson's correlation is limited since it only captures linear relationships. We developed a more generalized metric of FC based on information flow. This measure represents FC by abstracting the brain as a flow network of nodes that send bits of information to each other, where bits are quantified through an information theory statistic called transfer entropy.MethodsWith a sample of individuals performing a sustained attention task and resting during functional magnetic resonance imaging (fMRI) (n = 25), we use the CPM framework to build machine‐learning models that predict attention from FC patterns measured with information flow. Models trained on n − 1 participants’ task‐based patterns were applied to an unseen individual's resting‐state pattern to predict task performance. For further validation, we applied our model to two independent datasets that included resting‐state fMRI data and a measure of attention (Attention Network Task performance [n = 41] and stop‐signal task performance [n = 72]).ResultsOur model significantly predicted individual differences in attention task performance across three different datasets.ConclusionsInformation flow may be a useful complement to Pearson's correlation as a measure of FC because of its advantages for nonlinear analysis and network structure characterization.

A Network Flow Approach for Optimizing the Passenger Throughput at an Airport Security Checkpoint

This paper is intended to solve the checkpoint throughput optimization for an International Airport. We establish a network flow structure to analyze the bottleneck of the security system.After identifying the number of each person’s identity, the number of screening lanes, and the ratio of regular lanes to Precheck, we simulate the fluctuations of passenger flow, reduce the variance of waiting time and improve the passenger throughput process.

Flow based efficient data gathering in wireless sensor network using path-constrained mobile sink

In wireless sensor networks (WSNs), sensors are equipped with limited power batteries. Data collection from sensors is one of the fundamental tasks in WSNs. Maximizing the data collection with minimum energy consumption is one of the major challenging issues in WSNs. In this article, we consider data collection using a mobile sink, where the mobile sink efficiently collects data from nearby sensors while moving along a pre-specified path with constant speed. We refer this problem as a Maximizing Data Gathering with Minimum Energy Consumption (MDGMEC) problem. So far, existing works have heuristic algorithms for MDGMEC problem. Their solutions, being heuristic, could not ensure the optimality. In this article, we propose two efficient algorithms to improve the data gathering process. Our algorithms use network flow approach for efficient data forwarding. In the first proposed algorithm, the mobile sink can receive data from multiple nearby sensors simultaneously, while in the second, the mobile sink can receive data from only one nearby sensor at a time. The proposed algorithms run in polynomial time and are also scalable for large networks. We evaluate the proposed algorithms by implementing them in MATLAB. The obtained results show that our proposed schemes outperform other existing schemes in terms of collecting total data and energy efficiency.

Traffic Events Oriented Dynamic Traffic Assignment Model for Expressway Network: A Network Flow Approach

In this paper, we focus on the dynamic traffic assignment (DTA) problem on large-scale expressway networks especially under the condition of traffic events (such as severe weather, large traffic accidents etc.). We formulate the expressway network DTA problem as a nonconvex optimization problem. Considering the difficulty of solving the problem, we put forward an approximate solution algorithm based on the network flow theory with high computational efficiency and strong applicability. Specifically, a machine learning approach and a series of customization strategies of network flow model (including multi-origin and multidestination split, flow discretization and parallel edges addition methods) are proposed to transform the DTA problem into a resoluble network flow problem. After that, in order to improve the operational efficiency of an expressway network after traffic events occurring, the proposed network flow based two-layer DTA model (NTDM) is separated into two parts-traffic flow limitation model based on maximum flow algorithm and traffic assignment model based on minimum cost flow algorithm. Experiments on real expressway network data in some provinces of China show that our method can make a significant 26.03% reduction in saturation rate in a particular scenario. In efficiency test, the NTDM is at least 600 times faster than the traditional analytic method in a network with thousands of nodes.

Capacitated network-flow approach to the evacuation-location problem

Evacuating people to the safe zones is the most crucial operation in managing many disasters. A mathematical model is presented in this paper, combining locational decisions with the max-flow problem in order to select safe destinations which maximize the number of dispatched people. The existing frameworks for emergency logistics usually model the evacuation process based on fixed and pre-determined destinations with a strategic perspective. The unpredictable and turbulent nature of a disaster may; however, disrupt the predictions. Furthermore, the primary goal in emergency situations is to dispatch people from the danger zone to a safe place, no matter where. A mixed integer linear programming model is developed in this paper for selecting one or more destinations in a capacitated network. The special structure of the model and its similarity to the max-flow problem allow us to develop exact algorithms and heuristics both for the multiple and single destination location problem. The solution methods are based on existing algorithms for the max-flow problem. Our proposed heuristics use the idea of adding a super-sink to the network to generate upper bounds very fast. The exact algorithms as well as the heuristics are tested on randomly generated instances as well as a real world network. The most important statistics of their computation times are reported. They are also compared according to their performance (gap to optimality) and their behavior amongst different categories of the graphs. Finally we have presented a real-case addressing the problem of choosing a number of destination locations from a fixed set of pilot pre-determined locations. The problem of deciding on the destinations is considered under 5 grades of disaster severity and the related impacts on choosing the safe zones are analyzed.

An exact network flow formulation for cell‐based evacuation in urban areas

AbstractIn the literature two common macroscopic evacuation planning approaches exist: The dynamic network flow approach and the Cell–Transmission–Based approach. Both approaches have advantages and disadvantages. Many efficient solution approaches for the dynamic network flow approach exist so that realistic problem instances can be considered. However, the consideration of (more) realistic aspects (eg, density dependent travel times) results in non‐linear model formulations. The Cell‐Transmission‐Based approach on the other hand considers realistic traffic phenomena like shock waves and traffic congestion, but this approach leads to long computational times for realistic problem instances. In this article, we combine the advantages of both approaches: We consider a Cell‐Transmission‐Based Evacuation Planning Model (CTEPM) and present a network flow formulation that is equivalent to the cell‐based model. Thus, the computational costs of the CTEPM are enormously reduced due to the reformulation and the detailed representation of the traffic flow dynamics is maintained. We investigate the impacts of various evacuation scenario parameters on the evacuation performance and on the computational times in a computational study including 90 realistic instances.

The constrained-collaboration algorithm for intelligent resource distribution in supply networks

Manufacturing and supply strategies have evolved from the notion of mass production focusing on economies of scale, to flexible production systems seeking economies of scope, and recently, to the concept of enterprise and supply networks aiming for economies of collaboration. The emergence of supply networks poses new challenges derived from a growing complexity in coordinating the flow of resources, materials, and information within and among an increasing number of network participants. In such situations, an intelligent resource distribution under various constraints is one of the most critical problems. In this paper, we have developed a novel Constrained-Collaboration Algorithm (CCA) for physically cooperative resource distribution planning. Based on Collaborative Control Theory (CCT) with theoretical formulations and network flow approaches, the CCA addresses an efficient and effective resource distribution by a suitable form of physical cooperation. We have applied it to an actual industry case, in combination with Direct/Indirect Delivery Protocol (DIDP), introduced in previous research. As a result, the integrated model achieves 55% increase in resource utilization and 20% reduction in distribution cost, while accommodating external changes. Besides, the new formalism of the physical dimension of collaboration requirement planning introduced in this research with new CCA approach can be generalized for other improvements in supply-and-demand management decision support.

A time-space network flow approach to dynamic repositioning in bicycle sharing systems

Faced with increasing population density, rising traffic congestion, and the resulting upsurge in carbon emissions, several urban metropolitan areas have instituted public bicycle sharing system as a viable alternative mode of transportation to complement existing long-distance bus- and metro- transit systems. A pressing issue that needs to be addressed in bike sharing systems is the accrued imbalance of bicycles between commuter demands and inventory levels at stations. To overcome this issue, a commonly employed strategy is to reposition bicycles during off-peak periods (typically at night) when no new user arrivals are expected. However, when such an imbalance occurs during day-time peak hours, such a passive strategy would result in lower resource utilization rates. To overcome this drawback, in this study, we propose a dynamic bicycle repositioning methodology that considers inventory level forecasting, user arrivals forecasting, bicycle repositioning, and vehicle routing in a unified manner. A multi-commodity time-space network flow model is presented, which results in an underlying complex nonlinear optimization problem. This problem is then reformulated into an equivalent mixed-integer problem using a model transformation approach and a novel heuristic algorithm is proposed to efficiently solve this model. Specifically, the first stage involves solving the linear relaxation of the MIP model, and a set covering problem is subsequently solved in the second stage to assign routes to the repositioning vehicles. The proposed methodology is evaluated using standard test-bed instances from the literature, and our numerical results reveal that the heuristic algorithm can achieve a significant reduction in rejected user requests when compared to existing methods, while yet expending only minimal computational effort.