Generalized Network Flow Research Articles

Features of Network Flow Systems for Decision Making with Motivation Accounting

The present work investigates the problem of considering the influence of motivation in discrete network flow decision-making systems. Motivation is the primary factor that drives people to achieve their goals and plays a key role in decision-making systems. A method is proposed by which this influence is accounted for using the arc flow function amplification or attenuation coefficients. These operations are in the class of generalized network flows (flows with gains and losses). Methods to determine both the maximal and minimal value of the generalized network flow with consideration of the motivation are proposed A numerical example of a decision-making system based on a generalized network flow with motivation accounting is described, which confirms the obtained theoretical results.

Maximal Generalized Network Flow Accounting for Motivation

Maximal Generalized Network Flow Accounting for Motivation

Fast and Secure Routing Algorithms for Quantum Key Distribution Networks

We investigate the problem of fast and secure packet routing in multi-hop Quantum Key Distribution (QKD) networks. We consider a practical trusted-node setup where a QKD protocol randomly generates symmetric private key pairs over each QKD-enabled link in a network. Packets are first encrypted with the available quantum keys and then transmitted on a point-to-point basis. A fundamental problem in this setting is the design of a secure and capacity-achieving routing policy that takes into account the time-varying availability of the encryption keys and diverse physical-layer link capacities. To address this problem, we propose a new secure throughput-optimal policy called Tandem Queue Decomposition (TQD). The TQD policy is designed by incorporating the QKD process into the Universal Max Weight (UMW) routing policy. We show that the TQD policy achieves the entire secure capacity region for a broad class of traffic, including unicast, broadcast, multicast, and anycast. The TQD policy operates by reducing the problem to the generalized network flow problem without the key availability constraints over a transformed network. The throughput-optimality of the TQD policy is established using the Lyapunov stability theory by carefully analyzing the interdependent queueing process and the key-storage dynamics. Finally, we demonstrate the practical efficiency of the TQD policy over the existing routing algorithms by numerically comparing their performance on a realistic simulator built on top of the state-of-the-art OMNeT++ network simulator platform.

Decentralized Control of Distributed Cloud Networks With Generalized Network Flows

Emerging distributed cloud architectures, e.g., fog and mobile edge computing, are playing an increasingly important role in the efficient delivery of real-time stream-processing applications (also referred to as augmented information services), such as industrial automation and metaverse experiences (e.g., extended reality, immersive gaming). While such applications require processed streams to be shared and simultaneously consumed by multiple users/devices, existing technologies lack efficient mechanisms to deal with their inherent multicast nature, leading to unnecessary traffic redundancy and network congestion. In this paper, we establish a unified framework for distributed cloud network control with generalized (mixed-cast) traffic flows that allows optimizing the distributed execution of the required packet processing, forwarding, and replication operations. We first characterize the enlarged multicast network stability region under the new control framework (with respect to its unicast counterpart). We then design a novel queuing system that allows scheduling data packets according to their current destination sets, and leverage Lyapunov drift-plus-penalty control theory to develop the first fully decentralized, throughput- and cost-optimal algorithm for multicast flow control. Numerical experiments validate analytical results and demonstrate the performance gain of the proposed design over existing network control policies.

An analytical solution to the multicommodity network flow problem with weighted random routing

We derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the non-uniform multicommodity flow problem under weighted random routing. We show the mean load at each node, net of its demand and normalized by its (weighted) degree, is a constant equal to the trace of the product of two matrices: the Laplacian of the demand matrix and the generalized inverse of the graph Laplacian. For the case of uniform demand, this constant reduces to the sum of the inverses of the non-zero eigenvalues of the graph Laplacian. We note that such a closed-form expression for the network capacity for the general multicommodity network flow problem has not been reported before, and even though (weighted) random routing is not a practical procedure, it enables us to derive a (tight) upper bound for the capacity of the network under more standard routing policies. Using this new expression, we compute network capacity for a sample of demand matrices for some prototypical networks, including uniform demand (one unit between all node pairs) and broadcast demand (one unit between a source node and each other node as destination), and finally derive estimates of the mean load in some asymptotic cases.

Feasible Bases for a Polytope Related to the Hamilton Cycle Problem

We study a certain polytope depending on a graph G and a parameter β ∈ (0,1) that arises from embedding the Hamiltonian cycle problem in a discounted Markov decision process. Literature suggests a conjecture a lower bound on the proportion of feasible bases corresponding to Hamiltonian cycles in the set of all feasible bases. We make progress toward a proof of the conjecture by proving results about the structure of feasible bases. In particular, we prove three main results: (1) the set of feasible bases is independent of the parameter β when the parameter is close to one, (2) the polytope can be interpreted as a generalized network flow polytope, and (3) we deduce a combinatorial interpretation of the feasible bases. We also provide a full characterization for a special class of feasible bases, and we apply this to provide some computational support for the conjecture.

Maximizing positive influence in competitive social networks: A trust-based solution

Online social networks provide convenience for users to propagate ideas, products, opinions, and many other items that compete with different items for influence spread. How to accurately model the spread of competitive influence is still a challenging problem. Almost all reported methods ignore the effect of trust relationships in the spread of competitive influence. Maximizing competitive influence aims to detect the top-k positive or negative influential users in social networks with competing cascades. However, finding an optimal solution to this problem is NP-hard. This study focuses on exploring the above three issues by devising a trust-based solution. First, we established a new model of trust-based competitive influence diffusion that simulates the spread of positive and negative influence. Second, we estimated trust values via generalized network flows and used these values to calculate influence probabilities. Finally, we developed an efficient algorithm of trust-based competitive influence maximization through a heuristic pruning method. Extensive comparisons have been conducted on synthetic and real-world datasets. The effectiveness and efficiency of our approach are verified by analyzing the spread of competitive influence and the time complexity of detecting seed sets. Moreover, our approach is more practical than other baselines on real-world social networks.

Optimal spatial data matching for conflation: A network flow‐based approach

AbstractSpatial data conflation involves the matching and merging of counterpart features in multiple datasets. It has applications in practical spatial analysis in a variety of fields. Conceptually, the feature‐matching problem can be viewed as an optimization problem of seeking a match plan that minimizes the total discrepancy between datasets. In this article, we propose a powerful yet efficient optimization model for feature matching based on the classic network flow problem in operations research. We begin with a review of the existing optimization‐based methods and point out limitations of current models. We then demonstrate how to utilize the structure of the network‐flow model to approach the feature‐matching problem, as well as the important factors for designing optimization‐based conflation models. The proposed model can be solved by general linear programming solvers or network flow solvers. Due to the network flow formulation we adopt, the proposed model can be solved in polynomial time. Computational experiments show that the proposed model significantly outperforms existing optimization‐based conflation models. We conclude with a summary of findings and point out directions of future research.

Generalized Dynamic Flow on Lossy Network

Despite of implicit flow conservation on every arc of traditional network flow model, the generalized network flow model assumes the proportional and symmetric loss factor on each arc. This paper considers two terminal lossy networks specifying the portion of flow entering an arc at its tail node that reaches to its head node. We studied the generalized maximum continuous dynamic contraflow (GMCDCF) and generalized continuous earliest arrival contraflow (GCEACF) problems. The problems are efficiently solved with pseudo-polynomial time algorithms. Moreover, a fully polynomial time approximation scheme (FPTAS) is proposed in polynomial time.

Multi-warehouse package consolidation for split orders in online retailing

With the rapid growth of the online market in recent years, order splitting has become a great challenge to online retailers for fulfilling multi-item orders in a multi-warehouse storage network. Order splitting can lead to higher shipping costs, the use of more packages, and possible dissatisfaction from customers. This paper presents a multi-warehouse package consolidation approach aimed at consolidating multiple suborders’ stock-keeping units (SKUs) through transshipments among warehouses. A combined multi-commodity network flow model is proposed to determine the consolidation warehouses for each order and make transshipment decisions for individual SKUs. An enhanced logic-based Benders’ decomposition algorithm is proposed to decompose the model into a general multi-commodity network flow master problem and a set of bin packing with conflicts sub-problems. Two proposed Benders’ cuts guarantee the algorithm to converge to optimality. The proposed algorithm can generate the near-optimal result with only about 25% of the CPU time required by CPLEX to solve the proposed model. Numerical experiments reveal that the proposed package consolidation approach outperforms the order splitting fulfillment approach in reducing the total costs, the number of packages, and the delivery times, especially for cases with a small number of SKUs in each suborder which are typical for online retailers. Sensitivity analyses are performed to provide managerial insights of adopting the proposed approach in the real world where order splitting is a common phenomenon.

Evaluating National Multi-energy System Based on General Modeling Method

This paper uses an integrated evaluation framework to evaluate the possible national multi-energy flow in China in a near future. The framework includes an integrated modeling for national multi-energy system in China. These key and bone national energy facilities are all modeled in a generalized network flow formulation. The modeling considers the regional energy system, inter-regional power and natural gas transmission system and the district supply heat model. Specific modeling method is abstracted as some general modeling rules to tackle the difficulty of modeling so many different energy facilities through focus on the input energy flow and output energy flow of them. In addition, it also contains a short-term or mid-term (1~3 years) operation evaluation model based on the least socio-economic cost or national energy resource adequacy. The model is proposed to find the potential of Chinese bone national energy system in an integrated multi-energy perspective and to evaluate the impact of a short-term or mid-term national energy policy in technical way considering the coupling of different energy sub-systems. Although it is difficult to verify the national energy model, the open and known energy data of China in 2016 is used to verify the model. Then this model is employed to evaluate the China multi-energy system in 2020 to give some suggestions on the optimization of energy flow at the national scale and supply heat transition.

Material Flow Optimization with The Application of Generalized Network Flow Model

Abstract It is essential for every company to know their business processes well, because these companies must allocate their resources in an efficient way in order to keep or strengthen their market position. During the research we aimed at optimizing the material flow at a wooden box producer company with the use of the generalized network flow model as this model is widely used for modelling production processes. In the first part of our work we calculated the optimal material flows focusing on two objectives, and in the second part we determined a compromise solution. Finally, we compared and evaluated the results of the three models.

Optimal Control for Generalized Network-Flow Problems

We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast, and anycast traffic, in an arbitrary wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the problem efficiently. To the best of our knowledge, UMW is the first known throughput-optimal policy of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues . When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast with the well-known throughput-optimal back-pressure (BP) policy which allows for packet cycling, resulting in excessive latency. Extensive simulation results show that the proposed UMW policy incurs a substantially smaller delay as compared with the BP policy. The proof of throughput-optimality of the UMW policy combines ideas from the stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.

Convexification of generalized network flow problem

This paper is concerned with the minimum-cost flow problem over an arbitrary flow network. In this problem, each node is associated with some possibly unknown injection and each line has two unknown flows at its ends that are related to each other via a nonlinear function. Moreover, all injections and flows must satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which is shown to always obtain globally optimal injections. This relaxation may fail to find optimal flows because the mapping from injections to flows is not unique in general. We show that the proposed relaxation, named convexified GNF (CGNF), obtains a globally optimal flow vector if the optimal injection vector is a Pareto point. More generally, the network can be decomposed into two subgraphs such that the lines between the subgraphs are congested at optimality and that CGNF finds correct optimal flows over all lines of one of these subgraphs. We also fully characterize the set of all globally optimal flow vectors, based on the optimal injection vector found via CGNF. In particular, we show that this solution set is a subset of the boundary of a convex set, and may include an exponential number of disconnected components. A primary application of this work is in optimization over electrical power networks.

Trust Evaluation in Online Social Networks Using Generalized Network Flow

In online social networks (OSNs), to evaluate trust from one user to another indirectly connected user, the trust evidence in the trusted paths (i.e., paths built through intermediate trustful users) should be carefully treated. Some paths may overlap with each other, leading to a unique challenge of path dependence , i.e., how to aggregate the trust values of multiple dependent trusted paths. OSNs bear the characteristic of high clustering, which makes the path dependence phenomenon common. Another challenge is trust decay through propagation, i.e., how to propagate trust along a trusted path, considering the possible decay in each node. We analyze the similarity between trust propagation and network flow, and convert a trust evaluation task with path dependence and trust decay into a generalized network flow problem. We propose a modified flow-based trust evaluation scheme GFTrust , in which we address path dependence using network flow, and model trust decay with the leakage associated with each node. Experimental results, with the real social network data sets of Epinions and Advogato, demonstrate that GFTrust can predict trust in OSNs with a high accuracy, and verify its preferable properties.

Energy-Saving Generation Dispatch Using Minimum Cost Flow

This study uses a minimum cost flow method to solve a dispatch problem in order to minimize the consumption of coal in the dispatching of a thermal power system. Low-carbon generation dispatching is also considered here since the scheduling results are consistent with energy-saving generation dispatch. Additionally, this study employs minimum coal consumption as an objective function in considering the output constraints, load balance constraints, line loss, ramp rate limits, spinning reverse needs, prohibited operating zone requirements, security constraints, and other common constraints. The minimum cost flow problem, considering the loss of network flow, is known as a generalized network flow problem, which can be expressed as a quadratic programming problem in mathematics. Accordingly, the objective function was solved by LINGO11, which was used to calculate a network in a single time; a continuous period dispatch plan was obtained by accumulating each period network flow together. This analysis proves it feasible to solve a minimal cost flow problem with LINGO11. Theoretical analysis and numerical results prove the correctness and effectiveness of the proposed method.

Concave Generalized Flows with Applications to Market Equilibria

We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper [Truemper K (1978) Optimal flows in nonlinear gain networks. Networks 8(1):17–36] and by Shigeno [Shigeno M (2006) Maximum network flows with concave gains. Math. Programming 107(3):439–459]. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an ε-approximate solution in O(m(mσ+log n)log(MUm/ε)) arithmetic operations, where M and U are upper bounds on simple parameters, and σ is the complexity of a value oracle query for the gain functions. This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg et al. [Goldberg AV, Plotkin SA, Tardos É (1991) Combinatorial algorithms for the generalized circulation problem. Math. Oper. Res. 16(2):351–381], not using any cycle cancellations. We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately provides combinatorial algorithms for various extensions of these market models. This includes nonsymmetric Arrow-Debreu Nash bargaining, settling an open question by Vazirani [Vazirani VV (2012) The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game. J. ACM 59(2), Article 7].

A generalized network flow model for the multi-mode resource-constrained project scheduling problem with discounted cash flows

An effective project schedule is essential for enterprises to increase their efficiency of project execution, to maximize profit, and to minimize wastage of resources. Heuristic algorithms have been developed to efficiently solve the complicated multi-mode resource-constrained project scheduling problem with discounted cash flows (MRCPSPDCF) that characterize real problems. However, the solutions obtained in past studies have been approximate and are difficult to evaluate in terms of optimality. In this study, a generalized network flow model, embedded in a time–precedence network, is proposed to formulate the MRCPSPDCF with the payment at activity completion times. Mathematically, the model is formulated as an integer network flow problem with side constraints, which can be efficiently solved for optimality, using existing mathematical programming software. To evaluate the model performance, numerical tests are performed. The test results indicate that the model could be a useful planning tool for project scheduling in the real world.

Multichannel cooperative sensing for cognitive radio with users owning heterogeneous sensing ability

SUMMARYMultichannel cooperative sensing (MCS) is an effective method for dynamic spectrum access in cognitive radio networks. In contrast to most existing work on MCS that considered secondary users with homogeneous sensing ability, this paper studies the MCS problem for secondary users with heterogeneous sensing ability in terms of sensing accuracy. We further take into account different parameters of primary channels such as bandwidth, probability of being idle in each sensing period, and frequency selective fading at the sensing receiver. The MCS problem is formulated as a weapon target assignment problem, where more sensing resources are assigned to channels that are more valuable. This weapon target assignment problem is transformed to an integer generalized network flow problem with convex flow costs to obtain the lower bound solution, and then solved by the branch and bound algorithm with this bound to yield the exact scheme. To reduce computational complexity, a heuristic scheme is also proposed, which has approximate performance compared with the exact scheme. Finally, extensive simulation results for different scenarios illustrate the performance improvements of the proposed schemes over the existing scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Economic Modeling of Compressed Air Energy Storage

Due to the variable nature of wind resources, the increasing penetration level of wind power will have a significant impact on the operation and planning of the electric power system. Energy storage systems are considered an effective way to compensate for the variability of wind generation. This paper presents a detailed production cost simulation model to evaluate the economic value of compressed air energy storage (CAES) in systems with large-scale wind power generation. The co-optimization of energy and ancillary services markets is implemented in order to analyze the impacts of CAES, not only on energy supply, but also on system operating reserves. Both hourly and 5-minute simulations are considered to capture the economic performance of CAES in the day-ahead (DA) and real-time (RT) markets. The generalized network flow formulation is used to model the characteristics of CAES in detail. The proposed model is applied on a modified IEEE 24-bus reliability test system. The numerical example shows that besides the economic benefits gained through energy arbitrage in the DA market, CAES can also generate significant profits by providing reserves, compensating for wind forecast errors and intra-hour fluctuation, and participating in the RT market.