Minimum Cost Network Research Articles

Designing a multi-level reverse logistics network for waste batteries of electric vehicles under uncertainty—A case study in the Yangtze River Delta Urban Agglomerations of China

As a breakthrough for alleviating the impact of the energy crisis and improving the environment, the electric vehicle (EV) industry is entering a period of rapid development. The growth of this industry is expected to lead to a dramatic increase in the quantity of end-of-life EV traction batteries in the future, posing significant challenges to environmental pollution and the sustainable development of the EV industry. This study addresses the cascade utilization and uncertainties of waste batteries, by incorporating the development weight of the match degree between urban commercial environments and facility development, proposes a fuzzy chance constrained programming model for the design of multi-level reverse logistics network (RLN) for retired EV batteries. The objective is to minimize network costs and carbon emissions, determining optimal facility locations and transportation distribution schemes. The mathematical model is validated through a real case study in the Yangtze River Delta Urban Agglomerations in China, and sensitivity analysis is conducted to explore the impact of various influencing factors on network design. The results indicate that the development weight significantly influence facility location decisions, while the quantity and quality of battery recycling have a substantial impact on the operational quantities of network facilities at different levels.

Hydraulic-based optimization algorithm for the design of stormwater drainage networks

Stormwater drainage networks are designed to reduce the risk of rainwater damage to the served area. The purpose of optimizing a stormwater drainage system is to reduce overall construction costs and to meet hydraulic design requirements. Currently, designs that rely on software or manual calculations are limited by the available time and the designer’s capabilities. In fact, manual optimization for large networks consumes a lot of time and effort, and there is no guarantee that the optimal design is reached, also it is subject to human errors. In recent years, several researchers have focused on creating optimization design algorithms specifically for sewer and storm networks, such as genetic algorithm (GA), linear programming (LP), heuristic programming (HP),…etc. However, these studies were limited to covering one or two design parameters and constraints. Additionally, in some studies, the hydraulic performance of the designed network was not treated in a proper way, especially the water surface profile effects. So, the main objective of the study is to develop an effective hydraulic-based optimization algorithm (HBOA) that can dynamically get the optimal design with minimum total cost for a given storm network layout and meet all hydraulic requirements. To achieve this, a MATLAB code is created and coupled with SewerGEMS software that automatically simulates all expected optimization scenarios based on network hydraulic performance. The HBOA is validated economically and hydraulically using two benchmark examples from the literature. According to the economic validation, the total network cost generated by HBOA was the lowest when compared to the optimization methods found in the literature. During the hydraulic evaluation, it was observed that the optimization algorithm (GA-HP) used in the literature for the benchmark examples does not meet the hydraulic requirements where the networks are flooded, whereas HBOA meets the hydraulic requirements with minimal overall network cost. Also, the HBOA is applied to four real stormwater drainage networks that were already designed, constructed, and optimized manually. The four redesigned real cases using HBOA revealed a cost reduction of about 15% compared to the original designs, while consuming a few hours for the design and optimization processes. Finally, the developed HBOA is a robust, time-efficient, and cost-effective optimization and hydraulic design tool which could be used in the design of stormwater drainage networks with different design constraints with minimal human interference.

Optimizing service networks to support freight rail decarbonization: Flow selection, facility location, and energy sourcing

We present a framework to support decarbonization of energy intensive transportation systems offering periodic service on expansive networks (e.g., freight rail, trucking, and intercity bus services). The framework consists of two optimization problems that respectivelyaddress (i) flow selection and facility location, and (ii) energy sourcing/procurement at the service facilities to enable the selected flows. The framework generalizes mixed integer linear programming formulations for flow refueling facility location and flow-based set cover models appearing in the literature to situations where it is of interest to account for repositioning of assets along cyclical trajectories to allow for periodic service, and to account for intermediate flow capture (i.e., trip chaining). The framework also consists of a minimum cost network flow model to determine optimal energy sourcing and distribution strategies, which dictate capacity requirements at the service facilities. The energy demands are obtained from the solution to the flow selection and facility location model. To illustrate the framework, we analyze the deployment of charging stations to support battery-electric locomotive service on a subset of the US freight rail network (i.e., an aggregate network of 3 Class I Railroads). The results show that the deployment of 30 charging stations can support battery-electric locomotives (with 1600-km ranges) to serve 86% of distance-weighted flows (ton-km) and reduce emissions by approximately 50%.

Stochastic Resource Optimization for Wireless Powered Hybrid Coded Edge Computing Networks

With the ubiquitous sensing enabled by the Internet-of-Things (IoT), massive amount of data is generated every second, transforming the way we interact with the world. To manage big data and enable analytics at the edge of the network, large amount of computation power is required to perform the computation intensive tasks. However, the energy-constrained IoT devices are not able to perform the computation tasks without compromising the quality-of-service of the applications. In this paper, we propose a hybrid network in which users can fully offload their computation tasks to edge servers through coded edge offloading or perform local computation with the wireless power transfer derived from coalitions of unmanned aerial vehicles (UAVs) serving as mobile charging stations. To minimize the cost of the network, we consider a two-level optimization approach. At the lower level, an optimal UAV coalition that minimizes the network cost is formed. At the upper level, the computation approach for each user is decided while taking into account the stochastic nature of wireless charging efficiency. Given the interrelation between the two levels, we adopt the backward induction optimization strategy to jointly derive the optimal coalition structure and computation approach for each user. In the performance evaluation, we provide extensive sensitivity analyses to study the performance of the cost minimization approaches amid varying network parameters. Moreover, we show that our approach outperforms deterministic optimization approaches in network cost minimization.

Sustainable Placement with Cost Minimization in Wireless Digital Twin Networks

Sustainable Placement with Cost Minimization in Wireless Digital Twin Networks

Energy Cost Minimization in Wireless Rechargeable Sensor Networks

Mobile chargers (MCs) are usually dispatched to deliver energy to sensors in wireless rechargeable sensor networks (WRSNs) due to its flexibility and easy maintenance. This paper concerns the fundamental issue of charging path DEsign with the Minimized energy cOst (DEMO), i.e., given a set of rechargeable sensors, we appropriately design the MC’s charging path to minimize the energy cost which is due to the wireless charging and the MC’s movement, such that the different charging demand of each sensor is satisfied. Solving DEMO is NP-hard and involves handling the tradeoff between the charging efficiency and the moving cost. To address DEMO, we first investigate how to identify a single charging position where the MC could stay to charge a set of sensors distributed within a small area with the maximized charging efficiency. Then, based on the result obtained in the case of optimizing a single charging position, we develop a computational geometry-based algorithm to deploy multiple charging positions within the whole network, by considering the fixed and finite charging range of the MC. We prove that the designed algorithm has the approximation ratio of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\!\left(\ln\!N\right)$</tex-math> </inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> is the number of sensors. Then we construct the charging path by calculating the shortest Hamiltonian cycle passing through all the deployed charging positions within the network. In addition, we investigate the impact of the network topology as well as the distribution of charging demands among sensors on the MC’s energy cost during a charging tour. Extensive evaluations validate the superiority of our path design in terms of the MC’s energy cost minimization, compared with existing main algorithms.

Blockchain enabled task offloading based on edge cooperation in the digital twin vehicular edge network

The rapid development of the Internet of Vehicles (IoV) along with the emergence of intelligent applications have put forward higher requirements for massive task offloading. Even though Mobile Edge Computing (MEC) can diminish network transmission delay and ease network congestion, the constrained heterogeneous resources of a single edge server and the highly dynamic topology of vehicular edge networks may compromise the efficiency of task offloading, including latency and energy consumption. Vehicular edge networks are also vulnerable to malicious outside attacks. In this paper, we propose a new blockchain-enabled digital twin vehicular edge network (DTVEN) where digital twin (DT) is exploited to monitor network communication, computation, and caching (3C) resources management in real time to provide rich data for offloading decision-making, and blockchain is utilized to secure fair and decentralized offloading transactions among DTs. To ensure 3C resources sharing across edge servers, we design a DT-assisted edge cooperation scheme, which makes full use of edge resources in vehicular networks. Furthermore, a DT-based smart contract is built to achieve a quick and effective consensus process. Then, we apply a task offloading algorithm based on an improved cuckoo algorithm (ICA) and a resource allocation scheme based on greedy strategy to minimize network cost by comprehensively taking into account latency and energy consumption. Numerical results demonstrate that our proposed scheme outperforms the existing schemes in terms of network cost.

Variable Neighborhood Search Algorithm for the Single Assignment Incomplete Hub Location Problem with Modular Capacities and Direct Connections

In distribution systems such as airlines and express package delivery, the use of hub-and-spoke networks is common, and flow consolidation at hub facilities is essential for cost reduction. While a constant discount factor is typically used to model cost reduction in interhub links, this paper explores an extension of the incomplete hub location problem with modular capacity that enables direct connections between non-hub nodes. The modified approach, called MHLPDC, aims to locate a set of hub facilities, connect each non-hub node to a hub, and activate hub facility links, access arc links, and direct links between non-hub nodes to minimize network costs. The MHLPDC integrates link activation decisions into the decision-making process and utilizes modular arc costs to model the flow dependence of transportation costs in all arcs. To solve the problem, the paper presents a mixed-integer mathematical programming formulation and heuristic algorithm based on a greedy randomized adaptive search and variable neighborhood search approach. The proposed algorithm produces high-quality solutions, as demonstrated through computational experiments on benchmark instances with up to 40 nodes. Furthermore, a sensitivity analysis of the optimal network structure indicates that increasing the discount factor, by varying hub and access arc capacities as well as the associated variable costs, results in fewer hubs being established and more direct shipments between non-hub nodes being permitted.

Optimization of urban water pipe network design using fast-messy genetic algorithms (fmGA)

Abstract To have an efficient water distribution network, optimal design alternatives need to be identified and analysed using combined hydraulic modelling and optimization. This paper reports on the application of the fast-messy genetic algorithm (fmGA) coupled with hydraulic modelling tool EPANET to assess and select an optimum design and operational alternative for a water distribution pipe network. The sole objective of the optimization modelling was to minimize network costs subject to hydraulic and design constraints. The fmGA was first tested using the benchmark case study of the Hanoi network and then applied to the real network of Maun, Botswana which is considered as the case study. We have compared our results of the fmGA model application with other optimization techniques applied to the Hanoi network. The findings of the test revealed that the fmGA is superior to other popular metaheuristic optimization methods in terms of processing speed with comparable accuracy and pressure constraints fulfilled for all nodes. It also provides the best solution. For the water distribution network of Maun, the best pipeline configuration and route were determined, in which Configuration B is found to be the best and least cost solution to improve the water supply situation in Maun.

Scalable Computation of Dynamic Flow Problems via Multimarginal Graph-Structured Optimal Transport

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multicommodity minimum-cost network flow problem can be formulated as a multimarginal optimal transport problem, where the cost function and the constraints on the marginals are associated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy-regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities. Funding: This work was supported by KTH Digital Futures, Knut och Alice Wallenbergs Stiftelse [Grants KAW 2018.0349, KAW 2021.0274, the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation], Vetenskapsrådet [Grant 2020-03454], and the National Science Foundation [Grants 1942523 and 2206576].

Scalable Computation of Dynamic Flow Problems via Multimarginal Graph-Structured Optimal Transport

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multicommodity minimum-cost network flow problem can be formulated as a multimarginal optimal transport problem, where the cost function and the constraints on the marginals are associated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy-regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities. Funding: This work was supported by KTH Digital Futures, Knut och Alice Wallenbergs Stiftelse [Grants KAW 2018.0349, KAW 2021.0274, the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation], Vetenskapsrådet [Grant 2020-03454], and the National Science Foundation [Grants 1942523 and 2206576].

Risk‐averse optimization and resilient network flows

AbstractWe propose an approach to constructing metrics of network resilience, where resilience is understood as the network's amenability to restoring its optimal or near‐optimal operations subsequent to unforeseen (stochastic) disruptions of its topology or operational parameters, and illustrated it on the examples of the resilient maximum network flow problem and the resilient minimum cost network problem. Specifically, the network flows in these problems are designed for resilience against unpredictable losses of network carrying capacity, and the mechanism of attaining a degree of resilience is through preallocation of resources toward (at least partial) restoration of the capacities of the arcs. The obtained formulations of resilient network flow problems possess a number of useful properties, for example, similarly to the standard network flow problems, the network flow is integral if the arc capacities, costs, and so forth, are integral. It is also shown that the proposed formulations of resilient network flow problems can be viewed as “network measures of risk”, similar in properties and behavior to convex measures of risk. Efficient decomposition algorithms have been proposed for both the resilient maximum network flow problem and the resilient minimum cost network flow problem, and a study of the network flow resilience as a function of network's structure has been conducted on networks with three types of topology: that of uniform random graphs, scale‐free graphs, and grid graphs.

Modeling Minimum Cost Network Flows With Port‐Hamiltonian Systems

AbstractWe give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal control problems constrained by port‐Hamiltonian systems (pHS). The first‐order optimality system for the port‐Hamiltonian system‐constrained optimal control problem is formally derived. Then we propose a gradient‐based algorithm to find optimal controls. The port‐Hamiltonian system formulation naturally conserves flow and supports a wide array of further modeling options as, for example, node reservoirs, flow dependent costs, leaking pipes (dissipation) and coupled sub‐networks (ports). They thus provide a versatile alternative to state‐of‐the art approaches towards dynamic network flow problems, which are often based on computationally costly time‐expanded networks. We argue that this opens the door for a plethora of modeling options and solution approaches for network flow problems.

Joint chance-constrained multi-objective multi-commodity minimum cost network flow problem with copula theory

This study focuses on a specific problem in network optimization, namely the minimum cost multi-commodity network flow (MCNF) problem. The problem is complicated by the presence of uncertain parameters, including various types of costs associated with each arc in the network. The study presents a multi-objective approach to solving this problem, where the coefficients of the capacity constraints are modelled as random variables with a normal distribution, and the dependence between them is modelled using an Archimedean copula. The capacity constraints are presented as joint chance constraints, and a multi-objective problem is formulated to deal with the uncertainty. This uncertain multi-objective problem is then converted into a certain multi-objective problem using fuzzy programming. The resulting certain multi-objective MCNF problem is converted to a certain single objective problem using second-order cone programming (SOCP), which is solved using either piecewise tangent approximation or piecewise linear approximation methods. The proposed approaches are tested using numerical examples and experimental tests to demonstrate their effectiveness in solving large-scale network problems efficiently. The results show that the proposed approaches are a useful tool for solving uncertain multi-objective MCNF problems in real-world applications.

Online and Approximate Network Construction from Bounded Connectivity Constraints

The Network Construction problem, studied by Angluin et al., Hosoda et al., and others, asks for a minimum-cost network satisfying a set of connectivity constraints which specify subsets of the vertices in the network that have to form connected subgraphs. More formally, given a set [Formula: see text] of vertices, construction costs for all possible edges between pairs of vertices from [Formula: see text], and a sequence [Formula: see text] of connectivity constraints, the objective is to find a set [Formula: see text] of edges such that each [Formula: see text] induces a connected subgraph of the graph [Formula: see text] and the total cost of [Formula: see text] is minimized. First, we study the online version where every constraint must be satisfied immediately after its arrival and edges that have already been added can never be removed. We give an [Formula: see text]-competitive and [Formula: see text]-competitive polynomial-time algorithms, where [Formula: see text] is an upper bound on the size of constraints, while [Formula: see text] denote the number of constraints and the number of vertices, respectively. On the other hand, we observe that an [Formula: see text]-competitive lower bound as well as an [Formula: see text]-competitive lower bound in the cost-uniform case are implied by the known lower bounds for unbounded constraints. For the cost-uniform case with unbounded constraints, we provide an [Formula: see text]-competitive upper bound with high probability. The latter bound is against an oblivious adversary while our other randomized competitive bounds are against an adaptive adversary. Next, we discuss a hybrid approximation method for the (offline) Network Construction problem combining an approximation algorithm of Hosoda et al. with one of Angluin et al. and an application of the hybrid method to bioinformatics. Finally, we consider a natural strengthening of the connectivity requirements in the Network Construction problem, where each constraint has to induce a subgraph (of the constructed graph) of diameter at most [Formula: see text]. Among other things, we provide a polynomial-time [Formula: see text]-approximation algorithm for the Network Construction problem with the [Formula: see text]-diameter requirements, when each constraint has at most [Formula: see text] vertices, and show the APX-completeness of this variant.

A multi-objective model for cold chain logistics considering customer satisfaction

The cold chain logistics (CCL) distribution have been studied by considering customer satisfaction, we propose a multi-objective CCL model with the goals of minimal carbon transaction cost, minimal network cost and maximal customer satisfaction. According to the characteristics of the model, an improved Multi-Objective algorithm was designed, which integrates the dynamic crowding distance and differential mutation operator into non-dominated sorting genetic algorithm II (DDNSGA-II). The DDNSGA-II enhances the diversity of the initial population, the local search ability and search accuracy. Finally, the experimental data show that the proposed approaches effectively increase the customer satisfaction, reduce total distribution costs, and promote energy conservation and emission reduction.

Robust goal programming approach for healthcare network management for perishable products under disruption

In this paper, a robust goal programming model for a healthcare network design problem under disruption is developed. The objective of the proposed multi-period, multi-echelon model is to simultaneously optimize the total deviation from the considered three goals, including minimizing network cost, maximizing network coverage, and maximizing network reliability. Distribution uncertainty of healthcare demand and facility capacity is captured. The perishability of healthcare products is regarded with limited shelf-life. Using an option contract ensures appropriate coordination with suppliers during pre and post-disaster periods. Via handling the tractable robust budget-based counterpart model, suitable strategies are proposed to present the designed network's efficiency and effectiveness. Risk mitigation strategies deal with disrupted demand and supply in the healthcare network with specific impacts on coverage, cost, and reliability of the services. The proposed cooperate coverage mechanism provides appropriate service coverage under disruption propagation. Finally, the option contract has achieved cost-efficient coordination under demand uncertainty. Furthermore, practical managerial insights are demonstrated by investigating a real-life case study and conducting extensive sensitivity analyses.

Joint multiple resource allocation for offloading cost minimization in IRS-assisted MEC networks with NOMA

Effective resource allocation can exploit the advantage of intelligent reflective surface (IRS) assisted mobile edge computing (MEC) fully. However, it is challenging to balance the limited energy of MTs and the strict delay requirement of their tasks. In this paper, in order to tackle the challenge, we jointly optimize the offloading delay and energy consumption of mobile terminals (MTs) to realize the delay-energy tradeoff in an IRS-assisted MEC network, in which non-orthogonal multiple access (NOMA) and multiantenna are applied to improve spectral efficiency. To achieve the optimal delay-energy tradeoff, an offloading cost minimization model is proposed, in which the edge computing resource allocation, signal detecting vector, uplink transmission power, and IRS phase shift coefficient are needed to be jointly optimized. The optimization of the model is a multi-level fractional problem in complex fields with some coupled high dimension variables. To solve the intractable problem, we decouple the original problem into a computing subproblem and a wireless transmission subproblem based on the uncoupled relationship between different variable types. The computing subproblem is proved convex and the closed-form solution is obtained for the edge computing resource allocation. Further, the wireless transmission subproblem is solved iteratively through decoupling the residual variables. In each iteration, the closed-form solution of residual variables is obtained through different successive convex approximation (SCA) methods. We verify the proposed algorithm can converge to an optimum with polynomial complexity. Simulation results indicate the proposed method achieves average saved costs of 65.64%, 11.24%, and 9.49% over three benchmark methods respectively.

Effective multi-controller management and adaptive service deployment strategy in multi-access edge computing environment

With the popularity of emerging mobile services such as virtual reality and online gaming, users expect higher quality immersive experiences. In response to the communication reliability and latency performance problems between controllers and switches due to single link failure in the network, a framework for multi-access edge computing systems based on software-defined networking (SDN) has emerged, and this paper proposes a reliable placement method for controllers based on deployment cost and link failure probability. Reliability and worst-case propagation delay model based on link failure probability is constructed. A controller placement strategy with minimum network cost is solved by a controller layout algorithm based on density-peak clustering. A mobile-aware service adaptive deployment method is also proposed in this paper to address the problems of long user-perceived delays and high migration costs due to the limitations of edge server resources and coverage areas and the dynamic nature of user movement. A mobility model based on the probability density function of sojourn time and a service deployment overhead model based on user mobility are constructed. A quantum ant colony algorithm is used to solve the service adaptive deployment scheme. The proposed algorithm is compared with the benchmark algorithm using the vehicle detection benchmark application service. Experimental results show that the proposed controller placement algorithm weighs the deployment cost, worst-case propagation delay and reliability of controllers and gives a reasonable number of controllers and their locations. The proposed deployment algorithm can optimise the quality of the user experience.

A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: An interactive possibilistic programming approach for a real case study

In uncertain circumstances like the COVID-19 pandemic, designing an efficient Blood Supply Chain Network (BSCN) is crucial. This study tries to optimally configure a multi-echelon BSCN under uncertainty of demand, capacity, and blood disposal rates. The supply chain comprises blood donors, collection facilities, blood banks, regional hospitals, and consumption points. A novel bi-objective Mixed-Integer Linear Programming (MILP) model is suggested to formulate the problem which aims to minimize network costs and maximize job opportunities while considering the adverse effects of the pandemic. Interactive possibilistic programming is then utilized to optimally treat the problem with respect to the special conditions of the pandemic. In contrast to previous studies, we incorporated socio-economic factors and COVID-19 impact into the BSCN design. To validate the developed methodology, a real case study of a Blood Supply Chain (BSC) is analyzed, along with sensitivity analyses of the main parameters. According to the obtained results, the suggested approach can simultaneously handle the bi-objectiveness and uncertainty of the model while finding the optimal number of facilities to satisfy the uncertain demand, blood flow between supply chain echelons, network cost, and the number of jobs created.