Showing papers in "Networks in 2018"
TL;DR: This article describes the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning, and provides insights into widespread and emerging modeling approaches to civil applications of UAVs.
Abstract: Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult-to-access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.
576 citations
TL;DR: This paper presents exact solution approaches for the TSP‐D based on dynamic programming and provides an experimental comparison of these approaches and shows that the approach can solve larger problems than the mathematical programming approaches that have been presented in the literature thus far.
Abstract: A promising new delivery model involves the use of a delivery truck that collaborates with a drone to make deliveries. Effectively combining a truck and a drone gives rise to a new planning problem that is known as the traveling salesman problem with drone (TSP-D). This paper presents exact solution approaches for the TSP-D based on dynamic programming and provides an experimental comparison of these approaches. Our numerical experiments show that our approach can solve larger problems than the mathematical programming approaches that have been presented in the literature thus far. Moreover, we show that restrictions on the number of locations the truck can visit while the drone is away can help significantly reduce the solution times while having relatively little impact on the overall solution quality.
168 citations
TL;DR: This paper analyze how drones can be combined with regular delivery vehicles to improve same-day delivery performance and reveals that geographical districting is highly effective increasing the expected number of sameday deliveries and a combination of drone and vehicle fleets may reduce routing costs significantly.
Abstract: In this paper, we analyze how drones can be combined with regular delivery vehicles to improve same-day delivery performance. To this end, we present a dynamic vehicle routing problem with heterogeneous fleets. Customers order goods over the course of the day. These goods are delivered either by a drone or by a regular transportation vehicle within a delivery deadline. Drones are faster but have a limited capacity as well as charging times. Vehicles capacities are unlimited but vehicles are slow due to urban traffic. To decide whether an order is delivered by a drone or by a vehicle, we present a policy function approximation based on geographical districting. Our computational study reveals two major implications: First, geographical districting is highly effective increasing the expected number of sameday deliveries. Second, a combination of drone and vehicle fleets may reduce routing costs significantly.
136 citations
115 citations
TL;DR: This article addresses a heuristic solution of the parallel drone scheduling traveling salesman problem, recently introduced by Murray and Chu, and proposes an iterative two‐step heuristic, composed of a coding step that transforms a solution into a customer sequence, and a decoding step that decomposes the customer sequence into a tour for the vehicle and trips for the drones.
Abstract: A recent evolution in urban logistics involves the usage of drones In this article, we address a heuristic solution of the parallel drone scheduling traveling salesman problem, recently introduced by Murray and Chu In this problem, deliveries are split between a vehicle and drones The vehicle performs a classical delivery tour, while the drones are constrained to perform back and forth trips The objective is to minimize completion time We propose an iterative two-step heuristic, composed of: a coding step that transforms a solution into a customer sequence, and a decoding step that decomposes the customer sequence into a tour for the vehicle and trips for the drones Decoding is expressed as a bicriteria shortest path problem and is carried out by dynamic programming Experiments conducted on benchmark instances confirm the efficiency of the approach and give some insights on this drone delivery system
73 citations
TL;DR: This article proposes a formulation of this problem as an Integer Linear Program that allows one to find the best feasible paths and virtual function placement for a set of services with respect to a total financial cost, while taking into account the (total or partial) order constraints for Service Function Chains of each service.
Abstract: Software-Defined Networking and Network Function Virtualization are two paradigms that offer flexible software-based network management. Service providers are instantiating Virtualized Network Functions, for example, firewalls, DPIs, gateways—to highly facilitate the deployment and reconfiguration of network services with reduced time-to-value. They use Service Function Chaining technologies to dynamically reconfigure network paths traversing physical and virtual network functions. Providing a cost-efficient virtual function deployment over the network for a set of service chains is a key technical challenge for service providers, and this problem has recently caught much attention from both Industry and Academia. In this article, we propose a formulation of this problem as an Integer Linear Program that allows one to find the best feasible paths and virtual function placement for a set of services with respect to a total financial cost, while taking into account the (total or partial) order constraints for Service Function Chains of each service and other constraints such as end-to-end latency, anti-affinity rules between network functions on the same physical node and resource limitations in terms of network and processing capacities. Furthermore, we propose a heuristic algorithm based on a linear relaxation of the problem that performs close to optimum for large scale instances. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
47 citations
TL;DR: This research was supported by the Ministerio de Economia y Competitividad and FEDER - European Regional Development Fund, MTM2015-68097-P.
Abstract: This research was supported by the Ministerio de Economia y Competitividad and FEDER - European Regional Development Fund, MTM2015-68097-P.
42 citations
TL;DR: These works are reviewed and classify them with respect to the type of negative effects provoked by the customer‐based graph, a complete graph representing the road network.
40 citations
27 citations
TL;DR: An adjustable approach that explores the candidate solutions in order to identify common structures is proposed and shows that the new adjustable SAA heuristic performs better than the static one for most of the instances.
23 citations
TL;DR: This article addresses new technological features that have been recently proposed by Vattenfall's experts and shows how some new features can be modeled and solved using a Mixed‐Integer Linear Programming paradigm.
Abstract: Many EU countries aim at reducing fossil fuels in the near future, hence an efficient production of green energy is very important to reach this goal. In this paper we address the optimization of cable connections between turbines in an offshore wind park. Different versions of the problem have been studied in the recent literature. As turbines are becoming still more customized, it is important to be able to evaluate the impact of new technologies with a flexible optimization tool for scenario evaluation. In a previous joint project with Vattenfall BA Wind (a global leader in energy production) we have studied and modelled the main constraints arising in practical cases. Building on that model, in the present paper, we address new technological features that have been recently proposed by Vattenfall’s experts. We show how some new features can be modelled and solved using a Mixed-Integer Linear Programming paradigm. We report and discuss computational results on the performance of our new models on a set of real-world instances provided by Vattenfall.
TL;DR: A decomposition based method for solving mixed‐integer nonlinear optimization problems with “black‐box” nonlinearities, where the latter, for example, may arise due to differential equations or expensive simulation runs.
Abstract: We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinear equalities. The latter yield nonconvex feasible sets for the optimization model but we have to restrict ourselves to convex and monotone constraint functions. Under these assumptions, we prove that our algorithm finitely terminates with an approximate feasible global optimal solution of the mixed integer nonlinear problem. Additionally, we show the applicability of our approach for three applications from optimal control with integer variables, from the field of pressurized flows in pipes with elastic walls, and from steady-state gas transport. For the latter we also present promising numerical results of our method applied to real-world instances that particularly show the effectiveness of our method for problems defined on networks.
TL;DR: It is proved that the problem of choosing a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals is hard to solve, even in an approximate sense.
Abstract: We consider a population of interconnected individuals that, with respect to a piece of information, at each time instant can be subdivided into three (time-dependent) categories: agnostics, influenced, and evangelists A dynamical process of information diffusion evolves among the individuals of the population according to the following rules Initially, all individuals are agnostic Then, a set of people is chosen from the outside and convinced to start evangelizing, that is, to start spreading the information When a number of evangelists, greater than a given threshold, communicate with a node v, the node v becomes influenced, whereas, as soon as the individual v is contacted by a sufficiently much larger number of evangelists, it is itself converted into an evangelist and consequently it starts spreading the information The question is: How to choose a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals? We prove that the problem is hard to solve, even in an approximate sense On the positive side, we present exact polynomial time algorithms for trees and complete graphs For general graphs, we derive exact parameterized algorithms We also study the problem when the objective is to select a minimum number of evangelists capable of influencing the whole network Our motivations to study these problems come from the areas of Viral Marketing and spread of influence in social networks © 2017 Wiley Periodicals, Inc NETWORKS, 2017
TL;DR: This article considers multi‐scenario efficiency, flimsily and highly robust efficiency, and point‐based and set‐based minmax robust efficiency and proposes two approaches to extend a generic multi‐objective label correcting algorithm.
Abstract: We consider multi-objective shortest path problems in which the edge lengths are uncertain. Different concepts for finding so-called robust efficient solutions for multi-objective robust optimization exist. In this article, we consider multi-scenario efficiency, flimsily and highly robust efficiency, and point-based and set-based minmax robust efficiency. Labeling algorithms are an important class of algorithms for multi-objective (deterministic) shortest path problems. We analyze why it is, for most of the considered concepts, not straightforward to use labeling algorithms to find robust efficient solutions. We then show two approaches to extend a generic multi-objective label correcting algorithm for these cases. We finally present extensive numerical results on the performance of the proposed algorithms.
TL;DR: In this paper, a probabilistic generalization of the $N$-$k$ failure identification problem in power transmission networks is considered, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of $k$ components that maximizes disruption to the system loads weighted by the simultaneous failure of the components.
Abstract: This paper considers a probabilistic generalization of the $N$-$k$ failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of $k$ components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the $k$ components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the $N$-$k$ problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances, the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.
TL;DR: The node‐weighted Steiner tree (NWST) problem and the maximum‐weight connected subgraph (MWCS) problem, which have applications in the design of telecommunication networks and the analysis of biological networks, are considered and two algorithms with provable worst‐case runtimes are provided.
Abstract: This paper considers the node-weighted Steiner tree (NWST) problem and the maximum-weight connected subgraph (MWCS) problem, which have applications in the design of telecommunication networks and the analysis of biological networks. Exact algorithms with provable worst-case runtimes are provided. The first algorithm for NWST runs in time O(n) for n-vertex instances when the number of terminals is bounded. It is based on dynamic programming and generalizes a Steiner tree algorithm of Dreyfus and Wagner. When used alongside Hakimi’s spanning tree enumeration algorithm, it implies a time O(1.5296) algorithm for NWST. It is also shown that Hakimi’s 46-year-old algorithm for Steiner tree is essentially best-possible under the strong exponential time hypothesis (SETH). Then two algorithms for MWCS are provided. Their runtimes are polynomial in the number of vertices of the graph, but exponential in the number of vertices that have positive (or negative) weight. The latter is shown to be essentially best-possible under SETH. Together, they imply that MWCS can be solved in time O(1.5875). To the best of the authors’ knowledge, these are the first improvements over exhaustive search in the literature.
TL;DR: In this article, the authors reverse the two-phase approach by first flowing the containers through a relaxed network, and then design routes to match this flow, and the relaxed network reflects the ideas behind a physical internet of having a distributed multi-segment intermodal transport.
Abstract: Having a well-designed liner shipping network is paramount to ensure competitive freight rates, adequate capacity on trade-lanes, and reasonable transportation times. The most successful algorithms for liner shipping network design make use of a two-phase approach, where they first design the routes of the vessels, and then flow the containers through the network in order to calculate how many of the customers demands can be satisfied, and what the imposed operational costs are. In this paper we reverse the approach by first flowing the containers through a relaxed network, and then design routes to match this flow. This gives a better initial solution than starting from scratch, and the relaxed network reflects the ideas behind a physical internet of having a distributed multi-segment intermodal transport. Next, the initial solution is improved by use of a variable neighborhood search method, where six different operators are used to modify the network. Since each iteration of the local search method involves solving a very complex multi-commodity flow problem to route the containers through the network, the flow problem is solved heuristically by use of a fast Lagrange heuristic. Although the Lagrange heuristic for flowing containers is 2–5% from the optimal solution, the solution quality is sufficiently good to guide the variable neighborhood search method in designing the network. Computational results are reported, showing that the developed heuristic is able to find improved solutions for the large-scale world instances from LINERLIB, and it is the first heuristic to report results for the biggest WorldLarge instance.
TL;DR: Extensive computational experiments over existing benchmark instances show that the proposed approach leads to better results in less CPU time when compared to those obtained by state-of-the-art methods.
Abstract: Funding information Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil), Grant/Award Number: 132610/2014-0, 132789/2015-9, 305223/2015-1, 428549/2016-0, GDE 201222/2014-0 Abstract This article deals with the bi-objective pollution-routing problem (bPRP), a vehicle routing variant that arises in the context of green logistics. The two conflicting objectives considered are the minimization of the CO2 emissions and the costs related to driver’s wages. A multi-objective approach based on the two-phase Pareto local search heuristic is employed to generate a good approximation of the Pareto front. During the first phase of the method, a first set of potentially efficient solutions is obtained by solving a series of weighted sum problems with an efficient heuristic originally developed to solve the single-objective PRP. A dichotomous scheme is used to generate the different weight sets in an automatic way. In the second phase, the set is improved with an efficient Pareto local search (PLS) procedure. The use of PLS allows to limit the number of computational demanding weighted sum problems solved in the first phase, while keeping high-quality results. Extensive computational experiments over existing benchmark instances show that the proposed approach leads to better results in less CPU time when compared to those obtained by state-of-the-art methods.
TL;DR: The concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points are defined.
Abstract: Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G/S, we have w(C) ≥ w(D) whenever there is an edge between C and D. If the subgraph G(S) induced by a weighted safe set S is connected, then the set S is called a weighted connected safe set. In this article, we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlying tree is restricted to be a star, but it is polynomially solvable for paths. We also give an O(n log n) time 2-approximation algorithm for finding a weighted connected safe set with minimum weight in a weighted tree. Then, as a generalization of the concept of a minimum safe set, we define the concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points. We show that each of these central subgraphs includes a centroid point. © 2017 Wiley Periodicals, Inc.
TL;DR: A new domain clustering concept allowing one to artificially reduce the number of domains in an offline phase is devised in order to solve IDPC ‐ DU with lower complexity at run‐time and the impact of the inter‐domain treewidth on the computational speed‐up brought by proper clustering is shown.
Abstract: Correspondence Lorenzo Maggi, Mathematical and Algorithmic Sciences Lab, France Research Center, Huawei Technologies Co. Ltd, Shenzhen, China. Email: lorenzo.maggi84@gmail.com Abstract We consider a multi-domain network scenario and we study the Inter-Domain Path Computation problem under the Domain Uniqueness constraint (IDPC-DU), that is, a path cannot visit a domain twice. It is known that hierarchical Path Computation Element (h-PCE) architecture, that is commonly used to solve IDPC-DU, shows poor scalability with respect to the number of domains. For this reason, we devise a new domain clustering concept allowing one to artificially reduce the number of domains in an offline phase, in order to solve IDPC-DU with lower complexity at run-time. More specifically, we first prove the NP-completeness of the feasibility problem associated with IDPC-DU and the inapproximability of IDPC-DU itself. Yet, we show that the number of domains is the real computational bottleneck for the solution of IDPC-DU. Then we provide a necessary and sufficient condition for a domain clustering to be proper, that is, without loss of optimality. Such a condition can be verified offline on the inter-domain graph. We finally show via numerical experiments the impact of the inter-domain treewidth on the computational speed-up brought by proper clustering.
TL;DR: In this article, the authors considered a network design problem with random arc capacities and gave a formulation with a probabilistic capacity constraint on each cut of the network, and a separation procedure that solves a nonlinear minimum cut problem is introduced.
Abstract: We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentially-many probabilistic constraints a separation procedure that solves a nonlinear minimum cut problem is introduced. For the case with independent arc capacities, we exploit the supermodularity of the set function defining the constraints and generate cutting planes based on the supermodular covering knapsack polytope. For the general correlated case, we give a reformulation of the constraints that allows to uncover and utilize the submodularity of a related function. The computational results indicate that exploiting the underlying submodularity and supermodularity arising with the probabilistic constraints provides significant advantages over the classical approaches. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
TL;DR: This paper proposes an integer linear programming formulation of the multiple vehicle balancing problem and introduces strengthening valid inequalities, obtaining proven optimal solutions for MVBP instances with up to 25 stations.
Abstract: This paper deals with the Multiple Vehicle Balancing Problem (MVBP). Given a fleet of vehicles of limited capacity, a set of stations with initial and target inventory levels and a distribution network, the MVBP requires to design a set of routes and pickup and delivery operations along each route such that inventory is redistributed among the stations without exceeding the vehicle capacities and such that routing costs are minimized. The MVBP arises in bicycle sharing systems, where rebalancing is needed between stations when expected demand and number of available bicycles do not match. The MVBP turns out to be NP-hard, generalizing several problems in transportation like the Split Delivery Vehicle Routing Problem. We propose an integer linear programming formulation. Lower bounds to optimal solution values are computed by a column generation routine embedding an ad-hoc pricing algorithm; we also introduce strengthening valid inequalities. Upper bounds are obtained by a memetic algorithm based on a combinatorial encoding of the solutions that allows to focus on routing and to consider the pickup and delivery operations in a post-processing phase. We combine lower and upper bounding routines in both exact and matheuristic algorithms, obtaining proven optimal solutions for MVBP instances with up to 25 stations and an unbounded number of vehicles, or up to 20 stations and 5 vehicles.
TL;DR: It is proved that, any depth‐first search path is optimal for a given searcher start point, and the best start point is one of the leaf nodes.
Abstract: The authors study an optimal searcher path problem of the following type. A team of searchers tries to find an immobile target on a unit network (in a unit network, all edges are of unit length). The target is located at some point on this network, and its location probability distribution is known to the searcher team. Searchers move along the edges on the network at a constant speed. When one searcher passes the target location, detection happens and the search ends. The objective is to find paths for this team of searchers to minimize the expected search time. A linear binary programming model is built to find the optimal search strategy. Computational experiments are conducted to test the capability of this model, and to analyze how searcher team size and target distribution might affect the search time. Analytical results are given for a special problem scenario: one searcher searching for a uniformly distributed target on a tree. We prove that, any depth-first search path is optimal for a given searcher start point, and the best start point is one of the leaf nodes.
TL;DR: Several sets of projected inequalities, in the space of the arc and precedence variables, and in the spirit of many inequalities presented in Gouveia and Pesneau, are obtained by projecting these network flow based formulations.
Abstract: There are many ways of modeling the Asymmetric Traveling Salesman Problem (ATSP) and the related Precedence Constrained ATSP (PCATSP). In this paper we present new formulations for the two problems that result from combining precedence variable based formulations with network flow based formulations. The motivation for this work is a property of the so-called GDDL inequalities (Gouveia and Pesneau, Networks 48, 77–89, 2006), the “disjoint sub-paths” property, that is explored to create formulations that combine two (or more) disjoint path network flow based formulations. Several sets of projected inequalities, in the space of the arc and precedence variables, and in the spirit of many inequalities presented in Gouveia and Pesneau (Networks 48, 77–89, 2006), are obtained by projecting these network flow based formulations. Computational results are given for the PCATSP and the ATSP to evaluate the quality of the new inequalities. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
TL;DR: A stochastic network search algorithm that finds the most reliable flight itinerary (MRFI) is implemented and several ideas are implemented to improve the efficiency of this network search.
TL;DR: This work proposes to determine which arcs are most critical to the influence propagation process, and proves NP‐hardness of the problem.
Abstract: The influence class of network problems models the propagation of influence (an abstraction of cascading beliefs, behaviors, or physical phenomena) in a network. Such problems have applications in social networks, electrical networks, computer networks, viral spreading, and so on. These types of networks have also been studied through the lens of critical arcs detection; that is, which arcs (edges) are the most important for maintaining some property of the network (e.g., connectivity). We introduce a new class of problems at the intersection of these two models. Specifically, given a set of seed nodes and the linear threshold influence propagation model, our work proposes to determine which arcs (e.g., relationships in a social network or communication pathways in a telecommunication network) are most critical to the influence propagation process. We prove NP-hardness of the problem. Time-dependent and time-independent mixed-integer programming (MIP) models are introduced. Insights gleaned from MIP solutions leads to the development of an improved MIP-based exact algorithm rooted in the idea of diffusion expansion. A heuristic based upon a new centrality measure is also proposed, and computational results are presented. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
TL;DR: A new class of assignment‐based neighborhoods for symmetric and asymmetric traveling salesman problems that exhibits a combinatorial leverage property, by which a tour can be generated in polynomial time that dominates an exponential number of other tours.