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Suppose that a destroyed network needs to be restored by a number of servers (construction crews) that are initially located at some nodes of the network (depots). Each server can restore one unit of length of the network per unit of time. When several servers are simultaneously working at the same point, their restoration speeds combine additively. The servers can travel within the already restored...
We consider graph search problems involving an intruder and mobile searchers. The graph consists of nodes on which the intruder and searchers may be located, and edges on which these entities travel. Associated with each node is a set of nodes that are visible from that node. The goal is to find the minimum number of searchers needed to detect the intruder within a given time limit. We investigate...
The rural postman problem with time windows is the problem of serving some required edges with one vehicle; the vehicle must visit these edges during established time windows. This article presents a competitive adaptive large neighborhood search algorithm to solve the problem. Computational experiments are performed on a large set of instances with up to 104 required edges. The results show that...
The vehicle routing problem with drones (VRPD) is inspired by the increasing interest in commercial drone delivery by companies such as Amazon, Google, DHL, and Walmart. In our model, a fleet of m homogeneous trucks each carries k drones with a speed of α times that of the truck. Each drone may dispatch from the top of the truck and carry a package to a customer location. The drone then returns to...
The sample average approximation (SAA) approach is a widely used technique, based on Monte‐Carlo simulation, often applied to large‐scale stochastic optimization problems. In this approach, a set of sample average problems with multiple copies of sampled scenarios are generated and solved exactly. In other words, there is an implicit assumption that the sample average problems are solvable to optimality...
Minimum cost flow problems on infinite networks arise, for example, in infinite‐horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for linear costs using an infinite‐dimensional Simplex algorithm. Here, we use a different approach to derive duality results for convex costs. We formulate the primal and dual problems in appropriately...
Let G be a ‐connected or ‐edge‐connected graph, where . The k‐fault‐diameter and k‐edge‐fault‐diameter of G is the largest diameter of the subgraphs obtained from G by removing up to k vertices and edges, respectively. In this paper we give upper bounds on the k‐fault‐diameter and k‐edge‐fault‐diameter of graphs in terms of order. We show that the k‐fault‐diameter...
The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest...
Ring structures in molecules belong to the most important substructures for many applications in Computational Chemistry. One typical task is to find an implicit description of the ring structure of a molecule. We present efficient algorithms for cyclic graph invariants that may serve as molecular descriptors to accelerate database searches. Another task is to construct a well‐defined set of rings...
Broadcasting is a process in which an individual has an item of information which needs to be transmitted to all of the members in a network (which is viewed as a connected graph). k‐broadcasting is a variant of broadcasting in which each processor can transmit the message to up to k of its neighbors. Another variant of broadcasting is the concept of m‐time‐relaxed broadcasting, where we allow m additional...
We prove that any polynomial‐time ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where is the number of weakly connected components in the subgraph induced by the positive‐demand arcs—a small number in many applications...
Multi‐depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi‐cut constraints (MCC), which enforce this requirement in mathematical programming...
This article studies the snow plow routing problem, which is a modified version of the min–max problem with k‐vehicles for arc routing on a mixed graph with hierarchy. Each arc or edge is given a priority and instead of minimizing the overall finishing time, we minimize the latest finishing time for each priority class. We consider turn restrictions, route balancing, and variable vehicle speeds in...
The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs...
Money collection presents particular problems in terms of effective vehicle routing. Planning the collection or distribution of money for ATMs or parking meters gives rise to two problems: while the total collecting time should be minimized, tours on successive days should be different to prevent robberies. The combination of these two problems is named as the Dissimilar Routing Problem. When the...
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