
Ángel CorberánUniversity of Valencia | UV · Department of Statistics and Operations Research
Ángel Corberán
Doctor in Mathematics
About
109
Publications
34,340
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
3,187
Citations
Introduction
Angel Corberán currently works at the Department of Statistics and Operations Research, University of Valencia. Angel does research in Combinatorial Optimization. Their current projects are 'Close Enough Arc routing Problems' and 'Arc Routing Problems with drones'
Publications
Publications (109)
The Rural Postman Problem (RPP) is one of the most well-known problems in arc routing. Given an undirected graph, the RPP consists of finding a closed walk traversing and servicing a given subset of edges with minimum total cost. In the General Routing Problem (GRP), there is also a subset of vertices that must be visited. Both problems were introd...
In this article, we present and solve the multi-purpose K-drones general routing problem (MP K-DGRP). In this optimization problem, a fleet of multi-purpose drones, aerial vehicles that can both make deliveries and conduct sensing activities (e.g., imaging), have to jointly visit a set of nodes to make deliveries and map one or more continuous area...
The Length Constrained K–Drones Rural Postman Problem (LC K–DRPP) is a continuous optimization problem where a set of curved or straight lines of a network have to be traversed, in order to be serviced, by a fleet of homogeneous drones, with total minimum cost. Since the range and endurance of drones is limited, we consider here that the length of...
In this article we address the periodic rural postman problem with irregular services (PRPP–IS), where some arcs and/or edges of a mixed graph must be traversed (to be serviced) a certain number of times in some subsets of days of a given time horizon. The goal is to define a set of minimum cost tours, one for each day or period of the time horizon...
In this paper, we present and solve the multipurpose K-drones general routing problem (MP K-DGRP). In this optimization problem, a fleet of multipurpose drones, aerial vehicles that can both make deliveries and conduct sensing activities (e.g., imaging), have to jointly visit a set of nodes to make deliveries and map one or more continuous areas. T...
In this article, we deal with the Profitable Close-Enough Arc Routing Problem (PCEARP), which is an extension of the Close-Enough ARP (CEARP). The CEARP models the situation in which customers are not necessarily nodes of a network and the associated serviced can be performed from any traversed edge that is close enough to the customer. It consists...
Here we introduce the Min-Max Close-Enough Arc Routing Problem, where a fleet of vehicles must serve a set of customers while trying to balance the length of the routes. The vehicles do not need to visit the customers, since they can serve them from a distance by traversing arcs that are "close enough" to the customers. We present two formulations...
In this work we study a special case of the well-known Rural Postman Problem (RPP) with the characteristic of being defined in a graph that has a non-required edge parallel to each required one. We formulate the problem with three binary variables associated with the traversal of a required edge and its parallel non-required one. Although some vari...
In this paper we address the Length Constrained K-Drones Rural Postman Problem (LC K-DRPP). This is a continuous optimization problem where a fleet of homogeneous drones have to jointly service (traverse) a set of (curved or straight) lines of a network. Unlike the vehicles in classical arc routing problems, a drone can enter a line through any of...
Arc routing problems consist basically of finding one or several routes traversing a given set of arcs and/or edges that must be serviced. The Close-Enough Arc Routing Problem, or Generalized Directed Rural Postman Problem, does not assume that customers are located at specific arcs, but can be serviced by traversing any arc of a given subset. Real...
Arc routing problems consist basically of finding one or several routes traversing a given set of arcs and/or edges that must be serviced. The Close-Enough Arc Routing Problem, or Generalized Directed Rural Postman Problem, does not assume that customers are located at specific arcs, but can be serviced by traversing any arc of a given subset. Real...
This paper explores the concept of capacity transfer in the context of capacitated facility location problems. This is accomplished by assuming that facilities with surplus capacity/production can cooperate with those facing shortage by transferring part of that capacity/production. Such a transfer incurs a cost that nonetheless may be compensated...
Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications de...
In this paper we address the Length Constrained K-Drones Rural Postman Problem. This is an arc routing problem where there is a fleet of homogeneous drones that are used to service a set of edges of a graph. The drones routes have to start and end at a given vertex and, since the range of the drones is restricted, the length of each drone route is...
In this paper, we deal with an extension of the rural postman problem in which some links of a mixed graph must be traversed a given number of times over a time horizon. These links represent entities that must be serviced a specified number of times in some subsets of days (or periods) of the time horizon. The aim is to design a set of minimum-cos...
In this work, we propose a heuristic procedure for a stochastic version of the uncapacitated r-allocation p-hub median problem with nonstop services. In particular, we assume that the number of hubs to which a terminal can be allocated is bounded from above by r. Additionally, we consider the possibility of shipping traffic directly between termina...
This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number...
The Close-Enough Arc Routing Problem, also called Generalized Directed Rural Postman Problem, is an arc routing problem with interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets within a certain distance of a meter, the re...
In this article, we present some drone arc routing problems (Drone ARPs) and study their relation with well‐known postman ARPs. Applications for Drone ARPs include traffic monitoring by flying over roadways, infrastructure inspection such as by flying along power transmission lines, pipelines or fences, and surveillance along linear features such a...
In this article we present the Drone Arc Routing Problem (DARP) and study its relation with well-known Postman Arc Routing Problems. Applications for DARPs include traffic monitoring by flying over roadways, infrastructure inspection such as by flying along power transmission lines, pipelines or fences, and surveillance along linear features such a...
In this work we propose a heuristic procedure for a stochastic version of the Unca-pacitated r-Allocation p-Hub Median Problem with non-stop services. In particular, we assume that the number of hubs to which a terminal can be allocated is bounded from above by r. Additionally, we consider the possibility of shipping traffic directly between termin...
This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number...
We introduce an interesting variant of the well-known Chinese postman problem (CPP). While in the CPP the cost of traversing an edge is a constant (equal to its length), in the variant we present here the cost of traversing an edge depends on its length and on the weight of the vehicle at the moment it is traversed. This problem is inspired by the...
Hub networks are commonly used in telecommunications and logistics to connect origins to destinations in situations where a direct connection between each origin–destination (o-d) pair is impractical or too costly. Hubs serve as switching points to consolidate and route traffic in order to realize economies of scale. The main decisions associated w...
The aesthetic quality of routes is a feature of route planning that is of practical importance, but receives relatively little attention in the literature. Several practitioners have pointed out that the visual appeal of a proposed set of routes can have a strong influence on the willingness of a client to accept or reject a specific routing plan....
In this paper we study the hub location problem, where the goal is to identify an optimal subset of facilities (hubs) to minimize the transportation cost while satisfying certain capacity constraints. In particular, we target the single assignment version, in which each node in the transportation network is assigned to only one hub to route its tra...
In this paper, we study a variant of the directed rural postman problem (RPP) where profits are associated with arcs to be served, and incompatibility constraints may exist between nodes and profitable arcs leaving them. If convenient, some of the incompatibilities can be removed provided that penalties are paid. The problem looks for a tour starti...
We introduce an interesting variant of the well-known Chinese Postman Problem (CPP). While in the CPP the cost of traversing an edge is a constant (equal to its length), in the variant we present here the cost of traversing an edge depends on its length and on the weight of the vehicle at the moment it is traversed. This problem is inspired by the...
In this paper, we study a generalization of the Hierarchical Chinese Postman Problem on a mixed graph
where only a subset of arcs and edges require a service to be accomplished following a hierarchical order. The
problem, called Hierarchical Mixed Rural Postman Problem (HMRPP), also generalizes the Rural Postman
Problem and thus is NP-hard. We prop...
The Hierarchical Mixed Rural Postman Problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters that have to be serviced in a hierarchical order. The problem generalizes the Mixed Rural Postman Problem and thus is NP-hard. In this paper, we provide a polyhedral analysis of the problem and propose a bra...
In this paper we study the hub location problem. The goal is to identify an optimal subset of facilities (hubs) to minimize the transportation cost while satisfying certain capacity constraints. In particular, we target the single assignment version, in which each node in the transportation network is assigned to only one hub to route its traffic....
In this work we propose a heuristic procedure for a stochastic version of the Uncapacitated r-Allocation p-Hub Median Problem with non-stop services. In particular, we assume that the number of hubs to which a terminal can be allocated, is bounded from above by r. Additionally we consider the possibility of shipping traffic directly between termina...
The capacitated single assignment hub location problem with modular link capacities is a variant of the classical hub location problem in which the cost of using edges is not linear but stepwise, and the hubs are restricted in terms of transit capacity rather than in the incoming traffic. We propose a metaheuristic algorithm based on strategic osci...
In arc routing problems, customers are located on arcs, and routes of minimum cost have to
be identified. In the Orienteering Arc Routing Problem (OARP), in addition to a set of regular customers
that have to be serviced, a set of potential customers is available. From this latter set, customers have
to be chosen on the basis of an associated profi...
The generalized directed rural postman problem is an arc routing problem with many interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets closer than a certain distance to a meter, the receiver is able to record the gas, wat...
In the Team Orienteering Arc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profi...
The Generalized Directed Rural Postman Problem is an arc routing problem with many interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets closer than a certain distance to a meter, the receiver is able to record the gas, wat...
Scatter search is a population-based method that has been shown to yield high-quality outcomes for combinatorial optimization problems. It uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation for an -hard variant of the classic p-hub med...
In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the...
In this paper we deal with the polyhedral description and the resolution of the Directed General Routing Problem (DGRP) and the Stacker Crane Problem (SCP). The DGRP, in which the service activity occurs both at some of the nodes and at some of the arcs of a directed graph, contains a large number of important arc and node routing problems as speci...
In the Team Orienteering Arc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profi�t. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the prof...
Scatter search (SS) is a population-based metaheuristic that has been shown to yield high-quality outcomes for hard combinatorial optimization problems. It uses strategies for combining solution vectors, making limited use of randomization, that have proved effective in a variety of problem settings. The fundamental concepts and principles were fir...
In this paper we deal with the polyhedral description and the resolution of the Directed General Routing Problem (DGRP) and the Stacker Crane Problem (SCP). The DGRP, in which the service activity occurs both at some of the nodes and at some of the arcs of a directed graph, contains a large number of important arc and node routing problems as speci...
The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is associated with an arc of a directed graph. Each potential custom...
Mixed capacitated arc routing problems aim to identify a set of vehicle tours that, starting and ending at a depot node, serve a given number of links at minimum cost, while satisfying the vehicles capacity. If both profits and costs on arcs are considered, we may define the profitable mixed capacitated arc routing problem (PMCARP). In this paper w...
In this paper we propose a heuristic for the Uncapacitated rr-Allocation pp-Hub Median Problem. In the classical pp-hub location problem, given a set of nodes with pairwise traffic demands, we must select pp of them as hub locations and route all traffics through them at a minimum cost. We target here an extension, called the rr-allocation pp-hub m...
The min-max k-vehicles windy rural postman problem consists of minimizing the maximal distance traveled by a vehicle to find a set of balanced routes that jointly service all the required edges in a windy graph. This is a very difficult problem, for which a branch-and-cut algorithm has already been proposed, providing good results when the number o...
The Generalized Directed Rural Postman Problem, also known as the Close-Enough Arc Routing Problem, is an arc routing problem with some interesting real-life applications, such as routing for meter reading. In this article we introduce two new formulations for this problem as well as various families of new valid inequalities that are used to desig...
The min-max k-vehicles windy rural postman problem consists of
minimizing the maximal distance traveled by a vehicle in order to find a
set of balanced routes that jointly service all the required edges in a
windy graph. This is a very difficult problem, for which a branch-and-cut
algorithm has already been proposed, providing good results when the...
The Maximum Benefit Chinese Postman Problem (MBCPP) is an NP-hard problem that considers several benefits associated with each edge, one for each time the edge is traversed with a service. The objective is to find a closed walk with maximum benefit. We propose an IP formulation for the undirected MBCPP and, based on the description of its associate...
In this paper we propose a metaheuristic algorithm for the Stacker Crane Problem. This is an NP-hard arc routing problem whose name derives from the practical problem of operating a crane. Here we present a formulation and a lower bound for this problem and propose a metaheuristic algorithm based on the combination of a Multi-start and an Iterated...
The min–max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch-and-cut algori...
This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges...
In this paper we consider the capacitated arc routing problem, in which a fleet of K vehicles, all of them based on a specific vertex (the depot) and with a known capacity Q, must service a subset of the edges of the graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity. A heuristic algorithm fo...
In this paper we deal with the min–max version of the windy rural postman problem with K vehicles. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of
balanced tours for the vehicles, we present here a metaheuristic that produces very good feasible solutions in reasonable
computing times....
In this article the Min-Max version of the windy rural postman problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial des...
The Directed Rural Postman Problem (DRPP) is a general case of the Chinese Postman Problem where a subset of the set of arcs
of a given directed graph is ‘required’ to be traversed at minimum cost. If this subset does not form a weakly connected graph
but forms a number of disconnected components the problem is NP-Complete, and is also a generaliza...
Arc routing problems are vehicle routing problems in which the tasks to be performed are located on some arcs or edges of a network, e.g., spreading salt on a road or collecting municipal refuse in a street. They have been much less studied than node routing problems but impressive developments have been achieved in the last decade. The objective o...
In this chapter we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which
the demands of clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based
on the scatter search methodology, produces a feasible solution using the minimum number of vehicl...
The Windy Postman Problem consists of flnding a minimum cost traversal of all the edges of an undirected graph with two costs associated with each edge, representing the costs of traversing it in each direction. In this paper we deal with the Windy General Routing Problem (WGRP), in which only a subset of edges must be traversed and a subset of ver...
In this paper, we present an exact algorithm for the Windy General Routing Problem. This problem generalizes many important Arc Routing Problems and also has some interesting real-life applications. The Branch & Cut method presented here is based on a cutting-plane algorithm that identifies violated inequalities of several classes of facet-inducing...
In this paper we present several heuristic algorithms and a cutting-plane algorithm for the Windy Rural Postman Problem. This problem contains a big number of important Arc Routing Problems as special cases and has very interesting real-life applications. Extensive computational experiments over different sets of instances are also presented.
In this paper we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of the clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehi...
In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed
Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the
description of the polyhedron associated with the Windy Postman Problem over graphs with up to four verti...
Abstract Arc Routing Problems on mixed graphs have been modelled in the literature either using just one variable per edge or associating to each edge two variables, each one representing its traversal in the corresponding direction. In this paper, and using the Mixed General Routing Problem as an example, we compare theoretical and computationally...
In this paper we introduce a new class of facet-inducing inequalities for the Windy Rural Postman Problem and the Windy General Routing Problem. These inequalities are called Zigzag inequalities because they cut ofi fractional solutions containing a zigzag associated with variables with 0:5 value. Two difierent types of inequalities, the Odd Zigzag...
Without Abstract
In this paper we deal with the Windy Rural Postman Problem. This problem generalizes several important Arc Routing Problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a Scatter Search algorithm for the Windy Rural Postman Problem. Extensive computational experiments over die...
In this paper we present an exact algorithm for the Windy General Routing Problem. This problem generalizes many important Arc Routing Problems and also has some interesting real-life applications. The Branch & Cut method presented here is based on a cutting-plane algorithm that identifies violated inequalities of several classes of facet-inducing...
We deal with the polyhedral description and the resolution of the Mixed General Routing Problem. This problem, in which the service activity occurs both at some of the nodes and at some of the arcs and edges of a mixed graph, contains a large number of important arc and node routing problems as special cases. Here, a large family of facet-defining...
This report is more than just a summary of some results of the present state of the art in routing and location problems. It summarizes theoretical insights, modeling approaches, and heuristic and exact algorithms for routing and location presented at the CORAL 2003 Workshop held in Tenerife (Spain). © 2003 Wiley Periodicals, Inc.
In mid‐October 2001, a number of lecturers at the University of València received insulting, threatening and anonymous electronic mails. An investigation about this fact is only permitted under very restricted conditions, stipulated by Spanish law. Only one judicial authority is able to lift these restrictions and authorize information to be...
In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related
to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must
be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral invest...
Arc routing problems (ARPs) consist of finding a traversal on a graph satisfying some conditions related to the links of the graph. In the Chinese postman problem (CPP) the aim is to find a minimum cost tour (closed walk) traversing all the links of the graph at least once. Both the Undirected CPP, where all the links are edges that can be traverse...
In this paper we deal with a problem which generalizes the Rural Postman Problem defined on a mixed graph (MRPP). The generalization consists of associating a non-negative penalty to every turn as well as considering the existence of forbidden turns. This new problem fits real-world situations more closely than other simpler problems. A solution to...