Isaac Plana

University of Valencia | UV · Departamento de Matemáticas para la Economía y la Empresa

This paper studies the multidepot drone general routing problem with duration and capacity constraints (MDdGRP), an extension of the classical general routing problem with several depots. A fleet of drones with limited flight time and payload, each one located in a different depot, must jointly perform the service. In this continuous optimization p...

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...

In this paper we present a generalization of the Graphical Travelling Salesman Problem (GTSP). Given a communication graph in which not all direct connections are necessarily possible, the Graphical Travelling Salesman Problem consists of finding the shortest tour that visits each node at least once. In this work, we assume the availability of a bu...

This paper studies the Multi-Depot drone General Routing Problem with duration and capacity constraints (MD-dGRP), an extension of the classical GRP with several depots. A fleet of drones with limited flight time and payload, each one located in a different depot, must jointly perform the service. On this continuous optimization problem, a set of l...

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 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...

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...

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 paper, we deal with the Time-Dependent Asymmetric Traveling Salesman Problem with Time Windows. First, we prove that under special conditions the problem can be solved as an Asymmetric Traveling Salesman Problem with Time Windows, with suitable-defined time windows and (constant) travel times. Second, we show that, if the special conditions...

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...

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...

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 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 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...

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 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...

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...

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 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 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...

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...

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...

In this article we develop a greedy randomized adaptive search procedure (GRASP) for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix, which keeps the non-zero elements in a band that is as close as possible to the main diagonal. The proposed method may be co...