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Papers by Hipólito Hernández-Pérez

European Journal of Operational Research, 2022

Abstract This paper deals with the problem of designing a minimum-cost route for a capacitated ve... more Abstract This paper deals with the problem of designing a minimum-cost route for a capacitated vehicle moving a commodity between a set of customers, allowing two features uncommon in the pickup-and-delivery literature. One feature is that a customer accepts to be visited several times, i.e., splitting a customer demand is allowed. The other feature is that a customer may be used as an intermediate location to collect and deliver commodity temporarily. The problem is called Split-Delivery One-Commodity Pickup-and-Delivery Travelling Salesman Problem, and finds applications in bike sharing systems where a single vehicle moves bikes between bike stations of a city district during the night to set the network to an initial configuration. The paper proposes a new branch-and-cut algorithm to find optimal solutions. A master problem solves a relaxed Mixed Integer Programming model, i.e., a model allowing all feasible solutions and also some invalid ones. A subproblem checks the feasibility of the master solutions and generates valid cuts when they are infeasible. Computational results on benchmark instances demonstrate the good performance of the algorithm compared with others in the literature. In particular, it solves benchmark instances with 60 customers that were unsolved.

European Journal of Operational Research, 2016

We address in this article the multi-commodity pickup-and-delivery traveling salesman problem, wh... more We address in this article the multi-commodity pickup-and-delivery traveling salesman problem, which is a routing problem for a capacitated vehicle that has to serve a set of customers that provide or require certain amounts of m different products. Each customer must be visited exactly once by the vehicle, and it is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires that product. Each product is allowed to have several sources and several destinations. The objective is to minimize the total travel distance. We propose a hybrid three-stage heuristic approach that combines a procedure to generate initial solutions with several local search operators and shaking procedures, one of them based on solving an integer programming model. Extensive computational experiments on randomly generated instances with up to 400 locations and 5 products show the effectiveness of the approach.

The "multi-commodity Pickup-and-Delivery Traveling Salesman Problem" (m-PDTSP) is a generalizatio... more The "multi-commodity Pickup-and-Delivery Traveling Salesman Problem" (m-PDTSP) is a generalization of the well-known "Traveling Salesman Problem" in which cities correspond to customers providing or requiring known amounts of m different products, and the vehicle has a known capacity. Each customer must be visited exactly once by the vehicle serving the demands of the different products while minimizing the total travel distance. It is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires this product. We discuss heuristic algorithms for the m-PDTSP. First, we introduce a heuristic that finds a solution of the m-PDTSP. After, we present several procedures which improve a solution (even when this solution is infeasible). These improvement procedures include a branch-and-algorithm where some variables are fixed. Computational experiments on randomly generated instances.

Transportation Science, 2004

This paper deals with a generalisation of the well-known traveling salesman problem (TSP) in whic... more This paper deals with a generalisation of the well-known traveling salesman problem (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given upper limit capacity. Each customer must be visited exactly once by the vehicle serving the demands while minimising the total travel distance. It is assumed that any unit of product collected from a pickup customer can be delivered to any delivery customer. This problem is called one-commodity pickup-and-delivery TSP (1-PDTSP). We propose two heuristic approaches for the problem: (1) is based on a greedy algorithm and improved with a k-optimality criterion and (2) is based on a branch-and-cut procedure for finding an optimal local solution. The proposal can easily be used to solve the classical “TSP with pickup-and-delivery,” a version studied in literature and involving two commodities. The approaches have been applied to solve hard instances with up to 500 customers.

Networks, 2007

In the carrier-based coverage repair problem, a single mobile robot replaces damaged sensors by p... more In the carrier-based coverage repair problem, a single mobile robot replaces damaged sensors by picking up spare ones in the region of interest or carrying them from a base station in wireless sensor and robot networks. The objective is to find the shortest path of the robot. The problem is an extension of the traveling salesman problem (TSP). Thus, it is also called the one-commodity traveling salesman problem with selective pickup and delivery (1-TSP-SELPD). In order to solve this problem in a larger sensor distribution scenario more efficiently, we propose a two-stage approach in this paper. In the first stage, the mature and effective Lin-Kernighan-Helsgaun (LKH) algorithm is used to form a Hamiltonian cycle for all delivery nodes, which is regarded as a heuristic for the second stage. In the second stage, elliptical regions are set for selecting pickup nodes‚ and an edge-ordered list (candidate edge list, CEL) is constructed to provide major axes for the ellipses. The process of selecting pickup nodes and constructing the CEL is repeated until all the delivery nodes are visited. The final CEL stores a feasible solution. To update it, three operations-expansion, extension, and constriction-are applied to the CEL. The experimental results show that the proposed method reduces the computing time and achieves better results in higher-dimensional problems, which may facilitate the provision of solutions for more complicated sensor networks and can contribute to the development of effective and efficient algorithms for the one-commodity pickup-and-delivery traveling salesman problem (1-PDTSP).

European Journal of Operational Research, 2009

This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commod... more This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must visit each customer exactly once. This justifies the words "one-to-one" and "traveling salesman problem" in the name of the problem, respectively. We introduce a Mixer Integer Linear Programming model for the m-PDTSP, discuss decomposition techniques and describe some strategies to solve the problem based on a branchand-cut procedure. Preliminary computational experiments on randomly generated euclidian instances are shown.

Electronic Notes in Discrete Mathematics, 2013

ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO... more ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.

Discrete Applied Mathematics, 2004

We study a generalization of the well-known traveling salesman problem (TSP) where each customer ... more We study a generalization of the well-known traveling salesman problem (TSP) where each customer provides or requires a given non-zero amount of product, and the vehicle in a depot has a given capacity. Each customer and the depot must be visited exactly once by the vehicle supplying the demand while minimizing the total travel distance. We assume that the product collected from pickup customers can be delivered to delivery customers. We introduce a 0-1 integer linear model for this problem and describe a branch-and-cut procedure for ÿnding an optimal solution. The model and the algorithm are adapted to solve instances of TSP with pickup and delivery. Some computational results are presented to analyze the performance of our proposal.

Page 1. A New Heuristic Approach for the One-Commodity Pickup-and-Delivery Traveling Salesman Pro... more Page 1. A New Heuristic Approach for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem Hipólito Hernández-Pérez, DEIOC, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain Inmaculada Rodrıguez ...

Lecture Notes in Computer Science

This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle mo... more This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle moving a single commodity between a set of customers. The route must allow two characteristics uncommon in the literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as intermediate location to temporarily collect and deliver part of the load of the vehicle. Routes with these characteristics may lead to cost reductions when compared to routes without them. The paper describes a branch-and-cut algorithm based on a relaxation of a model of Mixed Integer Programming. Preliminary computational results on benchmark instances demonstrate the good performance of the algorithm compared with the original model.

Lecture Notes in Computer Science

Computers & Operations Research

Computers & Operations Research

This article deals with a new generalization of the well-known “Travelling Salesman Problem” (TSP... more This article deals with a new generalization of the well-known “Travelling Salesman Problem” (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given capacity and is located in a special city called depot. Each customer and the depot must be visited exactly once by the vehicle serving the demands while minimizing the total travel distance. It is assumed that the product collected from pickup customers can be delivered to delivery customers. The new problem is called “one-commodity Pickup-and-Delivery TSP” (1-PDTSP). We introduce a 0-1 Integer Linear Programming model for the 1-PDTSP and describe a simple branch-and-cut procedure for finding an optimal solution. The proposal can be easily adapted for the classical “TSP with Pickup-and- Delivery” (PDTSP). To our knowledge, this is the first work on an exact method to solve the classical PDTSP. Preliminary computational experiments on a test-bed PDTSP instance from the literature show the good performances of our proposal.

Discrete Applied Mathematics, 2004

Electronic Notes in Discrete Mathematics, 2013

ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO... more ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.

European Journal of Operational Research, 2022

Abstract This paper deals with the problem of designing a minimum-cost route for a capacitated ve... more Abstract This paper deals with the problem of designing a minimum-cost route for a capacitated vehicle moving a commodity between a set of customers, allowing two features uncommon in the pickup-and-delivery literature. One feature is that a customer accepts to be visited several times, i.e., splitting a customer demand is allowed. The other feature is that a customer may be used as an intermediate location to collect and deliver commodity temporarily. The problem is called Split-Delivery One-Commodity Pickup-and-Delivery Travelling Salesman Problem, and finds applications in bike sharing systems where a single vehicle moves bikes between bike stations of a city district during the night to set the network to an initial configuration. The paper proposes a new branch-and-cut algorithm to find optimal solutions. A master problem solves a relaxed Mixed Integer Programming model, i.e., a model allowing all feasible solutions and also some invalid ones. A subproblem checks the feasibility of the master solutions and generates valid cuts when they are infeasible. Computational results on benchmark instances demonstrate the good performance of the algorithm compared with others in the literature. In particular, it solves benchmark instances with 60 customers that were unsolved.

European Journal of Operational Research, 2016

We address in this article the multi-commodity pickup-and-delivery traveling salesman problem, wh... more We address in this article the multi-commodity pickup-and-delivery traveling salesman problem, which is a routing problem for a capacitated vehicle that has to serve a set of customers that provide or require certain amounts of m different products. Each customer must be visited exactly once by the vehicle, and it is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires that product. Each product is allowed to have several sources and several destinations. The objective is to minimize the total travel distance. We propose a hybrid three-stage heuristic approach that combines a procedure to generate initial solutions with several local search operators and shaking procedures, one of them based on solving an integer programming model. Extensive computational experiments on randomly generated instances with up to 400 locations and 5 products show the effectiveness of the approach.

The "multi-commodity Pickup-and-Delivery Traveling Salesman Problem" (m-PDTSP) is a generalizatio... more The "multi-commodity Pickup-and-Delivery Traveling Salesman Problem" (m-PDTSP) is a generalization of the well-known "Traveling Salesman Problem" in which cities correspond to customers providing or requiring known amounts of m different products, and the vehicle has a known capacity. Each customer must be visited exactly once by the vehicle serving the demands of the different products while minimizing the total travel distance. It is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires this product. We discuss heuristic algorithms for the m-PDTSP. First, we introduce a heuristic that finds a solution of the m-PDTSP. After, we present several procedures which improve a solution (even when this solution is infeasible). These improvement procedures include a branch-and-algorithm where some variables are fixed. Computational experiments on randomly generated instances.

Transportation Science, 2004

This paper deals with a generalisation of the well-known traveling salesman problem (TSP) in whic... more This paper deals with a generalisation of the well-known traveling salesman problem (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given upper limit capacity. Each customer must be visited exactly once by the vehicle serving the demands while minimising the total travel distance. It is assumed that any unit of product collected from a pickup customer can be delivered to any delivery customer. This problem is called one-commodity pickup-and-delivery TSP (1-PDTSP). We propose two heuristic approaches for the problem: (1) is based on a greedy algorithm and improved with a k-optimality criterion and (2) is based on a branch-and-cut procedure for finding an optimal local solution. The proposal can easily be used to solve the classical “TSP with pickup-and-delivery,” a version studied in literature and involving two commodities. The approaches have been applied to solve hard instances with up to 500 customers.

Networks, 2007

In the carrier-based coverage repair problem, a single mobile robot replaces damaged sensors by p... more In the carrier-based coverage repair problem, a single mobile robot replaces damaged sensors by picking up spare ones in the region of interest or carrying them from a base station in wireless sensor and robot networks. The objective is to find the shortest path of the robot. The problem is an extension of the traveling salesman problem (TSP). Thus, it is also called the one-commodity traveling salesman problem with selective pickup and delivery (1-TSP-SELPD). In order to solve this problem in a larger sensor distribution scenario more efficiently, we propose a two-stage approach in this paper. In the first stage, the mature and effective Lin-Kernighan-Helsgaun (LKH) algorithm is used to form a Hamiltonian cycle for all delivery nodes, which is regarded as a heuristic for the second stage. In the second stage, elliptical regions are set for selecting pickup nodes‚ and an edge-ordered list (candidate edge list, CEL) is constructed to provide major axes for the ellipses. The process of selecting pickup nodes and constructing the CEL is repeated until all the delivery nodes are visited. The final CEL stores a feasible solution. To update it, three operations-expansion, extension, and constriction-are applied to the CEL. The experimental results show that the proposed method reduces the computing time and achieves better results in higher-dimensional problems, which may facilitate the provision of solutions for more complicated sensor networks and can contribute to the development of effective and efficient algorithms for the one-commodity pickup-and-delivery traveling salesman problem (1-PDTSP).

European Journal of Operational Research, 2009

This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commod... more This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must visit each customer exactly once. This justifies the words "one-to-one" and "traveling salesman problem" in the name of the problem, respectively. We introduce a Mixer Integer Linear Programming model for the m-PDTSP, discuss decomposition techniques and describe some strategies to solve the problem based on a branchand-cut procedure. Preliminary computational experiments on randomly generated euclidian instances are shown.

Electronic Notes in Discrete Mathematics, 2013

ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO... more ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.

Discrete Applied Mathematics, 2004

We study a generalization of the well-known traveling salesman problem (TSP) where each customer ... more We study a generalization of the well-known traveling salesman problem (TSP) where each customer provides or requires a given non-zero amount of product, and the vehicle in a depot has a given capacity. Each customer and the depot must be visited exactly once by the vehicle supplying the demand while minimizing the total travel distance. We assume that the product collected from pickup customers can be delivered to delivery customers. We introduce a 0-1 integer linear model for this problem and describe a branch-and-cut procedure for ÿnding an optimal solution. The model and the algorithm are adapted to solve instances of TSP with pickup and delivery. Some computational results are presented to analyze the performance of our proposal.

Page 1. A New Heuristic Approach for the One-Commodity Pickup-and-Delivery Traveling Salesman Pro... more Page 1. A New Heuristic Approach for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem Hipólito Hernández-Pérez, DEIOC, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain Inmaculada Rodrıguez ...

Lecture Notes in Computer Science

This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle mo... more This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle moving a single commodity between a set of customers. The route must allow two characteristics uncommon in the literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as intermediate location to temporarily collect and deliver part of the load of the vehicle. Routes with these characteristics may lead to cost reductions when compared to routes without them. The paper describes a branch-and-cut algorithm based on a relaxation of a model of Mixed Integer Programming. Preliminary computational results on benchmark instances demonstrate the good performance of the algorithm compared with the original model.

Lecture Notes in Computer Science

Computers & Operations Research

Computers & Operations Research

This article deals with a new generalization of the well-known “Travelling Salesman Problem” (TSP... more This article deals with a new generalization of the well-known “Travelling Salesman Problem” (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given capacity and is located in a special city called depot. Each customer and the depot must be visited exactly once by the vehicle serving the demands while minimizing the total travel distance. It is assumed that the product collected from pickup customers can be delivered to delivery customers. The new problem is called “one-commodity Pickup-and-Delivery TSP” (1-PDTSP). We introduce a 0-1 Integer Linear Programming model for the 1-PDTSP and describe a simple branch-and-cut procedure for finding an optimal solution. The proposal can be easily adapted for the classical “TSP with Pickup-and- Delivery” (PDTSP). To our knowledge, this is the first work on an exact method to solve the classical PDTSP. Preliminary computational experiments on a test-bed PDTSP instance from the literature show the good performances of our proposal.

Discrete Applied Mathematics, 2004

Electronic Notes in Discrete Mathematics, 2013

ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO... more ABSTRACT International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.