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ROBERTO CALVO

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Full professor of Civil Law

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University College Cork

M. Grazia Speranza

University of Brescia

Fumitaka Kurauchi

Kelvin odame Kwakye

Juan G. Villegas

Universidad de Antioquia (Colombia)

Aalto University

Henrik Andersson

Cristian Cortes

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Papers by ROBERTO CALVO

A Matheuristic for the Dial-a-Ride Problem

Lecture Notes in Computer Science, 2011

The Dial-a-Ride is a transport system on demand. A fleet of vehicles, without fixed routes and sc... more The Dial-a-Ride is a transport system on demand. A fleet of vehicles, without fixed routes and schedules, carries people from their pickup points to their delivery points, during a pre-specified time interval. It can be modeled as an N P-hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too limited to tackle real-life instances: time dependent network, requests received on-line, different objective functions. In this paper we propose an algorithm to solve the off-line Dial-a-Ride Problem (DARP), based on a Granular Tabu Search method. This algorithm was fast and effective, when tested on instances created ad hoc using the Milan network.

El Mundo Rural: Cenicienta de la Crisis

Cultura Para La Esperanza Instrumento De Analisis De La Realidad, 2013

El Mundo Rural: Cenicienta de la Crisis

Cultura Para La Esperanza Instrumento De Analisis De La Realidad, 2013

On the Complexity of the Multiple Stack TSP, kSTSP

Lecture Notes in Computer Science, 2009

Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) con... more Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) consists in finding a pickup tour T 1 and a delivery tour T 2 of n items on two distinct graphs. The pickup tour successively stores the items at the top of k containers, whereas the delivery tour successively picks the items at the current top of the containers: thus, the couple of tours are subject to LIFO ("Last In First Out") constraints. This paper aims at finely characterizing the complexity of kSTSP in regards to the complexity of TSP. First, we exhibit tractable sub-problems: on the one hand, given two tours T 1 and T 2 , deciding whether T 1 and T 2 are compatible can be done within polynomial time; on the other hand, given an ordering of the n items into the k containers, the optimal tours can also be computed within polynomial time. Note that, to the best of our knowledge, the only family of combinatorial precedence constraints for which constrained TSP has been proven to be in P is the one of PQ-trees, [2]. Finally, in a more prospective way and having in mind the design of approximation algorithms, we study the relationship between optimal value of different TSP problems and the optimal value of kSTSP.

On the Complexity of the Multiple Stack TSP, kSTSP

Lecture Notes in Computer Science, 2009

Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) con... more Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) consists in finding a pickup tour T 1 and a delivery tour T 2 of n items on two distinct graphs. The pickup tour successively stores the items at the top of k containers, whereas the delivery tour successively picks the items at the current top of the containers: thus, the couple of tours are subject to LIFO ("Last In First Out") constraints. This paper aims at finely characterizing the complexity of kSTSP in regards to the complexity of TSP. First, we exhibit tractable sub-problems: on the one hand, given two tours T 1 and T 2 , deciding whether T 1 and T 2 are compatible can be done within polynomial time; on the other hand, given an ordering of the n items into the k containers, the optimal tours can also be computed within polynomial time. Note that, to the best of our knowledge, the only family of combinatorial precedence constraints for which constrained TSP has been proven to be in P is the one of PQ-trees, [2]. Finally, in a more prospective way and having in mind the design of approximation algorithms, we study the relationship between optimal value of different TSP problems and the optimal value of kSTSP.

Effect of draft tube position on the hydrodynamics of a draft tube slurry bubble column

The Chemical Engineering Journal and the Biochemical Engineering Journal, 1995

Two-and three-phase hydrodynanuc studies were conducted m an air lift bubble column with an inter... more Two-and three-phase hydrodynanuc studies were conducted m an air lift bubble column with an internal loop The bubble column had a conical dlstnbutor at the bottom, through which the gas was sparged, creating a hqmd or slurry circulation from the draft tube to the annular region The axial position of the draft tube was vaned with respect to the conical section The expenments were performed with the air-water system at ambient condltlons, usmg sihceous sand as the solid phase When the bottom of the draft tube was located precisely at the transltlon between the conical and cylmdncal regions, no hqmd circulation was observed When the draft tube was located m a lower posltlon, hqmd circulation started and its magmtude increased as the draft tube was further lowered mslde the conical region The results presented indicate that the hydrodynanuc behavlour of these systems can be effectively controlled by varying the axial position of the draft tube

An Effective Evolutionary Algorithm for the Cumulative Capacitated Vehicle Routing Problem

Lecture Notes in Computer Science, 2009

The Cumulative Capacitated Vehicle Routing Problem (or CCVRP) models transportation problems wher... more The Cumulative Capacitated Vehicle Routing Problem (or CCVRP) models transportation problems where the objective is to minimize the sum of arrival times at customers, taking into account capacity limitations. It generalizes the traveling repairman problem (or TRP), by adding capacity constraints and an homogeneous vehicle fleet. This paper presents the first metaheuristic designed for the CCVRP, taking into account specific

A Hybrid Tabu Search for the m-Peripatetic Vehicle Routing Problem

Matheuristics, 2009

This article presents a hybridization of a perfect b-matching within a tabu search framework for ... more This article presents a hybridization of a perfect b-matching within a tabu search framework for the m-Peripatetic Vehicle Routing Problem (m-PVRP). The m-PVRP models for example money transports and cash machines supply where, for security reasons, no path can be used more than once during m periods and the amount of money allowed per vehicle is limited. It consists in finding a set of routes of minimum total cost over m periods from an undirected graph such that each customer is visited exactly once per period and each edge can be used at most once during the m periods. Each route starts and finishes at the depot with a total demand not greater than vehicle capacity. The aim is to minimize the total cost of the routes. The m-PVRP can be considered as a generalization of two well-known NP-hard problems: the vehicle routing problem (VRP or 1-PVRP) and the m-Peripatetic Salesman Problem (m-PSP). Computational results show that the hybrid algorithm obtained improves the tabu search, not only on the m-PVRP in general, but also on the VRP and the m-PSP using classical VRP instances and TSPLIP instances.

An Effective Hybrid Evolutionary Local Search for Orienteering and Team Orienteering Problems with Time Windows

Parallel Problem Solving from Nature, PPSN XI, 2010

Abstract. The orienteering problem (OP) consists in finding an elemen-tary path over a subset of ... more Abstract. The orienteering problem (OP) consists in finding an elemen-tary path over a subset of vertices. Each vertex has associated a profit that is collected on the visitor's first visit. The objective is to maximize the collected profit with respect to a limit on the path's length. The team ...

A label correcting algorithm for the shortest path problem on a multi-modal route network

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012

We consider shortest paths on a multi-modal transportation network where restrictions or preferen... more We consider shortest paths on a multi-modal transportation network where restrictions or preferences on the use of certain modes of transportation may arise. The regular language constraint shortest path problem deals with this kind of problem. It models constraints by using regular languages. The problem can be solved efficiently by using a generalization of Dijkstra's algorithm (D RegLC). Recently a speed-up technique called SDALT has been proposed to speed up D RegLC. In this paper we present a new label correcting algorithm (lcSDALT) which overcomes some limitations of SDALT. We evaluated lcSDALT on a realistic multi-modal transportation network with various modes of transport and road types, including timedependent cost functions on arcs. We observed a speed-up of a factor 3 to 30, with respect to D RegLC and of up to 50% with respect to SDALT, while at the same time reducing memory requirements.

A Memetic Algorithm with Population Management for the Generalized Minimum Vertex-Biconnected Network Problem

2010 International Conference on Intelligent Networking and Collaborative Systems, 2010

We consider the generalized minimum vertexbiconnected network problem (GMVBCNP). Given a graph wh... more We consider the generalized minimum vertexbiconnected network problem (GMVBCNP). Given a graph where nodes are partitioned into clusters, the goal is to find a minimal cost subgraph containing exactly one node from each cluster and satisfying the vertex-biconnectivity constraint. The problem is NP-hard. The GMVBCNP has applications in the design of survivable backbone networks when single component outages are considered. We propose a Memetic Algorithm with two crossover operators, three mutation operators, and a local search component based on two neighborhood structures. Furthermore, two different population management approaches are investigated. Experimental results document the efficiency of the new approach. In particular, the local search component and the population management strategies have a substantial impact on solution quality as well as running time.

A New Heuristic for the Traveling Salesman Problem with Time Windows

Transportation Science, 2000

The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem wit... more The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem with Time Windows, based on the solution of an auxiliary problem. The idea is to solve an assignment problem with an ad hoc objective function to obtain a solution close enough to a feasible solution of the original problem. Given this solution, made by a long main tour containing the depot and few small subtours, it is easy to insert all the subtours into the main path using a greedy insertion procedure. The algorithm described applies the proposed constructive scheme and then uses a local search procedure to improve the initial solution. The computational results show the effectiveness of this approach.

Solving the electricity production planning problem by a column generation based heuristic

Journal of Scheduling, 2012

ABSTRACT This paper presents a heuristic method based on column generation for the EDF (Electrici... more ABSTRACT This paper presents a heuristic method based on column generation for the EDF (Electricité De France) long-term electricity production planning problem proposed as subject of the ROADEF/EURO 2010 Challenge. This is to our knowledge the first-ranked method among those methods based on mathematical programming, and was ranked fourth overall. The problem consists in determining a production plan over the whole time horizon for each thermal power plant of the French electricity company, and for nuclear plants, a schedule of plant outages which are necessary for refueling and maintenance operations. The average cost of the overall outage and production planning, computed over a set of demand scenarios, is to be minimized. The method proceeds in two stages. In the first stage, dates for outages are fixed once for all for each nuclear plant. Data are aggregated with a single average scenario and reduced time steps, and a set-partitioning reformulation of this aggregated problem is solved for fixing outage dates with a heuristic based on column generation. The pricing problem associated with each nuclear plant is a shortest path problem in an appropriately constructed graph. In the second stage, the reload level is determined at each date of an outage, considering now all scenarios. Finally, the production quantities between two outages are optimized for each plant and each scenario by solving independent linear programming problems.

A Metaheuristic to Solve a Location-Routing Problem with Non-Linear Costs

Journal of Heuristics, 2005

Page 1. Journal of Heuristics, 11: 375391, 2005 cс 2005 Springer Science + Business Media, Inc. ... more

An efficient heuristic approach to solve the unate covering problem

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2001

The classical solving approach for two-level logic minimisation reduces the problem to a special ... more The classical solving approach for two-level logic minimisation reduces the problem to a special case of unate covering and attacks the latter with a (possibly limited) branch-and-bound algorithm. We adopt this approach, but we propose a constructive heuristic algorithm that combines the use of Binary Decision Diagrams with the lagrangian relaxation. This technique permits to achieve an effective choice of the elements to include into the solution, as well as cost-related reductions of the problem and a good lower bound on the optimum. The results support the effectiveness of this approach: on a wide set of benchmark problems, the algorithm nearly always hits the optimum, and in most cases proves it to be such. On the problems whose optimum is actually unknown, the best known result is strongly improved.

An effective memetic algorithm for the cumulative capacitated vehicle routing problem

Computers & Operations Research, 2010

The cumulative capacitated vehicle routing problem (CCVRP) is a transportation problem which occu... more The cumulative capacitated vehicle routing problem (CCVRP) is a transportation problem which occurs when the objective is to minimize the sum of arrival times at customers, instead of the classical route length, subject to vehicle capacity constraints. This type of challenges arises whenever priority is given to the satisfaction of the customer need, e.g. vital goods supply or rescue after

A heuristic approach to the overnight security service problem

Computers & Operations Research, 2003

This paper introduces the overnight security service problem. The model obtained is a single-obje... more This paper introduces the overnight security service problem. The model obtained is a single-objective mixed integer programming problem. It is NP-hard in the strong sense, and exact approaches are not practicable when solving real-life instances. Thus, the model is solved heuristically, through a decomposition in two subproblem. The former is a capacitated clustering problem, the latter is a multiple travelling

Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem

Annals of Operations Research, 2006

This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the wel... more This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the well-known Set Covering Problem. The proposed approach is a two-phase heuristic method which has the particularity to be a constructive method using the primal-dual Lagrangian relaxation to solve single objective Set Covering problems. The results show that this algorithm finds several potentially supported and unsupported solutions. A comparison with an exact method (up to a medium size), shows that many Pareto-optimal solutions are retrieved and that the other solutions are well spread and close to the optimal ones. Moreover, the method developed compares favorably with the Pareto Memetic Algorithm proposed by Jaszkiewicz.

A Heuristic for the Vehicle Routing Problem with Time Windows

Journal of Heuristics, 2001

In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Win... more In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical k-opt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective function drives the search out of local optima. No parameter tuning is required

An effective and fast heuristic for the Dial-a-Ride problem

4OR, 2006

Page 1. 4OR (2007) 5:6173 DOI 10.1007/s10288-006-0018-0 REGULAR PAPER An effective and fast heur... more

A Matheuristic for the Dial-a-Ride Problem

Lecture Notes in Computer Science, 2011

The Dial-a-Ride is a transport system on demand. A fleet of vehicles, without fixed routes and sc... more The Dial-a-Ride is a transport system on demand. A fleet of vehicles, without fixed routes and schedules, carries people from their pickup points to their delivery points, during a pre-specified time interval. It can be modeled as an N P-hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too limited to tackle real-life instances: time dependent network, requests received on-line, different objective functions. In this paper we propose an algorithm to solve the off-line Dial-a-Ride Problem (DARP), based on a Granular Tabu Search method. This algorithm was fast and effective, when tested on instances created ad hoc using the Milan network.

El Mundo Rural: Cenicienta de la Crisis

Cultura Para La Esperanza Instrumento De Analisis De La Realidad, 2013

El Mundo Rural: Cenicienta de la Crisis

Cultura Para La Esperanza Instrumento De Analisis De La Realidad, 2013

On the Complexity of the Multiple Stack TSP, kSTSP

Lecture Notes in Computer Science, 2009

Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) con... more Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) consists in finding a pickup tour T 1 and a delivery tour T 2 of n items on two distinct graphs. The pickup tour successively stores the items at the top of k containers, whereas the delivery tour successively picks the items at the current top of the containers: thus, the couple of tours are subject to LIFO ("Last In First Out") constraints. This paper aims at finely characterizing the complexity of kSTSP in regards to the complexity of TSP. First, we exhibit tractable sub-problems: on the one hand, given two tours T 1 and T 2 , deciding whether T 1 and T 2 are compatible can be done within polynomial time; on the other hand, given an ordering of the n items into the k containers, the optimal tours can also be computed within polynomial time. Note that, to the best of our knowledge, the only family of combinatorial precedence constraints for which constrained TSP has been proven to be in P is the one of PQ-trees, [2]. Finally, in a more prospective way and having in mind the design of approximation algorithms, we study the relationship between optimal value of different TSP problems and the optimal value of kSTSP.

On the Complexity of the Multiple Stack TSP, kSTSP

Lecture Notes in Computer Science, 2009

Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) con... more Given a universal constant k, the multiple Stack Travelling Salesman Problem (kSTSP in short) consists in finding a pickup tour T 1 and a delivery tour T 2 of n items on two distinct graphs. The pickup tour successively stores the items at the top of k containers, whereas the delivery tour successively picks the items at the current top of the containers: thus, the couple of tours are subject to LIFO ("Last In First Out") constraints. This paper aims at finely characterizing the complexity of kSTSP in regards to the complexity of TSP. First, we exhibit tractable sub-problems: on the one hand, given two tours T 1 and T 2 , deciding whether T 1 and T 2 are compatible can be done within polynomial time; on the other hand, given an ordering of the n items into the k containers, the optimal tours can also be computed within polynomial time. Note that, to the best of our knowledge, the only family of combinatorial precedence constraints for which constrained TSP has been proven to be in P is the one of PQ-trees, [2]. Finally, in a more prospective way and having in mind the design of approximation algorithms, we study the relationship between optimal value of different TSP problems and the optimal value of kSTSP.

Effect of draft tube position on the hydrodynamics of a draft tube slurry bubble column

The Chemical Engineering Journal and the Biochemical Engineering Journal, 1995

Two-and three-phase hydrodynanuc studies were conducted m an air lift bubble column with an inter... more Two-and three-phase hydrodynanuc studies were conducted m an air lift bubble column with an internal loop The bubble column had a conical dlstnbutor at the bottom, through which the gas was sparged, creating a hqmd or slurry circulation from the draft tube to the annular region The axial position of the draft tube was vaned with respect to the conical section The expenments were performed with the air-water system at ambient condltlons, usmg sihceous sand as the solid phase When the bottom of the draft tube was located precisely at the transltlon between the conical and cylmdncal regions, no hqmd circulation was observed When the draft tube was located m a lower posltlon, hqmd circulation started and its magmtude increased as the draft tube was further lowered mslde the conical region The results presented indicate that the hydrodynanuc behavlour of these systems can be effectively controlled by varying the axial position of the draft tube

An Effective Evolutionary Algorithm for the Cumulative Capacitated Vehicle Routing Problem

Lecture Notes in Computer Science, 2009

The Cumulative Capacitated Vehicle Routing Problem (or CCVRP) models transportation problems wher... more The Cumulative Capacitated Vehicle Routing Problem (or CCVRP) models transportation problems where the objective is to minimize the sum of arrival times at customers, taking into account capacity limitations. It generalizes the traveling repairman problem (or TRP), by adding capacity constraints and an homogeneous vehicle fleet. This paper presents the first metaheuristic designed for the CCVRP, taking into account specific

A Hybrid Tabu Search for the m-Peripatetic Vehicle Routing Problem

Matheuristics, 2009

This article presents a hybridization of a perfect b-matching within a tabu search framework for ... more This article presents a hybridization of a perfect b-matching within a tabu search framework for the m-Peripatetic Vehicle Routing Problem (m-PVRP). The m-PVRP models for example money transports and cash machines supply where, for security reasons, no path can be used more than once during m periods and the amount of money allowed per vehicle is limited. It consists in finding a set of routes of minimum total cost over m periods from an undirected graph such that each customer is visited exactly once per period and each edge can be used at most once during the m periods. Each route starts and finishes at the depot with a total demand not greater than vehicle capacity. The aim is to minimize the total cost of the routes. The m-PVRP can be considered as a generalization of two well-known NP-hard problems: the vehicle routing problem (VRP or 1-PVRP) and the m-Peripatetic Salesman Problem (m-PSP). Computational results show that the hybrid algorithm obtained improves the tabu search, not only on the m-PVRP in general, but also on the VRP and the m-PSP using classical VRP instances and TSPLIP instances.

An Effective Hybrid Evolutionary Local Search for Orienteering and Team Orienteering Problems with Time Windows

Parallel Problem Solving from Nature, PPSN XI, 2010

Abstract. The orienteering problem (OP) consists in finding an elemen-tary path over a subset of ... more Abstract. The orienteering problem (OP) consists in finding an elemen-tary path over a subset of vertices. Each vertex has associated a profit that is collected on the visitor's first visit. The objective is to maximize the collected profit with respect to a limit on the path's length. The team ...

A label correcting algorithm for the shortest path problem on a multi-modal route network

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012

We consider shortest paths on a multi-modal transportation network where restrictions or preferen... more We consider shortest paths on a multi-modal transportation network where restrictions or preferences on the use of certain modes of transportation may arise. The regular language constraint shortest path problem deals with this kind of problem. It models constraints by using regular languages. The problem can be solved efficiently by using a generalization of Dijkstra's algorithm (D RegLC). Recently a speed-up technique called SDALT has been proposed to speed up D RegLC. In this paper we present a new label correcting algorithm (lcSDALT) which overcomes some limitations of SDALT. We evaluated lcSDALT on a realistic multi-modal transportation network with various modes of transport and road types, including timedependent cost functions on arcs. We observed a speed-up of a factor 3 to 30, with respect to D RegLC and of up to 50% with respect to SDALT, while at the same time reducing memory requirements.

A Memetic Algorithm with Population Management for the Generalized Minimum Vertex-Biconnected Network Problem

2010 International Conference on Intelligent Networking and Collaborative Systems, 2010

We consider the generalized minimum vertexbiconnected network problem (GMVBCNP). Given a graph wh... more We consider the generalized minimum vertexbiconnected network problem (GMVBCNP). Given a graph where nodes are partitioned into clusters, the goal is to find a minimal cost subgraph containing exactly one node from each cluster and satisfying the vertex-biconnectivity constraint. The problem is NP-hard. The GMVBCNP has applications in the design of survivable backbone networks when single component outages are considered. We propose a Memetic Algorithm with two crossover operators, three mutation operators, and a local search component based on two neighborhood structures. Furthermore, two different population management approaches are investigated. Experimental results document the efficiency of the new approach. In particular, the local search component and the population management strategies have a substantial impact on solution quality as well as running time.

A New Heuristic for the Traveling Salesman Problem with Time Windows

Transportation Science, 2000

The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem wit... more The aim of this paper is to present a new heuristic method for the Traveling Salesman Problem with Time Windows, based on the solution of an auxiliary problem. The idea is to solve an assignment problem with an ad hoc objective function to obtain a solution close enough to a feasible solution of the original problem. Given this solution, made by a long main tour containing the depot and few small subtours, it is easy to insert all the subtours into the main path using a greedy insertion procedure. The algorithm described applies the proposed constructive scheme and then uses a local search procedure to improve the initial solution. The computational results show the effectiveness of this approach.

Solving the electricity production planning problem by a column generation based heuristic

Journal of Scheduling, 2012

ABSTRACT This paper presents a heuristic method based on column generation for the EDF (Electrici... more ABSTRACT This paper presents a heuristic method based on column generation for the EDF (Electricité De France) long-term electricity production planning problem proposed as subject of the ROADEF/EURO 2010 Challenge. This is to our knowledge the first-ranked method among those methods based on mathematical programming, and was ranked fourth overall. The problem consists in determining a production plan over the whole time horizon for each thermal power plant of the French electricity company, and for nuclear plants, a schedule of plant outages which are necessary for refueling and maintenance operations. The average cost of the overall outage and production planning, computed over a set of demand scenarios, is to be minimized. The method proceeds in two stages. In the first stage, dates for outages are fixed once for all for each nuclear plant. Data are aggregated with a single average scenario and reduced time steps, and a set-partitioning reformulation of this aggregated problem is solved for fixing outage dates with a heuristic based on column generation. The pricing problem associated with each nuclear plant is a shortest path problem in an appropriately constructed graph. In the second stage, the reload level is determined at each date of an outage, considering now all scenarios. Finally, the production quantities between two outages are optimized for each plant and each scenario by solving independent linear programming problems.

A Metaheuristic to Solve a Location-Routing Problem with Non-Linear Costs

Journal of Heuristics, 2005

Page 1. Journal of Heuristics, 11: 375391, 2005 cс 2005 Springer Science + Business Media, Inc. ... more

An efficient heuristic approach to solve the unate covering problem

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2001

The classical solving approach for two-level logic minimisation reduces the problem to a special ... more The classical solving approach for two-level logic minimisation reduces the problem to a special case of unate covering and attacks the latter with a (possibly limited) branch-and-bound algorithm. We adopt this approach, but we propose a constructive heuristic algorithm that combines the use of Binary Decision Diagrams with the lagrangian relaxation. This technique permits to achieve an effective choice of the elements to include into the solution, as well as cost-related reductions of the problem and a good lower bound on the optimum. The results support the effectiveness of this approach: on a wide set of benchmark problems, the algorithm nearly always hits the optimum, and in most cases proves it to be such. On the problems whose optimum is actually unknown, the best known result is strongly improved.

An effective memetic algorithm for the cumulative capacitated vehicle routing problem

Computers & Operations Research, 2010

The cumulative capacitated vehicle routing problem (CCVRP) is a transportation problem which occu... more The cumulative capacitated vehicle routing problem (CCVRP) is a transportation problem which occurs when the objective is to minimize the sum of arrival times at customers, instead of the classical route length, subject to vehicle capacity constraints. This type of challenges arises whenever priority is given to the satisfaction of the customer need, e.g. vital goods supply or rescue after

A heuristic approach to the overnight security service problem

Computers & Operations Research, 2003

This paper introduces the overnight security service problem. The model obtained is a single-obje... more This paper introduces the overnight security service problem. The model obtained is a single-objective mixed integer programming problem. It is NP-hard in the strong sense, and exact approaches are not practicable when solving real-life instances. Thus, the model is solved heuristically, through a decomposition in two subproblem. The former is a capacitated clustering problem, the latter is a multiple travelling

Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem

Annals of Operations Research, 2006

This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the wel... more This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the well-known Set Covering Problem. The proposed approach is a two-phase heuristic method which has the particularity to be a constructive method using the primal-dual Lagrangian relaxation to solve single objective Set Covering problems. The results show that this algorithm finds several potentially supported and unsupported solutions. A comparison with an exact method (up to a medium size), shows that many Pareto-optimal solutions are retrieved and that the other solutions are well spread and close to the optimal ones. Moreover, the method developed compares favorably with the Pareto Memetic Algorithm proposed by Jaszkiewicz.

A Heuristic for the Vehicle Routing Problem with Time Windows

Journal of Heuristics, 2001

In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Win... more In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical k-opt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective function drives the search out of local optima. No parameter tuning is required

An effective and fast heuristic for the Dial-a-Ride problem

4OR, 2006

Page 1. 4OR (2007) 5:6173 DOI 10.1007/s10288-006-0018-0 REGULAR PAPER An effective and fast heur... more