Rafael Andrade - Academia.edu (original) (raw)
Papers by Rafael Andrade
Computers & Operations Research, 2017
This work deals with a class of problems under interval data uncertainty, namely interval robusth... more This work deals with a class of problems under interval data uncertainty, namely interval robusthard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-ofthe-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.
Management Science, Sep 1, 2006
In this paper we present branch-and-bound (B&B) strategies for two-stage stochast... more In this paper we present branch-and-bound (B&B) strategies for two-stage stochastic integer network design-based models with integrality constraints in the first-stage variables. These strategies are used within L-shaped decomposition-based B&B framework. We propose a valid ...
Electronic Notes in Discrete Mathematics, 2016
Networks, 2015
ABSTRACT In this article, we investigate the stochastic maximum weight forest problem. We present... more ABSTRACT In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some insight about the complexity of this problem. We introduce an L-shaped decomposition approach for the polynomial formulation, thus allowing the optimal solution of large scale instances with up to 90 nodes. Finally, we propose a Kruskal based variable neighborhood search (VNS) metaheuristic to compute near optimal solutions with significantly less computational effort. Our numerical results show that the VNS approach provides tight near optimal solutions with a gap less than 1% for most of the instances. © 2015 Wiley Periodicals, Inc. NETWORKS, 2015
Electronic Notes in Discrete Mathematics, 2013
ABSTRACT Let G=(V,ED∪ES)G=(V,ED∪ES) be a non directed graph with set of nodes V and set of weight... more ABSTRACT Let G=(V,ED∪ES)G=(V,ED∪ES) be a non directed graph with set of nodes V and set of weighted edges ED∪ESED∪ES. The edges in EDED and ESES have deterministic and uncertain weights, respectively, with ED∩ES=∅ED∩ES=∅. Let S={1,2,⋯,P}S={1,2,⋯,P} be a given set of scenarios for the uncertain weights of the edges in ESES. The stochastic maximum weight forest (SMWF) problem consists in determining a forest of G, one for each scenario s∈Ss∈S, sharing the same deterministic edges and maximizing the sum of the deterministic weights plus the expected weight over all scenarios associated with the uncertain edges. In this work we present two formulations for this problem. The first model has an exponential number of constraints, while the second one is a new compact extended formulation based on a new theorem characterizing forests in graphs. We give a proof of the correctness of the new formulation. It generalizes existing related models from the literature for the spanning tree polytope. Preliminary results evidence that the SMWF problem can be NP-hard.
Discrete Applied Mathematics, 2006
In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanni... more In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanning tree problem. The heuristic uses Lagrangian relaxation information to guide the construction of feasible solutions to the problem. The scheme operates, within a Lagrangian relaxation ...
Computational Optimization and Applications, 2000
The expansion of telecommunication services has increased the number of users sharing network res... more The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona's volume approach and the Benders decomposition.
Annals of Operations Research, 2012
ABSTRACT The problem of designing high speed networks using different modules of link capacities,... more ABSTRACT The problem of designing high speed networks using different modules of link capacities, in the same model, in order to meet uncertain demands obtained from different probability distribution functions (PDF) is a very hard and challenging real network design problem. The novelty of the new model, compared to previous ones, is to allow installing more than one module per link having equal or different capacities. Moreover, the scenarios of traffic can be generated, according to practical observations, from the main classes of uncertain demands (multi-service) simulated from different PDFs, including heavy tailed ones. These classes of traffic are considered simultaneously for the scenario generation, different from related works in the literature that use only one probability distribution function to simulate the scenarios of traffic. In this work we present the problem formulation and report computational results using branch-and-bound and L-shaped decomposition solution approaches. We consider in the same model up to three different types of modular capacities (multi-facility), since it seems that using more than this can lead to an intractable model. The objective is to minimize penalty (in case of unmet demands) and investment costs. We obtain confidence intervals (with 95% of covering rate) on the expected optimal solution value for the resulting two-stage stochastic integer-modular problem and discuss when they are meaningful. Numerical experiments show that our model can handle up to medium real size instances.
Annals of Operations Research, 2005
The purpose of this paper is to investigate branch and bound strategies and the comparison of bra... more The purpose of this paper is to investigate branch and bound strategies and the comparison of branch and cut with pure branch and bound approaches on high speed telecommunication network design under uncertainty. We model the problem as a two-stage stochastic program with discrete first-stage (investment) variables. Two formulations of the problem are used. The first one with general integer investment variables and the second one, a variant of the first model, with 0-1 investment variables. We present computational results for three solution approaches: the integer L-shaped (Benders) decomposition, a branch and bound framework and a disjunctive cutting plane method.
Computers & Operations Research, 2017
This work deals with a class of problems under interval data uncertainty, namely interval robusth... more This work deals with a class of problems under interval data uncertainty, namely interval robusthard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-ofthe-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.
Management Science, Sep 1, 2006
In this paper we present branch-and-bound (B&B) strategies for two-stage stochast... more In this paper we present branch-and-bound (B&B) strategies for two-stage stochastic integer network design-based models with integrality constraints in the first-stage variables. These strategies are used within L-shaped decomposition-based B&B framework. We propose a valid ...
Electronic Notes in Discrete Mathematics, 2016
Networks, 2015
ABSTRACT In this article, we investigate the stochastic maximum weight forest problem. We present... more ABSTRACT In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some insight about the complexity of this problem. We introduce an L-shaped decomposition approach for the polynomial formulation, thus allowing the optimal solution of large scale instances with up to 90 nodes. Finally, we propose a Kruskal based variable neighborhood search (VNS) metaheuristic to compute near optimal solutions with significantly less computational effort. Our numerical results show that the VNS approach provides tight near optimal solutions with a gap less than 1% for most of the instances. © 2015 Wiley Periodicals, Inc. NETWORKS, 2015
Electronic Notes in Discrete Mathematics, 2013
ABSTRACT Let G=(V,ED∪ES)G=(V,ED∪ES) be a non directed graph with set of nodes V and set of weight... more ABSTRACT Let G=(V,ED∪ES)G=(V,ED∪ES) be a non directed graph with set of nodes V and set of weighted edges ED∪ESED∪ES. The edges in EDED and ESES have deterministic and uncertain weights, respectively, with ED∩ES=∅ED∩ES=∅. Let S={1,2,⋯,P}S={1,2,⋯,P} be a given set of scenarios for the uncertain weights of the edges in ESES. The stochastic maximum weight forest (SMWF) problem consists in determining a forest of G, one for each scenario s∈Ss∈S, sharing the same deterministic edges and maximizing the sum of the deterministic weights plus the expected weight over all scenarios associated with the uncertain edges. In this work we present two formulations for this problem. The first model has an exponential number of constraints, while the second one is a new compact extended formulation based on a new theorem characterizing forests in graphs. We give a proof of the correctness of the new formulation. It generalizes existing related models from the literature for the spanning tree polytope. Preliminary results evidence that the SMWF problem can be NP-hard.
Discrete Applied Mathematics, 2006
In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanni... more In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanning tree problem. The heuristic uses Lagrangian relaxation information to guide the construction of feasible solutions to the problem. The scheme operates, within a Lagrangian relaxation ...
Computational Optimization and Applications, 2000
The expansion of telecommunication services has increased the number of users sharing network res... more The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona's volume approach and the Benders decomposition.
Annals of Operations Research, 2012
ABSTRACT The problem of designing high speed networks using different modules of link capacities,... more ABSTRACT The problem of designing high speed networks using different modules of link capacities, in the same model, in order to meet uncertain demands obtained from different probability distribution functions (PDF) is a very hard and challenging real network design problem. The novelty of the new model, compared to previous ones, is to allow installing more than one module per link having equal or different capacities. Moreover, the scenarios of traffic can be generated, according to practical observations, from the main classes of uncertain demands (multi-service) simulated from different PDFs, including heavy tailed ones. These classes of traffic are considered simultaneously for the scenario generation, different from related works in the literature that use only one probability distribution function to simulate the scenarios of traffic. In this work we present the problem formulation and report computational results using branch-and-bound and L-shaped decomposition solution approaches. We consider in the same model up to three different types of modular capacities (multi-facility), since it seems that using more than this can lead to an intractable model. The objective is to minimize penalty (in case of unmet demands) and investment costs. We obtain confidence intervals (with 95% of covering rate) on the expected optimal solution value for the resulting two-stage stochastic integer-modular problem and discuss when they are meaningful. Numerical experiments show that our model can handle up to medium real size instances.
Annals of Operations Research, 2005
The purpose of this paper is to investigate branch and bound strategies and the comparison of bra... more The purpose of this paper is to investigate branch and bound strategies and the comparison of branch and cut with pure branch and bound approaches on high speed telecommunication network design under uncertainty. We model the problem as a two-stage stochastic program with discrete first-stage (investment) variables. Two formulations of the problem are used. The first one with general integer investment variables and the second one, a variant of the first model, with 0-1 investment variables. We present computational results for three solution approaches: the integer L-shaped (Benders) decomposition, a branch and bound framework and a disjunctive cutting plane method.