In this paper we consider an integrated berth allocation and quay crane assignment and scheduling... more In this paper we consider an integrated berth allocation and quay crane assignment and scheduling problem motivated by a real case where a heterogeneous set of cranes is considered. A first mathematical model based on the relative position formulation (RPF) for the berth allocation aspects is presented. Then, a new model is introduced to avoid the big-M constraints included in the RPF. This model results from a discretization of the time and space variables. For the new discretized model several enhancements, such as valid inequalities, are introduced. In order to derive good feasible solutions, a rolling horizon heuristic (RHH) is presented. A branch and cut approach that uses the enhanced discretized model and incorporates the upper bounds provided by the RHH solution is proposed. Computational tests are reported to show (i) the quality of the linear relaxation of the enhanced models; (ii) the effectiveness of the exact approach to solve to optimality a set of real instances; and (iii) the scalability of the RHH based on the enhanced mathematical model which is able to provide good feasible solutions for large size instances.
Proximity search is an iterative method to solve complex mathematical programming problems. At ea... more Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by the Hamming distance function to a given solution, and a cutoff constraint is added to impose that any new obtained solution improves the objective function value. A mixed integer programming solver is used to find a feasible solution to this modified problem, yielding an improved solution to the original problem. This paper introduces the concept of weighted Hamming distance that allows to design a new method called weighted proximity search. In this new distance function, low weights are associated with the variables whose value in the current solution is promising to change in order to find an improved solution, while high weights are assigned to variables that are expected to remain unchanged. The weights help to distinguish between alternative solutions in the neighborhood of the current solution, and provide...
We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical... more We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical results are established to compare upper bounds obtained from different techniques, including bounds from quadratic programming, Lagrangian relaxation and integer programming. This general problem includes well-known subproblems as particular cases of k. In this paper we focus on two particular cases. The case k = 1 which is the maximal cardinality strong-matching and the case of finding the maximal cardinality family of induced cycles (k = 2). For each one of the two cases, combinatorial algorithms are presented to solve the problem when graphs have particular structures and polyhedral descriptions of the convex hull of the corresponding feasible set are given. Computational tests are reported to compare the different upper bounds with the optimal values for different values of k, and to test the effectiveness of the inequalities introduced.
We consider a wireless network where a given set of stations is continuously generating informati... more We consider a wireless network where a given set of stations is continuously generating information. A single vehicle, located at a base station, is available to collect the information via wireless transfer. The wireless transfer vehicle routing problem (WTVRP) is to decide which stations should be visited in the vehicle route, how long shall the vehicle stay in each station, and how much information shall be transferred from the nearby stations to the vehicle during each stay. The goal is to collect the maximum amount of information during a time period after which the vehicle returns to the base station. The WTVRP is NP-hard. Although it can be solved to optimality for small size instances, one needs to rely on good heuristic schemes to obtain good solutions for large size instances. In this work, we consider a mathematical formulation based on the vehicle visits. Several heuristics strategies are proposed, most of them based on the mathematical model. These strategies include constructive and improvement heuristics. Computational experiments show that a strategy that combines a combinatorial greedy heuristic to design a initial vehicle route, improved by a fix-and-optimize heuristic to provide a local optimum, followed by an exchange heuristic, affords good solutions within reasonable amount of running time.
e onsider single produt mritime inventory routing prolem in whih the prodution nd onsumption rtes... more e onsider single produt mritime inventory routing prolem in whih the prodution nd onsumption rtes re onstnt over the plnning horizonF he prolem involves heterogeneous)eet nd multiple prodution nd onsumption ports with limited storge pityF writime trnsporttion is hrterized y high levels of unertintyD nd siling times n e severely in)uened y vrying nd unpreditle wether onditionsF o del with the unertintyD this pper investigtes the use of dptle roust optimizE tion where the siling times re ssumed to elong to the wellEknown udget polytope unertinty setF sn the reourse modelD the routingD the order of port visitsD nd the quntities to lod nd unlod re (xed efore the unertinty is reveledD while the visit time to ports nd the stok levels n e djusted to the senrioF e propose deomposition lgorithm tht itertes etween mster prolem tht onsiders suset of senrios nd n dversril seprtion prolem tht serhes for senrios tht mke the solution from the mster prolem infesileF everl improvement strtegies re proposed iming t reduing the running time of the mster prolem nd reduing the numer of itertions of the deomposition lgorithmF en iterted lol serh heuristi is lso introdued to improve the deomposition lgorithmF e omputtionl study is reported sed on set of rel instnesF
We consider a stochastic single item production-inventory-routing problem with a single producer,... more We consider a stochastic single item production-inventory-routing problem with a single producer, multiple clients and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then the candidate solutions are tested on a larger sample and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the rststage decision variables are xed and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.
International Transactions in Operational Research
The Distance Geometry Problem (DGP) consists in finding an embedding in a metric space of a given... more The Distance Geometry Problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming models (IP) and a constraint programming (CP) approach are presented to test feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities and the CP approach is improved with the use of an algorithm to perform a domain reduction. The main motivation to this work is to derive new pruning devices within branch and prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.
The p-median problem seeks for the location of p facilities on the vertices (customers) of a grap... more The p-median problem seeks for the location of p facilities on the vertices (customers) of a graph to minimize the sum of transportation costs for satisfying the demands of the customers from the facilities. In many real applications of the p-median problem the underlying graph is disconnected. That is the case of p-median problem defined over split administrative regions or regions geographically apart (e.g. archipelagos), and the case of problems coming from industry such as the optimal diversity management problem. In such cases the problem can be decomposed into smaller p-median problems which are solved in each component k for different feasible values of p k , and the global solution is obtained by finding the best combination of p k medians. This approach has the advantage that it permits to solve larger instances since only the sizes of the connected components are important and not the size of the whole graph. However, since the optimal number of facilities to select from each component is not known, it is necessary to solve p-median problems for every feasible number of facilities on each component. In this paper we give a decomposition algorithm that uses a procedure to reduce the number of subproblems to solve. Computational tests on real instances of the optimal diversity management problem and on simulated instances are reported showing that the reduction of subproblems is significant, and that optimal solutions were found within reasonable time.
In this paper we consider an integrated berth allocation and quay crane assignment and scheduling... more In this paper we consider an integrated berth allocation and quay crane assignment and scheduling problem motivated by a real case where a heterogeneous set of cranes is considered. A first mathematical model based on the relative position formulation (RPF) for the berth allocation aspects is presented. Then, a new model is introduced to avoid the big-M constraints included in the RPF. This model results from a discretization of the time and space variables. For the new discretized model several enhancements, such as valid inequalities, are introduced. In order to derive good feasible solutions, a rolling horizon heuristic (RHH) is presented. A branch and cut approach that uses the enhanced discretized model and incorporates the upper bounds provided by the RHH solution is proposed. Computational tests are reported to show (i) the quality of the linear relaxation of the enhanced models; (ii) the effectiveness of the exact approach to solve to optimality a set of real instances; and (iii) the scalability of the RHH based on the enhanced mathematical model which is able to provide good feasible solutions for large size instances.
Proximity search is an iterative method to solve complex mathematical programming problems. At ea... more Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by the Hamming distance function to a given solution, and a cutoff constraint is added to impose that any new obtained solution improves the objective function value. A mixed integer programming solver is used to find a feasible solution to this modified problem, yielding an improved solution to the original problem. This paper introduces the concept of weighted Hamming distance that allows to design a new method called weighted proximity search. In this new distance function, low weights are associated with the variables whose value in the current solution is promising to change in order to find an improved solution, while high weights are assigned to variables that are expected to remain unchanged. The weights help to distinguish between alternative solutions in the neighborhood of the current solution, and provide...
We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical... more We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical results are established to compare upper bounds obtained from different techniques, including bounds from quadratic programming, Lagrangian relaxation and integer programming. This general problem includes well-known subproblems as particular cases of k. In this paper we focus on two particular cases. The case k = 1 which is the maximal cardinality strong-matching and the case of finding the maximal cardinality family of induced cycles (k = 2). For each one of the two cases, combinatorial algorithms are presented to solve the problem when graphs have particular structures and polyhedral descriptions of the convex hull of the corresponding feasible set are given. Computational tests are reported to compare the different upper bounds with the optimal values for different values of k, and to test the effectiveness of the inequalities introduced.
We consider a wireless network where a given set of stations is continuously generating informati... more We consider a wireless network where a given set of stations is continuously generating information. A single vehicle, located at a base station, is available to collect the information via wireless transfer. The wireless transfer vehicle routing problem (WTVRP) is to decide which stations should be visited in the vehicle route, how long shall the vehicle stay in each station, and how much information shall be transferred from the nearby stations to the vehicle during each stay. The goal is to collect the maximum amount of information during a time period after which the vehicle returns to the base station. The WTVRP is NP-hard. Although it can be solved to optimality for small size instances, one needs to rely on good heuristic schemes to obtain good solutions for large size instances. In this work, we consider a mathematical formulation based on the vehicle visits. Several heuristics strategies are proposed, most of them based on the mathematical model. These strategies include constructive and improvement heuristics. Computational experiments show that a strategy that combines a combinatorial greedy heuristic to design a initial vehicle route, improved by a fix-and-optimize heuristic to provide a local optimum, followed by an exchange heuristic, affords good solutions within reasonable amount of running time.
e onsider single produt mritime inventory routing prolem in whih the prodution nd onsumption rtes... more e onsider single produt mritime inventory routing prolem in whih the prodution nd onsumption rtes re onstnt over the plnning horizonF he prolem involves heterogeneous)eet nd multiple prodution nd onsumption ports with limited storge pityF writime trnsporttion is hrterized y high levels of unertintyD nd siling times n e severely in)uened y vrying nd unpreditle wether onditionsF o del with the unertintyD this pper investigtes the use of dptle roust optimizE tion where the siling times re ssumed to elong to the wellEknown udget polytope unertinty setF sn the reourse modelD the routingD the order of port visitsD nd the quntities to lod nd unlod re (xed efore the unertinty is reveledD while the visit time to ports nd the stok levels n e djusted to the senrioF e propose deomposition lgorithm tht itertes etween mster prolem tht onsiders suset of senrios nd n dversril seprtion prolem tht serhes for senrios tht mke the solution from the mster prolem infesileF everl improvement strtegies re proposed iming t reduing the running time of the mster prolem nd reduing the numer of itertions of the deomposition lgorithmF en iterted lol serh heuristi is lso introdued to improve the deomposition lgorithmF e omputtionl study is reported sed on set of rel instnesF
We consider a stochastic single item production-inventory-routing problem with a single producer,... more We consider a stochastic single item production-inventory-routing problem with a single producer, multiple clients and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then the candidate solutions are tested on a larger sample and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the rststage decision variables are xed and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.
International Transactions in Operational Research
The Distance Geometry Problem (DGP) consists in finding an embedding in a metric space of a given... more The Distance Geometry Problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming models (IP) and a constraint programming (CP) approach are presented to test feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities and the CP approach is improved with the use of an algorithm to perform a domain reduction. The main motivation to this work is to derive new pruning devices within branch and prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.
The p-median problem seeks for the location of p facilities on the vertices (customers) of a grap... more The p-median problem seeks for the location of p facilities on the vertices (customers) of a graph to minimize the sum of transportation costs for satisfying the demands of the customers from the facilities. In many real applications of the p-median problem the underlying graph is disconnected. That is the case of p-median problem defined over split administrative regions or regions geographically apart (e.g. archipelagos), and the case of problems coming from industry such as the optimal diversity management problem. In such cases the problem can be decomposed into smaller p-median problems which are solved in each component k for different feasible values of p k , and the global solution is obtained by finding the best combination of p k medians. This approach has the advantage that it permits to solve larger instances since only the sizes of the connected components are important and not the size of the whole graph. However, since the optimal number of facilities to select from each component is not known, it is necessary to solve p-median problems for every feasible number of facilities on each component. In this paper we give a decomposition algorithm that uses a procedure to reduce the number of subproblems to solve. Computational tests on real instances of the optimal diversity management problem and on simulated instances are reported showing that the reduction of subproblems is significant, and that optimal solutions were found within reasonable time.
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Papers by Agostinho Agra