We consider problems requiring to allocate a set of rectangular items to larger rectangular stand... more We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width, and the objective is to pack all the items within the minimum height.
MIC-97: meta-heuristics international …, Jan 1, 1999
Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an... more Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an unlimited number of identical rectangular large stock pieces. We consider the problem of determining the guillotine-cuttable patterns that provide all the pieces, such that the total number of required stock pieces is minimized. We show how some classical greedy algorithms given in the literature for the case where no rotation is allowed can be adapted to our problem; in addition, an original heuristic algorithm is presented. We then introduce a ...
Abstract In the three-dimensional bin packing problem the task is to orthogonally pack a given se... more Abstract In the three-dimensional bin packing problem the task is to orthogonally pack a given set of rectangular items into a minimum number of three-dimensional rectangular bins. We give a characterization of the algorithm proposed by Martello et al.(2000) for the exact solution of the problem, showing that not all orthogonal packings can be generated by the proposed algorithm. The packings, however, have the property of being robot packings, which is relevant in practical settings. References to the modified algorithm, which solves ...
Abstract The solution of a vehicle routing problem calls for the determination of a set of routes... more Abstract The solution of a vehicle routing problem calls for the determination of a set of routes, each performed by a single vehicle which starts and ends at its own depot, such that all the requirements of the customers are fulfilled and the global transportation cost is ...
Abstract In this paper we consider the minimum makespan Open Shop problem without preemption. It ... more Abstract In this paper we consider the minimum makespan Open Shop problem without preemption. It is well-known that the case with only two machines can be optimally solved in linear time, whereas the problem with an arbitrary number of machines is NP-hard in the ...
Constraint Programming techniques have been successfully applied to several combinatorial optimiz... more Constraint Programming techniques have been successfully applied to several combinatorial optimization problems. One of their advantages is the availability of complex global constraints performing efficient propagation and interacting with each other through shared variables. However, Constraint Programming techniques have shown their limitations in dealing with objective functions, since they are usually able to prune only few levels of the search tree when most decision variables have been already instantiated. In ...
Chapter 8 VRP with Backhauls Paolo Toth Daniele Vigo 8.1 Introduction In this chapter we consider... more Chapter 8 VRP with Backhauls Paolo Toth Daniele Vigo 8.1 Introduction In this chapter we consider the VRP with Backhauls (VRPB), also known as the linehaul-backhaul problem, an extension of the Capacitated VRP (CVRP) where the customer set is partitioned into two subsets. ...
We consider problems requiring to allocate a set of rectangular items to larger rectangular stand... more We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width, and the objective is to pack all the items within the minimum height.
MIC-97: meta-heuristics international …, Jan 1, 1999
Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an... more Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an unlimited number of identical rectangular large stock pieces. We consider the problem of determining the guillotine-cuttable patterns that provide all the pieces, such that the total number of required stock pieces is minimized. We show how some classical greedy algorithms given in the literature for the case where no rotation is allowed can be adapted to our problem; in addition, an original heuristic algorithm is presented. We then introduce a ...
Abstract In the three-dimensional bin packing problem the task is to orthogonally pack a given se... more Abstract In the three-dimensional bin packing problem the task is to orthogonally pack a given set of rectangular items into a minimum number of three-dimensional rectangular bins. We give a characterization of the algorithm proposed by Martello et al.(2000) for the exact solution of the problem, showing that not all orthogonal packings can be generated by the proposed algorithm. The packings, however, have the property of being robot packings, which is relevant in practical settings. References to the modified algorithm, which solves ...
Abstract The solution of a vehicle routing problem calls for the determination of a set of routes... more Abstract The solution of a vehicle routing problem calls for the determination of a set of routes, each performed by a single vehicle which starts and ends at its own depot, such that all the requirements of the customers are fulfilled and the global transportation cost is ...
Abstract In this paper we consider the minimum makespan Open Shop problem without preemption. It ... more Abstract In this paper we consider the minimum makespan Open Shop problem without preemption. It is well-known that the case with only two machines can be optimally solved in linear time, whereas the problem with an arbitrary number of machines is NP-hard in the ...
Constraint Programming techniques have been successfully applied to several combinatorial optimiz... more Constraint Programming techniques have been successfully applied to several combinatorial optimization problems. One of their advantages is the availability of complex global constraints performing efficient propagation and interacting with each other through shared variables. However, Constraint Programming techniques have shown their limitations in dealing with objective functions, since they are usually able to prune only few levels of the search tree when most decision variables have been already instantiated. In ...
Chapter 8 VRP with Backhauls Paolo Toth Daniele Vigo 8.1 Introduction In this chapter we consider... more Chapter 8 VRP with Backhauls Paolo Toth Daniele Vigo 8.1 Introduction In this chapter we consider the VRP with Backhauls (VRPB), also known as the linehaul-backhaul problem, an extension of the Capacitated VRP (CVRP) where the customer set is partitioned into two subsets. ...
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