Showing papers by "Daniele Vigo published in 1999"

Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems

Abstract: Two-dimensional bin packing problems consist of allocating, without overlapping, a given set of small rectangles (items) to a minimum number of large identical rectangles (bins), with the edges of the items parallel to those of the bins. According to the specific application, the items may either have a fixed orientation or they can be rotated by 90°. In addition, it may or not be imposed that the items are obtained through a sequence of edge-to-edge cuts parallel to the edges of the bin. In this article, we consider the class of problems arising from all combinations of the above requirements. We introduce a new heuristic algorithm for each problem in the class, and a unified tabu search approach that is adapted to a specific problem by simply changing the heuristic used to explore the neighborhood. The average performance of the single heuristics and of the tabu search are evaluated through extensive computational experiments.

Theory and Methodology A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls

Abstract: We consider an extension of the capacitated Vehicle Routing Problem (VRP), known as the Vehicle RoutingProblem with Backhauls (VRPB), in which the set of customers is partitioned into two subsets: Linehaul and Backhaulcustomers. Each Linehaul customer requires the delivery of a given quantity of product from the depot, whereas a givenquantity of product must be picked up from each Backhaul customer and transported to the depot. VRPB is known tobe NP-hard in the strong sense, and many heuristic algorithms were proposed for the approximate solution of theproblem with symmetric or Euclidean cost matrices. We present a cluster-first-route-second heuristic which uses a newclustering method and may also be used to solve problems with asymmetric cost matrix. The approach exploits theinformation of the normally infeasible VRPB solutions associated with a lower bound. The bound used is a Lagrangianrelaxation previously proposed by the authors. The final set of feasible routes is built through a modified TravelingSalesman Problem (TSP) heuristic, and inter-route and intra-route arc exchanges. Extensive computational tests onsymmetric and asymmetric instances from the literature show the e•ectiveness of the proposed approach. O 1999Elsevier Science B.V. All rights reserved.Keywords: Vehicle routing; Lagrangian relaxation; Heuristic algorithms; Local search

Bin Packing Approximation Algorithms: Combinatorial Analysis

Abstract: In the classical version of the bin packing problem one is given a list L = (a 1,...,a n ) of items (or elements) and an infinite supply of bins with capacity C. A function s(a i ) gives the size of item a i , and satisfies 0 < s(a i )≤C, 1 ≤ i ≤ n. The problem is to pack the items into a minimum number of bins under the constraint that the sum of the sizes of the items in each bin is no greater than C. In simpler terms, a set of numbers is to be partitioned into a minimum number of blocks subject to a sum constraint common to each block. We use the bin packing terminology, as it eases considerably the problem of describing and analyzing algorithms.

Solution of Large-Scale Railway Crew Planning Problems: the Italian Experience

Abstract: Crew scheduling is a very well known problem which has been historically associated with airlines and mass transit companies; recently railway applications have also come on the scene. This is especially true in Europe, where deregulation and privatization edicts are forcing a re-organization of the rail industry and better productivity and more efficient services are strongly required by the market and the public. Therefore, this sector is showing increasing interest in Operations Research and Management Science. Railway crew planning represents a hard problem due to both the dimensions and the operational/regulation constraints involved. This paper describes the development of a new crew planning system set up by Ferrovie dello Stato SpA (the Italian railway company) in co-operation with the University of Bologna.

Neighborhood Search Algorithm for the Guillotine Non-Oriented Two-Dimensional Bin Packing Problem

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 tabu search approach to the problem, and analyze its average performance through extensive computational testing.