Fabrizio Rossi

Sequence Finishing and Mapping of Drosophila melanogaster Heterochromatin

Genome sequences for most metazoans and plants are incomplete because of the presence of repeated DNA in the heterochromatin. The heterochromatic regions of Drosophila melanogaster contain 20 million bases (Mb) of sequence amenable to mapping, sequence assembly, and finishing. We describe the generation of 15 Mb of finished or improved heterochromatic sequence with the use of available clone resources and assembly methods. We also constructed a bacterial artificial chromosome–based physical map that spans 13 Mb of the pericentromeric heterochromatin and a cytogenetic map that positions 11 Mb in specific chromosomal locations. We have approached a complete assembly and mapping of the nonsatellite component of Drosophila heterochromatin. The strategy we describe is also applicable to generating substantially more information about heterochromatin in other species, including humans.

Orbital branching

We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symmetry remaining in the problem after branching, including symmetry that is not present at the root node. These groups of equivalent variables, called orbits, are used to create a valid partitioning of the feasible region that significantly reduces the effects of symmetry while still allowing a flexible branching rule. We also show how to exploit the symmetries present in the problem to fix variables throughout the branch-and-bound tree. Orbital branching can easily be incorporated into standard integer programming software. Through an empirical study on a test suite of symmetric integer programs, the question as to the most effective orbit on which to base the branching decision is investigated. The resulting method is shown to be quite competitive with a similar method known as isomorphism pruning and significantly better than a state-of-the-art commercial solver on symmetric integer programs.

A Lagrangian heuristic for satellite range scheduling with resource constraints

The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred.We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques.To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems.

Scheduling of flexible flow lines in an automobile assembly plant

This paper deals with the material flow management in a large-scale manufacturing process, namely the assembly of automobiles in a highly automated plant in Italy. After a detailed description of the plant from the viewpoint of material flow issues, the modeling process and the methodologies employed to address the problems are illustrated. The decision models were validated by means of simulations of the real plant in several different production scenarios (varying demand volume and mix, resource availability etc.).

A branch-and-cut algorithm for the maximum cardinality stable set problem

We propose a branch-and-cut algorithm for the Maximum Cardinality Stable Set problem. Rank constraints of general structure are generated by executing clique separation algorithms on a modified graph obtained with edge projections. A branching scheme exploiting the available inequalities is also introduced. A computational experience on the DIMACS benchmark graphs validates the effectiveness of the approach.

Constraint orbital branching

Orbital branching is a method for branching on variables in integer programming that reduces the likelihood of evaluating redundant, isomorphic nodes in the branch-and-bound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an arbitrary constraint. Many important families of integer programs are structured such that small instances from the family are embedded in larger instances. This structural information can be exploited to define a group of strong constraints on which to base the orbital branching disjunction. The symmetric nature of the problems is further exploited by enumerating non-isomorphic solutions to instances of the small family and using these solutions to create a collection of typically easy-to-solve integer programs. The solution of each integer program in the collection is equivalent to solving the original large instance. The effectiveness of this methodology is demonstrated by computing the optimal incidence width of Steiner Triple Systems and minimum cardinality covering designs.

Orbital Branching

We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symmetry remaining in the problem after branching, including symmetry which is not present at the root node. These groups of equivalent variables, called orbits, are used to create a valid partitioning of the feasible region which significantly reduces the effects of symmetry while still allowing a flexible branching rule. We also show how to exploit the symmetries present in the problem to fix variables throughout the branch-and-bound tree. Orbital branching can easily be incorporated into standard IP software. Through an empirical study on a test suite of symmetric integer programs, the question as to the most effective orbit on which to base the branching decision is investigated. The resulting method is shown to be quite competitive with a similar method known as isomorphism pruningand significantly better than a state-of-the-art commercial solver on symmetric integer programs.

The Network Packing Problem in Terrestrial Broadcasting

The introduction of digital terrestrial broadcasting all over Europe requires a complete and challenging replanning of in-place analog systems. However, an abrupt migration of resources (transmitters and frequencies) from analog to digital networks cannot be accomplished because the analog services must be preserved temporarily. Hence, a multiobjective problem arises, in which several networks sharing a common set of resources have to be designed. This problem is referred to as the network packing problem. In Italy, this problem is particularly challenging because of a large number of transmitters, orographical features, and strict requirements imposed by Italian law. In this paper, we report our experience in developing solution methods at the major Italian broadcaster Radiotelevisione Italiana (RAI S.p.A.). We propose a two-stage heuristic. In the first stage, emission powers are assigned to each network separately. In the second stage, frequencies are assigned to all networks so as to minimize the loss from mutual interference. A software tool incorporating our methodology is currently in use at RAI to help discover and select high-quality alternatives for the deployment of digital equipment.

Batch scheduling in a two-machine flow shop with limited buffer

This paper deals with the problem of makespan minimization in a flow shop with two machines when the input buffer of the second machine can only host a limited number c of parts. This problem has been shown to be NP-hard for any c > 0 and c < n-1, where n is the number of jobs, by Papadimitriou and Kanellakis (1980). Here we analyze the problem in the context of batch processing, i.e., when identical parts must be processed consecutively. Each set of identical parts forms a batch. The number of parts in the batch is the size of the batch. We first prove that, if the size of the i-th batch is larger than a value b i *, then the makespan minimization problem can be formulated as a special case of TSP and solved in polynomial time. The cost structure of this TSP generalizes the one defined for the two machine no-wait flow shop, i.e., when c=0. However, when the same algorithm is applied to batch sizes smaller than b i * the error goes to zero as the batch sizes approach the values b i *. Hence, we give a closed form expression for b i *.

A set packing model for the ground holding problem in congested networks

Abstract Air traffic flow management (ATFM) consists of several activities performed by control authorities in order to reduce delays due to traffic congestion. Ground holding decisions restrict certain flights from tacking off at the scheduled departure time if congestion is expected at the destination airport. They are motivated by the fact that it is safer to hold an aircraft on the ground than in the air. Several integer linear programming models have been proposed to efficiently solve the ground holding problem (GHP). In this paper we investigate a set packing formulation of the GHP and design a branch-and-cut algorithm to solve the problem in high congestion scenarios, i.e., when lack of capacity induces flights cancellation. The constraint generation is carried out by heuristically solving the separation problem associated with a large class of rank inequalities. This procedure exploits the special structure of the GHPs intersection graphs. The computational results indicate that the proposed algorithm outperforms other algorithms in which flight cancellation has been allowed.