Arnaldo Vieira Moura

Hybrid Column Generation Approaches for Urban Transit Crew Management Problems

This article considers the overall crew management problem arising from the daily operation of an urban transit bus company that serves the metropolitan area of the city of Belo Horizonte, Brazil. Due to its intrinsic complexity, the problem is divided in two distinct subproblems:crew scheduling andcrew rostering. We have investigated each of these problems using mathematical programming (MP) and constraint logic programming (CLP) approaches. In addition, we developed hybrid column generation algorithms for solving these problems, combining MP and CLP. The hybrid algorithms always performed better, when obtaining optimal solutions, than the two previous isolated approaches. In particular, they proved to be much faster for the scheduling problem. All the proposed algorithms have been implemented and tested over real-world data obtained from the aforementioned company. The coefficient matrix of the linear program associated with some instances of the scheduling problem contains tens of millions of columns; this number is even larger for the rostering problem. The analysis of our experiments indicates that it was possible to find high-quality, and many times optimal, solutions that were suitable for the companys needs. These solutions were obtained within reasonable computational times on a desktop PC.

Vehicle and crew scheduling for urban bus lines

A solution to the urban transportation problem is given by vehicle and crew schedules. These schedules must meet the passenger demand and satisfy technical and contractual restrictions stemming from the daily operation of the lines, while optimizing some measure of operational cost. This work describes a computational tool developed to solve the urban transportation problem in the large metropolitan area of Sao Paulo, Brazil. The techniques used are based on integer programming models coupled with heuristics. The former produces good feasible solutions, and the latter improves the quality of the final solutions. While the operational and labor restrictions are specific to the city of Sao Paulo, the same ideas can inspire similar approaches for solving the urban transportation problem arising in other metropolitan areas.

Constructing nurse schedules at large hospitals

Several heuristics, based on evolutive algorithms and local search, are used to solve the nurse scheduling problem at a large hospital. Due to several intricate and specific restrictions imposed on the schedules, the problem is a difficult one to solve by hand. Moreover, some of the restrictions have a subjective value attached to them, and this constrains the use of exact methods that search for global optima. In order to facilitate the use of the solver modules by the hospital staff, a user interface was also implemented.

A hybrid model for a multiproduct pipeline planning and scheduling problem

Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult planning and scheduling problem: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. In spite of being more economical and environmentally safer, the use of a complex pipeline network poses serious operational difficulties related to resource allocation and temporal constraints. The current approaches known from the literature only consider a few types of constraints and restricted topologies, hence they are far from being applicable to real instances from petrobras. We propose a hybrid framework based on a two-phase problem decomposition strategy. A novel Constraint Programming (CP) model plays a key role in modelling operational constraints that are usually overlooked in literature, but that are essential in order to guarantee viable solutions. The full strategy was implemented and produced very adequate results when tested over large real instances.

A GRASP strategy for a more constrained School Timetabling Problem

This work treats a more constrained School Timetabling Problem (STP). It consists of scheduling a set of lectures and teachers in a prefixed period of time, satisfying a set of operational requirements. We applied a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, combined with a path-relinking improvement. During execution of the GRASP heuristic, the local search procedure interleaves two types of movements. In addition, the path-relinking strategy was itself enhanced by a local search procedure. The algorithms were tested with real instances and proved to be good approaches to solve this problem. Although some restrictions are specific to Brazilian educational institutions, the same ideas can inspire similar approaches for solving the STP in other situations.

Planning and Scheduling the Operation of a Very Large Oil Pipeline Network

Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult over-constrained planning challenge: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. In spite of being more economical and environmentally safer, the use of a complex pipeline network poses serious operational difficulties. The network has a complex topology, with around 30 interconnecting pipelines, over 30 different products in circulation, and about 14 distribution depots which harbor more than 200 tanks, with a combined capacity for storing up to 65 million barrels. The problem is how to schedule individual pumping operations, given the daily production and demand of each product, at each location in the network, over a given time horizon. We describe a solution based on a two-phase problem decomposition strategy. A novel Constraint Programming (CP) model plays a key role in modeling operational constraints that are usually overlooked in literature, but that are essential in order to guarantee viable solutions. The use of CP was crucial, since it allowed the modeling of complex constraints, including nonlinearities. The full strategy was implemented and produced very adequate results when tested over large real instances. In contrast, other approaches known from the literature failed, even when applied to much less complex networks.

Generating invariants for non-linear hybrid systems by linear algebraic methods

We describe powerful computational methods, relying on linear algebraic methods, for generating ideals for non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces by encoding the new consecution requirements as specific morphisms represented by matrices. More specifically, we establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our methods also embody a strategy to estimate degree bounds, leading to the discovery of rich classes of inductive, i.e. provable, invariants. Our approach avoids first-order quantifier elimination, Grobner basis computation or direct system resolution, thereby circumventing difficulties met by other recent techniques.

A Hybrid Approach for Solving Large Scale Crew Scheduling Problems

We consider several strategies for computing optimal solutions to large scale crew scheduling problems. Provably optimal solutions for very large real instances of such problems were computed using a hybrid approach that integrates mathematical and constraint programming techniques. The declarative nature of the latter proved instrumen- tal when modeling complex problem restrictions and, particularly, in efficiently searching the very large space of feasible solutions. The code was tested on real problem instances, containing an excess of 1:8 x 109 entries, which were solved to optimality in an acceptable running time when executing on a typical desktop PC.

Solving very large crew scheduling problems to optimality

In this article, we present a hybrid methodology for the exact solution of large scale real world crew scheduling problems. Our approach integrates mathematical programming and constraint satisfaction techniques, taking advantage of their particular abilities in modeling and solving specific parts of the problem. An Integer Programming framework was responsible for guiding the overall search process and for obtaining lower bounds on the value of the optimal solution. Complex constraints were easily expressed, in a declarative way, using a Constraint Logic Programming language. Moreover, with an effective constraint-based model, the huge space of feasible solutions could be implicitly considered in a fairly efficient way. Our code was tested on real problem instances arising from the daily operation of an ordinary urban transit company that serves a major metropolitan area with an excess of two million inhabitants. Using a typical desktop PC, we were able find, in an acceptable running time, an optimal solution to instances with more than 1.5 billion entries.

Transcendental inductive invariants generation for non-linear differential and hybrid systems

We present the first verification methods that automatically generate bases of invariants expressed by multivariate formal power series and transcendental functions. We discuss the convergence of solutions generated over hybrid systems that exhibit non-linear models augmented with parameters. We reduce the invariant generation problem to linear algebraic matrix systems, from which one can provide effective methods for solving the original problem. We obtain very general sufficient conditions for the existence and the computation of formal power series invariants over multivariate polynomial continuous differential systems. The formal power series invariants generated are often composed by the expansion of some well-known transcendental functions like log or exp and have an analysable closed-form. This facilitates their use to verify safety properties. Moreover, we generate inequality and equality invariants. Our examples, dealing with non-linear continuous evolution similar to those present today in many critical hybrid embedded systems, show the strength of our results and prove that some of them are beyond the limits of other recent approaches.