Catálogo de publicaciones - libros

The minimal Steiner tree problem is a classical NP-complete problem that has several applications in the communication and transportation sectors. It has recently emerged as a subproblem in decomposition techniques such as column generation and Lagrangian schemes. This has set new computational challenges to the state of the art solving approaches. Our goal is to improve on existing branch-and-cut algorithms so that our approach successfully serves as a fast subproblem solver in a decomposition context. Compared with existing literature, our technical contributions include 1) a new preflow-push cutting strategy, revisiting a little known graph algorithm, that halves the runtime of the separation step, and 2) a branching scheme that fairly balances the search tree and speeds up the search. An evaluation in a multicast design application shows that the algorithm enhances a column generation hybrid. Moreover, our approach offers a significant speedup factor on a publicly available set of challenging Steiner tree benchmarks.

The Employee Timetabling Problem (ETP) is a general class of problems widely encountered in service organizations (such as call centers for instance). Given a set of activities, a set of demand curves (specifying the demand in terms of employees for each activity for each time period) the problem consists of constructing a set of work shifts such that each activity is at all time covered by a sufficient number of employees. Work shifts can cover many activities and must meet work regulations such as breaks, meals and maximum working time constraints. Furthermore, it is often desired to optimize a global objective function such as minimizing labor costs or maximizing a quality of service measure. This paper presents variants of this problem which are modeled with the Dantzig formulation. This approach consists of first generating all feasible work shifts and then selecting the optimal set. We propose to address the shift generation problem with constraint satisfaction techniques based on expressive and efficient global constraints such as and . The selection problem, which is modeled with an integer linear program, is solved by a standard MIP solver for smaller instances and addressed by column generation for larger ones. Since a column generation procedure needs to generate only shifts of negative reduced cost, the optimization constraint is introduced and described. Preliminary experimental results are given on a typical ETP.

The scheduling of social golfers has attracted significant attention in recent years because of its highly symmetrical and combinatorial nature. In particular, it has become one of the standard benchmarks for symmetry breaking in constraint programming. This paper presents a very effective, local search, algorithm for scheduling social golfers. The algorithm find the first known solutions to 11 instances and matches, or improves, state-of-the-art results from constraint programming on all but 3 instances. Moreover, most instances of the social golfers are solved within a couple of seconds. Interestingly, the algorithm does not incorporate any symmetry-breaking scheme and illustrates the nice complementarity between constraint programming and local search on this scheduling application.

We propose a natural generalization of arc-consistency, which we call multiconsistency: A value in the domain of a variable is -multiconsistent with respect to a constraint if there are at least solutions to in which is assigned the value . We present algorithms that determine which variable-value pairs are -multiconsistent with respect to several well known global constraints. In addition, we show that finding super solutions is strictly harder than finding arbitrary solutions and suggest multiconsistency as an alternative way to search for robust solutions.

We describe the problem of scheduling astronomy observations for the Stratospheric Observatory for Infrared Astronomy, an airborne telescope. The problem requires maximizing the number of requested observations scheduled subject to a mixture of discrete and continuous constraints relating the feasibility of an astronomical observation to the position and time at which the observation begins, telescope elevation limits, Special Use Airspace limitations, and available fuel. Solving the problem requires making discrete choices (e.g. selection and sequencing of observations) and continuous ones (e.g. takeoff time and setup actions for observations by repositioning the aircraft). Previously, we developed an incomplete algorithm called ForwardPlanner using a combination of AI and OR techniques including progression planning, lookahead heuristics, stochastic sampling and numerical optimization, to solve a simplified version of this problem. While initial results were promising, ForwardPlanner fails to scale when accounting for all relevant constraints. We describe a novel combination of Squeaky Wheel Optimization (SWO), an incomplete algorithm designed to solve scheduling problems, with previously devised numerical optimization methods and stochastic sampling approaches, as well as heuristics based on reformulations of the SFPP to traditional OR scheduling problems. We show that this new algorithm finds as good or better flight plans as the previous approaches, often with less computation time.

Recently, new cost-based filtering algorithms for shorter-path constraints have been developed. However, so far only the theoretical properties of shorter-path constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource constrained shortest path problem. We show how reasoning about path-substructures in combination with CP-based Lagrangian relaxation can help to improve significantly over previously developed problem-tailored filtering algorithms and investigate the impact of required-edge detection, undirected versus directed filtering, and the choice of the algorithm optimizing the Lagrangian dual.

Constraint programming (CP) based column generation uses CP to solve the pricing subproblem. We consider a set partitioning formulation with a huge number of variables, each of which can be generated by solving a CP subproblem. We propose two customized search strategies to solve the CP subproblem, which aim to improve the coordination between the master problem and the subproblem. Specifically, these two strategies attempt to generate more promising columns for the master problem in order to counter the effect of slow convergence and the difficulty of reaching integer solutions. The first strategy uses the dual variables to direct the search towards columns that drive the relaxed master problem faster to optimality. The second strategy exploits the structure of the constraints in the master problem to generate columns that help to reach integer solutions more quickly. We use a physician scheduling problem to test the strategies.

Producing work schedules for airline crew normally results in individually different schedules. Some airlines do however want to give the same schedule to groups of people. The construction of such groups must respect certain rules, provide a good matching of certain factors and fit well into the normal process of producing anonymous trips starting and ending at the home base and assigning these to the crew. In this paper we present an application, implemented and delivered to a large European airline, which addresses these needs. The problem is challenging to solve for certain cases. Hence two different approaches have been applied, one using constraint programming and the other using column generation. These two methods are described and compared – along with computational results.

We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogood-based methods, partial-order dynamic backtracking, various local search metaheuristics, and GRASPs (greedy randomized adaptive search procedures). The framework allows elements of different solution methods to be combined at will, resulting in a variety of integrated methods. These include continuous relaxations for global constraints, the linking of integer and constraint programming via Benders decomposition, constraint propagation in global optimization, relaxation bounds in local search and GRASPs, and many others.

This paper presents a CSPs filtering method combining arc-consistency and dual Lagrangean relaxation techniques. First, we model the constraint satisfaction problem as a 0/1 linear integer program (IP); then, the consistency of a value is defined as an optimization problem on which a dual Lagrangean relaxation is defined. While solving the dual Lagrangean relaxation, values inconsistencies may be detected (dual Lagrangean inconsistent values); the constraint propagation of this inconsistency can be performed by arc-consistency. After having made the CSP arc-consistent, the process iteratively selects values of variables which may be dual Lagrangean inconsistent. Computational experiments performed over randomly generated problems show the advantages of the hybrid filtering technique combining arc-consistency and dual Lagrangean relaxation.