Showing papers by "Marc E. Pfetsch published in 2011"

Large Neighborhood Search beyond MIP

Abstract: Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.

Disruption Management With Rescheduling of Trips and Vehicle Circulations

Abstract: This paper introduces a combined approach for the recovery of a timetable by rescheduling trips and vehicle circulations for a rail-based transportation system subject to disruptions. The authors propose a novel event-based integer programming (IP) model. Features include shifting and canceling of trips as well as modifying the vehicle schedules by changing or truncating the circulations. The objective maximizes the number of recovered trips, possibly with delay, while guaranteeing a conflict-free new timetable for the estimated time window of the disruption. The authors demonstrate the usefulness of the approach through experiments for real-life test instances of relevant size, arising from the subway system of Vienna. The authors focus on scenarios in which one direction of one track is blocked, and trains have to be scheduled through this bottleneck. Solving these instances is made possible by contracting parts of the underlying event-activity graph; this allows a significant size reduction of the IP. Usually, the solutions found within one minute are of good quality and can be used as good estimates of recovery plans in an online context.

Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry

Abstract: Given an undirected graph and a positive integer k, themaximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a non-trivial graph automorphism gives equivalent solutions. It is well known that such symmetries have negative effects on the performance of constraint/integer programming solvers. We investigate the integration of a branch-and-cut algorithm for solving the maximum k-colorable subgraph problem with constraint propagation techniques to handle the symmetry arising from the graph. The latter symmetry is handled by (non-linear) lexicographic ordering constraints and linearizations thereof. In experiments, we evaluate the influence of several components of our algorithm on the performance, including the different symmetry handling methods. We show that several components are crucial for an efficient algorithm; in particular, the handling of graph symmetries yields a significant performance speed-up.

Optimierung Technischer Kapazitäten in Gasnetzen

Abstract: Die mittel- und langerfristige Planung fur den Gastransport hat sich durch Anderungen in den regulatorischen Rahmenbedingungen stark verkompliziert. Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel diskutiert die hieraus resultierenden mathematischen Planungsprobleme, welche als Validierung von Nominierungen und Buchungen, Bestimmung der technischen Kapazitat und Topologieplanung bezeichnet werden. Diese mathematischen Optimierungsprobleme werden vorgestellt und Losungsansatze skizziert.

Disruption Management with Rescheduling of Trips and Vehicle Circulations

Abstract: This paper introduces a combined approach for the recovery of a timetable by rescheduling trips and vehicle circulations for a rail-based transportation system subject to disruptions. We propose a novel event-based integer programming (IP) model. Features include shifting and canceling of trips as well as modifying the vehicle schedules by changing or truncating the circulations. The objective maximizes the number of recovered trips, possibly with delay, while guaranteeing a conflict-free new timetable for the estimated time window of the disruption. We demonstrate the usefulness of our approach through experiments for real-life test instances of relevant size, arising from the subway system of Vienna. We focus on scenarios in which one direction of one track is blocked, and trains have to be scheduled through this bottleneck. Solving these instances is made possible by contracting parts of the underlying event-activity graph; this allows a significant size reduction of the IP. Usually, the solutions found within one minute are of good quality and can be used as good estimates of recovery plans in an online context.

An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections

Abstract: We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Nevertheless, we provide conditions which ensure convergence to an optimal feasible point under suitable assumptions. One convergence result deals with step size sequences that are fixed a priori. Two other results handle dynamic Polyak-type step sizes depending on a lower or upper estimate of the optimal objective function value, respectively. Additionally, we briefly sketch two applications: Optimization with convex chance constraints, and finding the minimum l1-norm solution to an underdetermined linear system, an important problem in Compressed Sensing.

An Infeasible-Point Subgradient Method using Approximate Projections

Abstract: We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm) In particular, the iterates in our method can be infeasible throughout the whole procedure Nevertheless, we provide conditions which ensure convergence to an optimal feasible point under suitable assumptions One convergence result deals with step size sequences that are fixed a priori Two other results handle dynamic Polyak-type step sizes depending on a lower or upper estimate of the optimal objective function value, respectively Additionally, we briefly sketch two applications: Optimization with convex chance constraints, and finding the minimum l1-norm solution to an underdetermined linear system, an important problem in Compressed Sensing