Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

On the reformulation of vehicle routing problems and scheduling problems

We can reformulate a vehicle routing problem (VRP) as an open shop scheduling problem (SSP) by representing visits as activities, vehicles as resources on the factory floor, and travel as set up costs between activities. In this paper we present two reformulations: from VRP to open shop, and the inverse, from SSP to VRP. Not surprisingly, VRP technology performs poorly on reformulated SSP's, as does scheduling technology on reformulated VRP's. We present a pre-processing transformation that "compresses" the VRP, transforming an element of travel into the duration of the visits. The compressed VRP's are then reformulated as scheduling problem, to determine if it is primarily distance in the VRP that causes scheduling technology to degrade on the reformulated problem. This is a step towards understanding the features of a problem that make it more amenable to one technology rather than another

Graph transformations for the vehicle routing and job shop scheduling problems

The vehicle routing problem (VRP) and job shop scheduling problem (JSP) are two common combinatorial problems that can be naturally represented as graphs. A core component of solving each problem can be modeled as finding a minimum cost Hamiltonian path in a complete weighted graph. The graphs extracted from VRPs and JSPs have different characteristics however, notably in the ratio of edge weight to node weight. Our long term research question is to determine the extent to which such graph characteristics impact the performance of algorithms commonly applied to VRPs and JSPs. As a preliminary step, in this paper we investigate five transformations for complete weighted graphs that preserve the cost of Hamiltonian paths. These transformations are based on increasing node weights while reducing edge weights or the inverse. We demonstrate how the transformations affect the ratio of edge to node weight and how they change the relative weights of edges at a node. Finally, we conjecture how the different transformations will impact the performance of existing VRP and JSP solving techniques

Trying again to fail-first

For constraint satisfaction problems (CSPs), Haralick and Elliott [1] introduced the Fail-First Principle and defined in it terms of minimizing branch depth. By devising a range of variable ordering heuristics, each in turn trying harder to fail first, Smith and Grant [2] showed that adherence to this strategy does not guarantee reduction in search effort. The present work builds on Smith and Grant. It benefits from the development of a new framework for characterizing heuristic performance that defines two policies, one concerned with enhancing the likelihood of correctly extending a partial solution, the other with minimizing the effort to prove insolubility. The Fail-First Principle can be restated as calling for adherence to the second, fail-first policy, while discounting the other, promise policy. Our work corrects some deficiencies in the work of Smith and Grant, and goes on to confirm their finding that the Fail-First Principle, as originally defined, is insufficient. We then show that adherence to the fail-first policy must be measured in terms of size of insoluble subtrees, not branch depth. We also show that for soluble problems, both policies must be considered in evaluating heuristic performance. Hence, even in its proper form the Fail-First Principle is insufficient. We also show that the “FF” series of heuristics devised by Smith and Grant is a powerful tool for evaluating heuristic performance, including the subtle relations between heuristic features and adherence to a policy

GAMMA-RAY TRANSITION ENERGY CORRELATIONS IN 156Er AND 160Yb

No abstract availabl

Temporal evolution of the Evershed flow in sunspots. I. Observational characterization of Evershed clouds

[Abridged] The magnetic and kinematic properties of the photospheric Evershed flow are relatively well known, but we are still far from a complete understanding of its nature. The evolution of the flow with time, which is mainly due to appearance of velocity packets called Evershed clouds (ECs), may provide information to further constrain its origin. Here we undertake a detailed analysis of the evolution of the Evershed flow by studying the properties of ECs. In this first paper we determine the sizes, proper motions, location in the penumbra, and frequency of appearance of ECs, as well as their typical Doppler velocities, linear and circular polarization signals, Stokes V area asymmetries, and continuum intensities. High-cadence, high-resolution, full vector spectropolarimetric measurements in visible and infrared lines are used to derive these parameters. We find that ECs appear in the mid penumbra and propage outward along filaments with large linear polarization signals and enhanced Evershed flows. The frequency of appearance of ECs varies between 15 and 40 minutes in different filaments. ECs exhibit the largest Doppler velocities and linear-to-circular polarization ratios of the whole penumbra. In addition, lines formed deeper in the atmosphere show larger Doppler velocities, much in the same way as the ''quiescent'' Evershed flow. According to our observations, ECs can be classified in two groups: type I ECs, which vanish in the outer penumbra, and type II ECs, which cross the outer penumbral boundary and enter the sunspot moat. Most of the observed ECs belong to type I. On average, type II ECs can be detected as velocity structures outside of the spot for only about 14 min. Their proper motions in the moat are significantly reduced with respect to the ones they had in the penumbra.Comment: Accepted for publication in A&

Double π0\pi^0 Photoproduction off the Proton at Threshold

The reaction $\gamma p \to \pi^0 \pi^0 p$ has been measured using the TAPS BaF$_2$ calorimeter at the tagged photon facility of the Mainz Microtron accelerator. Chiral perturbation theory (ChPT) predicts that close to threshold this channel is significantly enhanced compared to double pion final states with charged pions. In contrast to other reaction channels, the lower order tree terms are strongly suppressed in 2$\pi^0$ photoproduction. The consequence is the dominance of pion loops in the 2$\pi^0$ channel close to threshold - a result that opens new prospects for the test of ChPT and in particular its inherent loop terms. The present measurement is the first which is sensitive enough for a conclusive comparison with the ChPT calculation and is in agreement with its prediction. The data also show good agreement with a calculation in the unitary chiral approach.Comment: Submitted to PL

On Selecting and Scheduling Assembly Plans Using Constraint Programming

This work presents the application of Constraint Programming to the problem of selecting and sequencing assembly operations. The set of all feasible assembly plans for a single product is represented using an And/Or graph. This representation embodies some of the constraints involved in the planning problem, such as precedence of tasks, and the constraints due to the completion of a correct assembly plan. The work is focused on the selection of tasks and their optimal ordering, taking into account their execution in a generic multi-robot system. In order to include all different constraints of the problem, the And/Or graph representation is extended, so that links between nodes corresponding to assembly tasks are added, taking into account the resource constraints. The resultant problem is mapped to a Constraint Satisfaction Problem (CSP), and is solved using Constraint Programming, a powerful programming paradigm that is increasingly used to model and solve many hard real-life problems