Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table

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

Collective proposal distributions for nonlinear MCMC samplers : Mean-field theory and fast implementation

Funding Information: ∗This research was conducted while A.D. was supported by an EPSRC-Roth scholarship co-funded by the Engineering and Physical Sciences Research Council and the Department of Mathematics at Imperial College London. Publisher Copyright: © 2022, Institute of Mathematical Statistics. All rights reserved.Over the last decades, various “non-linear” MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a non-linear generalization of the Metropolis-Hastings algorithm to a proposal that depends not only on the current state, but also on its law. We propose to simulate this dynamics as the mean field limit of a system of interacting particles, that can in turn itself be understood as a generalisation of the Metropolis-Hastings algorithm to a population of particles. Under the double limit in number of iterations and number of particles we prove that this algorithm converges. Then, we propose an efficient GPU implementation and illustrate its performance on various examples. The method is particularly stable on multimodal examples and converges faster than the classical methods.Peer reviewe

August Strobel et Stephan Wimmer, Kallirrhoë (‘Ēn ez-Zāra). Dritte Grabungskampagne des Deutschen evangelischen Instituts für Altertumswissenschaft des Heiligen Landes und Exkursionen in Süd-Peräa

L’oasis de ‘Aïn ez-Zâra (Jordanie) est située sur le rivage nord-est de la mer Morte dans un environnement de hautes falaises, au sud de la gorge du wadi Zarqâ Ma‘în. Cette oasis, qui s’est développée grâce à la présence de nombreuses sources pérennes chaudes, conserve sur une surface d’environ 2 km2 différents vestiges archéologiques à l’intérieur d’un rempart. De ce fait, ce site a été identifié comme l’ancienne Callirrhoé, une station thermale où Hérode le Grand chercha à la fin de sa vie ..

August Strobel et Stephan Wimmer, Kallirrhoë (‘Ēn ez-Zāra). Dritte Grabungskampagne des Deutschen evangelischen Instituts für Altertumswissenschaft des Heiligen Landes und Exkursionen in Süd-Peräa

L’oasis de ‘Aïn ez-Zâra (Jordanie) est située sur le rivage nord-est de la mer Morte dans un environnement de hautes falaises, au sud de la gorge du wadi Zarqâ Ma‘în. Cette oasis, qui s’est développée grâce à la présence de nombreuses sources pérennes chaudes, conserve sur une surface d’environ 2 km2 différents vestiges archéologiques à l’intérieur d’un rempart. De ce fait, ce site a été identifié comme l’ancienne Callirrhoé, une station thermale où Hérode le Grand chercha à la fin de sa vie ..

Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost that is associated with their generation. We propose a novel approach to generate APDs with prescribed statistical properties, including fine control over the size of individual grains. To this end, we rely on fast optimal transport algorithms that stream well on Graphics Processing Units (GPU) and handle non-uniform, anisotropic distance functions. This allows us to find large APDs that best fit experimental data and generate synthetic high-resolution microstructures in (tens of) seconds. This unlocks their use for computational homogenisation, which is especially relevant to machine learning methods that require the generation of large collections of representative microstructures as training data. The paper is accompanied by a Python library, PyAPD, which is freely available at: www.github.com/mbuze/PyAPD.Comment: 25 pages, 6 figure