Search results for "Mathematica"
showing 10 items of 7971 documents
Corrigendum to “Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations” [19 (6) (2014) 1746–1769]
2015
Corrigendum Corrigendum to ‘‘Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations’’ [19 (6) (2014) 1746–1769] M. Russo , S. Roy Choudhury , T. Rehman , G. Gambino b University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., Orlando, USA University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 Palermo, Italy
New insights into the OCST problem
2009
This paper considers the Euclidean variant of the optimal communciation spanning tree (OCST) problem. Researches have analyzed the structure of the problem and found that high quality solutions prefer edges of low cost. Further, edges pointing to the center of the network are more likely to be included in good solutions. We add to the literature and provide additional insights into the structure of the OCST problem. Therefore, we investigate properies of the whole tree, such as node degrees and the Wiener index. The results reveal that optimal solutions are structured in a star-like manner. There are few nodes with high node degrees, these nodes are located next to the graph's center. The m…
THE IMPACT OF ELECTION RESULTS ON THE MEMBER NUMBERS OF THE LARGE PARTIES IN BAVARIA AND GERMANY
2005
In this paper, we investigate the relations between the numbers of members of various parties and their results in the elections in Bavaria and in Germany. Deriving from the finding that there is a strong time-delayed correlation between these data-sets for the two largest parties in Bavaria, we show in a simulation based on the Sznajd model that such a correlation leads to very stable majorities, just as in Bavaria.
On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
2018
Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…
Fast Poisson solvers for graphics processing units
2013
Two block cyclic reduction linear system solvers are considered and implemented using the OpenCL framework. The topics of interest include a simplified scalar cyclic reduction tridiagonal system solver and the impact of increasing the radix-number of the algorithm. Both implementations are tested for the Poisson problem in two and three dimensions, using a Nvidia GTX 580 series GPU and double precision floating-point arithmetic. The numerical results indicate up to 6-fold speed increase in the case of the two-dimensional problems and up to 3- fold speed increase in the case of the three-dimensional problems when compared to equivalent CPU implementations run on a Intel Core i7 quad-core CPU…
Solving a large multicontainer loading problem in the car manufacturing industry
2017
Abstract Renault, a large car manufacturer with factories all over the world, has a production system in which not every factory produces all the parts required to assemble a vehicle. Every day, large quantities of car parts are sent from one factory to another, defining very large truck/container transportation problems. The main challenge faced by the Renault logistics platforms is to load the items into trucks and containers as efficiently as possible so as to minimize the number of vehicles sent. Therefore, the problem to be solved is a multicontainer loading problem in which, besides the usual geometric constraints preventing items from overlapping and exceeding the dimensions of the c…
Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows
2018
In this paper, we present a new branch-and-price-and-cut algorithm to solve the truck-and-trailer routing problem with time windows (TTRPTW) and two real-world extensions. In all TTRPTW variants, the fleet consists of one or more trucks that may attach a trailer. Some customers are not accessible with a truck-and-trailer combination, but can however be serviced by one if the trailer is previously detached and parked at a suitable location. In the first extension, the planning horizon comprises two days and customers may be visited either on both days or only once, in which case twice the daily supply must be collected. The second extension incorporates load transfer times depending on the …
Mathematical models for multicontainer loading problems
2017
Abstract This paper deals with the problem of a distribution company that has to serve its customers by putting first the products on pallets and then loading the pallets onto trucks. We approach the problem by developing and solving integer linear models. We start with basic models, that include the essential features of the problem, such as respecting the dimensions of the truck, and not exceeding the total weight capacity and the maximum weigh capacity on each axle. Then, we add progressively new conditions to consider the weight and volume of pallet bases and to include other desirable features for the solutions to be useful in practice, such as the position of the center of gravity and…
Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem
2018
This paper presents a branch-and-price-and-cut algorithm for the exact solution of the active-passive vehicle-routing problem (APVRP). The APVRP covers a range of logistics applications where pickup-and-delivery requests necessitate a joint operation of active vehicles (e.g., trucks) and passive vehicles (e.g., loading devices such as containers or swap bodies). The objective is to minimize a weighted sum of the total distance traveled, the total completion time of the routes, and the number of unserved requests. To this end, the problem supports a flexible coupling and decoupling of active and passive vehicles at customer locations. Accordingly, the operations of the vehicles have to be s…
Mathematical models for Multi Container Loading Problems with practical constraints
2019
Abstract We address the multi container loading problem of a company that serves its customers’ orders by building pallets with the required products and loading them into trucks. The problem is solved by using integer linear models. To be useful in practice, our models consider three types of constraints: geometric constraints, so that pallets lie completely inside the trucks and do not overlap; weight constraints, defining the maximum weights supported by a truck and by each axle, as well as the position of the centre of gravity of the cargo; and dynamic stability constraints. These last constraints forbid empty spaces between pallets to avoid cargo displacement when the truck is moving, …