Search results for "Polyhedron"
showing 10 items of 38 documents
A branch-and-cut algorithm for the Orienteering Arc Routing Problem
2016
[EN] In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP),in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route.In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds…
A simplified predictive control of constrained Markov jump system with mixed uncertainties
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/475808 Open Access A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent pre…
An exact algorithm for the min-cost network containment problem
2004
A network design problem which arises in the distribution of a public utility provided by several competitive suppliers is studied. The problem addressed is that of determining minimum-cost (generalized) arc capacities in order to accommodate any demand between given source–sink pairs of nodes, where demands are assumed to fall within predetermined ranges. Feasible flows are initially considered as simply bounded by the usual arc capacity constraints. Then, more general linear constraints are introduced which may limit the weighted sum of the flows on some subsets of arcs. An exact cutting plane algorithm is presented for solving both of the above cases and some computational results are re…
A branch-and-cut algorithm for the pallet loading problem
2005
We propose a branch-and-cut algorithm for the pallet loading problem. The 0-1 formulation proposed by Beasley for cutting problems is adapted to the problem, adding new constraints and new procedures for variable reduction. We then take advantage of the relationship between this problem and the maximum independent set problem to use the partial linear description of its associated polyhedron. Finally, we exploit the specific structure of our problem to define the solution graph and to develop efficient separation procedures. We present computational results for the complete sets Cover I (up to 50 boxes) and Cover II (up to 100 boxes).
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
Almost square dual Banach spaces
2020
Abstract We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on l ∞ . As a consequence we get that every dual Banach space containing c 0 has an equivalent almost square dual norm. Finally we characterize separable real almost square spaces in terms of their position in their fourth duals.
Asplund Operators on Locally Convex Spaces
2000
We study the relationship between the local Radon-Nikodým property, introduced by Defant [4] as a generalization of the Radon-Nikodým property to duals of locally convex spaces, and the Asplund operators, introduced by Robertson [7]. We also give a characterization of Asplund symmetric tensor products of Banach spaces in terms of Asplund maps.
Acute Type Refinements of Tetrahedral Partitions of Polyhedral Domains
2001
We present a new technique to perform refinements on acute type tetrahedral partitions of a polyhedral domain, provided that the center of the circumscribed sphere around each tetrahedron belongs to the tetrahedron. The resulting family of partitions is of acute type; thus, all the tetrahedra satisfy the maximum angle condition. Both these properties are highly desirable in finite element analysis.
Ontological information system for the selection of technologies for the treatment and disposal of organic waste: engineering and educational aspects
2021
The article proves a problem of information processing in the field of the structuring of information and decision-making in environmental engineering, including education in this field. This article presents the ontology-information model that was used to systematize waste treatment equipment. The article presents the use of an ontological algorithm “Polyhedron” for engineers and teachers. The algorithm consists of integrating ontological solutions from abstract to specific. The proposed model consists of a general ontology of “waste treatment technologies selection”, “waste treatment equipment selection” and “Ontology for the analysis of scientific publications”. Users of the system can i…
High temperature neutron diffraction study of sodium di-tin tri-phosphate
1992
Abstract High temperature high resolution neutron diffraction study of the crystal chemistry of NaSn 2 (PO 4 ) 3 has been completed, at four different temperatures, applying the Rietveld method to the experimental neutron diffraction profile of a synthetic crystalline powder. Below the phase transition (∼860 K) the space group has been determined to be R3 which changes to R3c in the high temperature phase. No chemical bond breaks through the transition. The change in temperature makes the SnO 6 polyhedra rotate around the three fold axis in both structures. The PO 4 polyhedra rotate strictly around the two fold axis in the high temperature phase, but around the [0001] direction in the low t…