Publication

Reconstruction of polycrystalline structures: a new application of combinatorial optimization

Thomas Liebling
1987
Journal Articles

Abstract

Many known materials possess polycrystalline structure. The images produced by plane cuts through such structures are polygonal complexes. The problem of finding the edges, when only the vertices of a given polygonal complex are known, is considered. A combinatorial optimization model is proposed whose solution yields an approximation of the complex. The problem itself is solved using simulated annealing. Encouraging first experiments are presented.

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Thomas Liebling
1987
Journal Articles

Abstract

Official source

Related concepts (32)

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Polygon

In geometry, a polygon (ˈpɒlɪɡɒn) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain.

Polygonal chain

In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain P is a curve specified by a sequence of points called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. A simple polygonal chain is one in which only consecutive segments intersect and only at their endpoints. A closed polygonal chain is one in which the first vertex coincides with the last one, or, alternatively, the first and the last vertices are also connected by a line segment.

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Reconstruction of polycrystalline structures: a new application of combinatorial optimization

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