Given a set of rectangular pieces and a container of fixed width and variable length, the two-dimensional strip packing problem (2D-SPP) consists of orthogonally placing all the pieces within the container, without overlapping, such that the overall length of the layout is minimised. Until now mainly heuristics, for example genetic algorithms (GA), were proposed for the 2D-SPP which use encoded...

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether be extended to higher-dimensional systems is nontrivial. In this work, we construct two classes of two-dimensional by reducing problem that for 1D model. these systems, get generalized Brillouin zone complex wave vector and investigate topological properties. model Cher...

The two-dimensional knapsack problem consists in packing rectangular items into a single box such that the total value of packed is maximized. In this article, we restrict to 2-stage non-exact guillotine cut packings and consider variant with splittable items: each item can be horizontally as many times needed, may contain only portion an item. This arises semifluid items, like tubes small radi...

We consider the well-known one-dimensional cutting stock problem (1CSP). It is shown that all possible instances of the 1CSP can be divided into a finite number of equivalence classes when the number of items m is fixed. A method for enumerating all these classes is investigated. This method is improved for searching proper non-IRUP instances with minimal number of items. We found the minimal n...

In a two-photon femtosecond laser system of three-dimensional micro-fabrication, a model of micro-device is fabricated layer by layer along its contours of cross-sections. So it is necessary to generate cutting path. In this paper, we present an efficient algorithm to generate cutting path which is a series of ordered contour points on each cross-section of a model. Keyword. Micro-fabrication, ...