Name
Abstract | ||
|---|---|---|
We further develop our phi-function technique for solving Cutting and Packing problems. Here we introduce quasi-phi-functions for an analytical description of non-overlapping and containment constraints for 2D- and 3D-objects which can be continuously rotated and translated. These new functions can work well for various types of objects, such as ellipses, for which ordinary phi-functions are too complicated or have not been constructed yet. We also define normalized quasi-phi-functions and pseudonormalized quasi-phi-functions for modeling distance constraints. To show the advantages of our new quasi-phi-functions we apply them to the problem of placing a given collection of ellipses into a rectangular container of minimal area. We use radical free quasi-phi-functions to reduce it to a nonlinear programming problem and develop an efficient solution algorithm. We present computational results that compare favourably with those published elsewhere recently. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s10898-015-0331-2 | J. Global Optimization |
Keywords | Field | DocType |
Quasi-phi-functions,Object continuous rotations,Non-overlapping,Distance constraints,Ellipse packing,Mathematical model,Nonlinear optimization | Mathematical optimization,Normalization (statistics),Packing problems,Nonlinear programming,Ellipse,Mathematics | Journal |
Volume | Issue | ISSN |
65 | 2 | 0925-5001 |
Citations | PageRank | References |
7 | 0.53 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yu. G. Stoyan | 1 | 94 | 7.91 |
| Aleksandr Pankratov | 2 | 17 | 2.46 |
| T. Romanova | 3 | 65 | 7.04 |