Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization
| Autor: | Aleksandr V. Pankratov, Yuriy Stoyan, Tatiana E. Romanova |
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| Rok vydání: | 2016 |
| Předmět: |
Marketing
0209 industrial biotechnology Mathematical optimization Sequence 021103 operations research Strategy and Management Spectrum (functional analysis) 0211 other engineering and technologies 02 engineering and technology Management Science and Operations Research Management Information Systems Nonlinear programming Packing problems 020901 industrial engineering & automation Line segment Bounded function Benchmark (computing) Representation (mathematics) Mathematics |
| Zdroj: | Journal of the Operational Research Society. 67:786-800 |
| ISSN: | 1476-9360 0160-5682 |
| DOI: | 10.1057/jors.2015.94 |
| Popis: | We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances. |
| Databáze: | OpenAIRE |
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