Placement Problems for Irregular Objects: Mathematical Modeling, Optimization and Applications

Yuriy Stoyan (), Alexandr Pankratov and Tatiana Romanova ()
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Yuriy Stoyan: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
Alexandr Pankratov: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
Tatiana Romanova: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine

A chapter in Optimization Methods and Applications, 2017, pp 521-559 from Springer

Abstract: Abstract We describe our methodology for solving NP-hard irregular placement problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their free rotations within a container. We formulate a basic irregular placement problem (IRPP), which covers a wide spectrum of practical packing, cutting, nesting, clustering, and layout problems. We provide a nonlinear programming (NLP) model of the problem, employing the phi-function technique. Our model involves a large number of inequalities with nonsmooth functions. We describe a solution tree for our placement problem and evaluate the number of its terminal nodes. We reduce IRPP problem to a sequence of NLP-subproblems with smooth functions. Our solution strategy is based on combination of discrete and continuous optimization methods. We employ two approaches to solve IRPP problem: a branching scheme algorithm and an efficient optimization algorithm, which involves a feasible starting point and local optimization procedures. To show the benefits of our methodology we present computational results for a number of new challenger and the best known benchmark instances.

Keywords: Irregular Objects; Feasible Starting Points; Local Optimal Placement; Minimum Allowable Distance; True Ellipse (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-68640-0_25

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DOI: 10.1007/978-3-319-68640-0_25

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