Constraint Aggregation in Non-linear Programming Models for Nesting Problems

Pedro Rocha (), A. Miguel Gomes (), Rui Rodrigues (), Franklina M. B. Toledo () and Marina Andretta ()
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Pedro Rocha: Universidade do Porto
A. Miguel Gomes: Universidade do Porto
Rui Rodrigues: Universidade do Porto
Franklina M. B. Toledo: Universidade de São Paulo
Marina Andretta: Universidade de São Paulo

A chapter in Computational Management Science, 2016, pp 175-180 from Springer

Abstract: Abstract The Nesting problem is a complex problem that arises in industries where sets of pieces or space must be efficiently placed or allocated in order to minimize wasted space or wasted raw materials, without overlaps between pieces and fully contained inside a container. This paper analyses the impact that aggregating constraints can achieve in the reduction of computational cost of a Non-Linear Programming model for Nesting problems with continuous rotations. This is achieved by aggregating non-overlapping constraints and using spatial partition and hierarchical overlap detection methods. When aggregating constraints there is also an effect of reducing the sensitivity of the solver, which may reduce the quality of the final layout. Analyzing the trade-off between constraints aggregation and the impact on the quality of the final solution is an important issue to handle nesting instances with a large number of pieces. Computational experiments show that aggregating non-overlapping constraints allows the Non-Linear Programming model for Nesting problems to scale well to tackle large size real world problems with continuous rotations.

Keywords: Continuous Rotation; Constraint Aggregation; Spatial Partition; Summation Term; Augmented Lagrangian Multiplier (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-20430-7_22

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DOI: 10.1007/978-3-319-20430-7_22

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