A real-valued genetic algorithm for gemstone cutting

Silva, Victor Billy da; Ritt, Marcus; Carvalho, João Batista Pereira de; Brusso, Marcos José; Silva, Juliano Tonezer da; Zanatta, Alexandre Lazaretti

doi:10.1109/clei.2012.6427153

Cited by 3 publications

(1 citation statement)

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“…Da Silva et al (2012) develop a two-level heuristic approach to solve the gemstone cutting problem. The first of these levels finds the largest scaling factor for a given orientation and translation, while the second deploys a genetic algorithm to maximize the scaling factor over all orientations and translations.…”

Section: Diamond and Gemstone Cuttingmentioning

confidence: 99%

Extracting maximal objects from three-dimensional solid materials

Silva

Çalık

Vancroonenburg

et al. 2021

Computers & Operations Research

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In the problem of extracting maximal items/objects from three-dimensional materials, we are given a piece of solid material and an object with predefined ratios. The goal is to extract the largest possible convex or non-convex object from the solid material. There are two variants of the problem: the general case where the solid material is non-convex and its special case consisting of a convex solid material. We propose a matheuristic approach for solving both problems. For the special case, the problem is also modeled as a non-linear programming formulation. Meanwhile, for the general case a mixed integer linear programming formulation is provided based on the decomposition of the non-convex material into a finite number of convex regions. Computational experiments evaluate the performance of both models for small-scale instances considering objects with at most 1400 and 370 vertices for the special and general case, respectively. We observe that the required computational effort increases with the number of vertices of the objects, therefore, it is also evaluated the efficiency of the proposed matheuristic approach for more complicated instances, considering objects with a higher number of vertices.In order to establish benchmark instances for future research, all instances used are publicly available.

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Section: Diamond and Gemstone Cuttingmentioning

confidence: 99%