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Publicações

Publicações por António Miguel Gomes

2015

Two-Phase Approach to the Nesting problem with continuous rotations

Autores
Rocha, P; Rodrigues, R; Miguel Gomes, AM; Toledo, FMB; Andretta, M;

Publicação
IFAC PAPERSONLINE

Abstract
This paper presents an approaches. that assists in producing highly compacted Nesting layouts with irregular pieces using free rotations. This approach consists in the selection and compaction of big pieces in a first phase, while in a second phase, places the remaining small pieces between the big pieces, compacting all of them. The effect of several parameters are analyzed, such as minimum length to be achieved in the first phase, attraction of the pieces to the edges of the container, attraction between each pair of pieces, among others. This approach can provide good compaction results, while improving computational cost in some cases, which cart allow to tackle real world problems more effectively mkt efficiently.

2016

Constraint aggregation in non-linear programming models for nesting problems

Autores
Rocha, P; Gomes, AM; Rodrigues, R; Toledo, FMB; Andretta, M;

Publicação
Lecture Notes in Economics and Mathematical Systems

Abstract

2013

Preface to the Special Issue on Contributions to Applied Combinatorial Optimization

Autores
Viana, A; Miguel Gomes, AM; Costa, T;

Publicação
INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

Abstract

2013

The Dotted-Board Model: A new MIP model for nesting irregular shapes

Autores
Toledo, FMB; Carravilla, MA; Ribeiro, C; Oliveira, JF; Gomes, AM;

Publicação
INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS

Abstract
The nesting problem, also known as irregular packing problem, belongs to the generic class of cutting and packing (C&P) problems. It differs from other 2-D C&P problems in the irregular shape of the pieces. This paper proposes a new mixed-integer model in which binary decision variables are associated with each discrete point of the board (a dot) and with each piece type. It is much more flexible than previously proposed formulations and solves to optimality larger instances of the nesting problem, at the cost of having its precision dependent on board discretization. To date no results have been published concerning optimal solutions for nesting problems with more than 7 pieces. We ran computational experiments on 45 problem instances with the new model, solving to optimality 34 instances with a total number of pieces ranging from 16 to 56, depending on the number of piece types, grid resolution and the size of the board. A strong advantage of the model is its insensitivity to piece and board geometry, making it easy to extend to more complex problems such as non-convex boards, possibly with defects. Additionally, the number of binary variables does not depend on the total number of pieces but on the number of piece types, making the model particularly suitable for problems with few piece types. The discrete nature of the model requires a trade-off between grid resolution and problem size, as the number of binary variables grows with the square of the selected grid resolution and with board size.

2016

Preface to the Special Issue on Cutting and Packing

Autores
Gomes, AM; Goncalves, JF; Alvarez Valdes, R; de Carvalho, JV;

Publicação
International Transactions in Operational Research

Abstract

2015

GPU-based computing for nesting problems: The importance of sequences in static selection approaches

Autores
Rocha, P; Rodrigues, R; Miguel Gomes, A; Alves, C;

Publicação
Operations Research and Big Data: IO2015-XVII Congress of Portuguese Association of Operational Research (APDIO)

Abstract
In this paper, we address the irregular strip packing problem (or nesting problem) where irregular shapes have to be placed on strips representing a piece of material whose width is constant and length is virtually unlimited. We explore a constructive heuristic that relies on the use of graphical processing units to accelerate the computation of different geometrical operations. The heuristic relies on static selection processes, which assume that a sequence of pieces to be placed is defined a priori. Here, the emphasis is put on the analysis of the impact of these sequences on the global performance of the solution algorithm. Computational results on benchmark datasets are provided to support this analysis, and guide the selection of the most promising methods to generate these sequences.

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