A Metaheuristic Approach and Mathematical Programming for Packing Objects in a Rectangular Container

A Metaheuristic Approach and Mathematical Programming for Packing Objects in a Rectangular Container

Rafael Torres-Escobar (Universidad Anahuac, Campus Norte, Facultad de Ingeniería, Naucalpan de Juárez, Mexico), Jose Antonio Marmolejo-Saucedo (Universidad Panamericana, Facultad de Ingeniería, Ciudad de Mexico, Mexico) and Igor Litvinchev (Universidad Autonoma de Nuevo Leon, San Nicolás de los Garza, Mexico)
Copyright: © 2020 |Pages: 12
DOI: 10.4018/IJAMC.2020070106


The problem of packing non-congruent circles within bounded regions is considered. The aim is to maximize the number of circles placed into a rectangular container or minimize the waste. The circle is considered as a set of points that are all the same distance (not necessarily Euclidean) from a given point. An integer programming model is proposed using a dotted-board approximating the container and considering the dots as potential positions for assigning centers of the circles. The packing problem is then stated as a large scale linear 0–1 optimization problem. Binary decision variables are associated with each discrete point of the board (a dot) and with each object. Then, the same grid is used to prove a population-based metaheuristic. This metaheuristic is inspired by the monkeys' behavior. The resulting binary problem is then solved by using Gurobi Solver and Python Programming Language as Interface
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Mathematical Programming Approach

The main idea of this model was first implemented in Beasley (1985), later a similar approach was used in Galiev & Lisafina (2013) and Toledo et. al. (2013). This article is a continuation of the work proposed by Litvinchev et. al (2015), Litvinchev & Ozuna Espinosa (2014).

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