IDEAS home Printed from https://ideas.repec.org/a/igg/jamc00/v11y2020i3p108-119.html
   My bibliography  Save this article

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

Author

Listed:
  • 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)

  • Igor Litvinchev

    (Universidad Autonoma de Nuevo Leon, San Nicolás de los Garza, Mexico)

Abstract

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

Suggested Citation

  • Rafael Torres-Escobar & Jose Antonio Marmolejo-Saucedo & Igor Litvinchev, 2020. "A Metaheuristic Approach and Mathematical Programming for Packing Objects in a Rectangular Container," International Journal of Applied Metaheuristic Computing (IJAMC), IGI Global, vol. 11(3), pages 108-119, July.
    • Handle: RePEc:igg:jamc00:v:11:y:2020:i:3:p:108-119
    as

    Download full text from publisher

    File URL: http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/IJAMC.2020070106
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:igg:jamc00:v:11:y:2020:i:3:p:108-119. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Journal Editor (email available below). General contact details of provider: https://www.igi-global.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.