A Metaheuristic Approach and Mathematical Programming for Packing Objects in a Rectangular Container-Reference-Cited by-同舟云学术

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

Published:2020-07 Issue:3 Volume:11 Page:108-119
ISSN:1947-8283
Container-title:International Journal of Applied Metaheuristic Computing
language:en
Short-container-title:

Author:

Torres-Escobar Rafael¹,Marmolejo-Saucedo Jose Antonio²^ORCID,Litvinchev Igor³

Affiliation:

1. Universidad Anahuac, Campus Norte, Facultad de Ingeniería, Naucalpan de Juárez, Mexico

2. Universidad Panamericana, Facultad de Ingeniería, Ciudad de Mexico, Mexico

3. 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

Publisher

IGI Global

Subject

Decision Sciences (miscellaneous),Computational Mathematics,Computational Theory and Mathematics,Control and Optimization,Computer Science Applications,Modeling and Simulation,Statistics and Probability

Reference29 articles.

1. Packing circles in the smallest circle: An adaptive hybrid algorithm.;I.Al-Mudahka;The Journal of the Operational Research Society,2011

2. Beasley, J. E. (1985). An exact two-dimensional non-guillotine cutting tree search procedure.Operations Research, 33(1), 49–64.

3. Applications of Nonlinear Programming to Packing Problems

4. Solving circle packing problems by global optimization: Numerical results and industrial applications

5. A global optimization point of view to handle non-standard object packing problems