Algoritma Ant Colony Optimization pada Quadratic Assignment Problem

Oni Soesanto, Pardi Affandi, Nurul Dasima Astuti

Abstract


Quadratic Assignment Problem (QAP) is one extension of the assignment problem by setting n facilities to n certain locations to minimize the total assignment costs. QAP is also a combinatorial optimization problem that is a problem that has a finite set of solutions. Basically the solution of combinatorial problems can be obtained with the right results but for complex problems with larger data sizes it is quite difficult to calculate because the time used is long enough for the completion process. One of the algorithms implemented in the completion of QAP is the Ant Colony Optimization (ACO) algorithm is an algorithm that mimics the behavior of ants in finding food from the nest to a food source with the help of indirect communication called pheromone, so that pheromone is used to find optimal solutions with quite a short time. in this research ACO is used to solve the QAP problem by using a random proportional of rule formula then getting the smallest solution and renewing the pheromone until the assignment is stable and the solution obtained is fixed until the maximum assignment solution. The results obtained to complete the Quadratic Assignment Problem with the Ant Colony Optimization algorithm to get a solution to the QAP problems tested in the Nugent case resulted in a more minimal solution and the placement of appropriate location facilities through pheromone assistance and stored in a taboo list so that all facilities get a decent location with a worth it short time in completion.

Keywords


Quadratic Assignment Problem; Ant Colony Optimization; Tabu List; Pheromone

References


Hillier, S.F., & Lieberman, 2004, Introduction to Operations Research, Eighth Edition, New York: Mc Graw-Hil

Erlanda, C., 1998, The Quadratic Assignment Problem, Springer Science and Business Media Dordrecht

Dorigo, M. & Stutzle, T., 2004, Ant Colony Optimization, Massachusetts Institute of Technology

Hahn, P. & Grant, T., 1998, Lower Bounds for the Quadratic Assignment Problem Based Upon a Dual Formulation, Operation Research, Vol. 46, No. 6

Bidyarthy, S.A. & Vivek, G., 2013, Ant Colony Optimization for Quadratic Assignment Problem and School Bus Routing Problem. Departement of Mathematics Indian Institute of Technology Guwahati

Davendra, D. & Zelinka, I., 2009, Optimization of Quadratic Assignment Problem Using Self Organising Migrating Algorithm, Computing and Informatics, Vol. 28: 1001–1012

Christopher, N.E, 1967, An Experimental Comparison of Tech-Niques for the Assignment of Facilities to Locations INFORMS

Axel, N., 2014, Some Reformulations for the Quadratic Assignment Problem, Department of Chemical Engineering Åbo Akademi University http://www.qaplib/inst.html




DOI: https://doi.org/10.34312/jjom.v1i2.2353

Copyright (c) 2019 Jambura Journal of Mathematics





                         EDITORIAL OFFICE OF JAMBURA JOURNAL OF MATHEMATICS

 Department of Mathematics, Universitas Negeri Gorontalo
Jl. Jenderal Sudirman No.6, Kota Gorontalo, Provinsi Gorontalo 96128, Indonesia
 Email: info.jjom@ung.ac.id
 +62-852-55230451 (Call/SMS/WA)
 Jambura Journal of Mathematics (p-ISSN: 2654-5616 | e-ISSN: 2656-1344) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.