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Advances in Operations Research
Volume 2017, Article ID 7048042, 10 pages
https://doi.org/10.1155/2017/7048042
Research Article

Towards Merging Binary Integer Programming Techniques with Genetic Algorithms

School of Computing and Information Technology, Wollongong University, Wollongong, NSW 2522, Australia

Correspondence should be addressed to Reza Zamani; ua.ude.wou@azer

Received 10 June 2017; Revised 27 August 2017; Accepted 6 September 2017; Published 17 October 2017

Academic Editor: Demetrio Laganà

Copyright © 2017 Reza Zamani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable with binary restriction, is considered as real number between 0 and 1, with the penalty of , in which is a large number. Values not near to the boundary extremes of 0 and 1 make the component of large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future.