A Method to Convert Integer Variables of Mixed Integer Programming Problems into Continuous Variables

Chung-Chien Hong () and Yu-Hsin Huang ()
Additional contact information
Chung-Chien Hong: National Pingtung University of Science and Technology
Yu-Hsin Huang: National Pingtung University of Science and Technology

A chapter in Proceedings of 2013 4th International Asia Conference on Industrial Engineering and Management Innovation (IEMI2013), 2014, pp 1023-1033 from Springer

Abstract: Abstract A mixed integer programming problem, is an optimization problem that includes both integer decision variables and continuous ones. Many engineering and management problems are mixed integer programming problems, most of which are NP-hard and take a long time to approach the optimal solution. Therefore, this paper proposes a method to convert the integer variables of a mixed integer programming problem into continuous variables. Then a mixed integer programming problem becomes an equivalent nonlinear programming problem or linear programming problem. And then, well developed nonlinear programming or linear programming solvers can be employed to efficiently and effectively search for the solution of a mixed integer programming problem. In addition to describing processes for converting integer variables into continuous ones, this paper provides two examples to demonstrate the conversion process and the benefits coming from the conversion methodology in the process of approaching the optimal solutions. Once the mixed integer programming is converted to an equivalent one where the decision variables are continuous, a nonlinear programming problem solver such as a differential evolutionary algorithm, can be used to solve the new equivalent problem. We show the procedure by solving a practical mixed integer programming problem that arises in a typical mechanical design problem. The result shows our solution is better than the ones from other four published mixed integer programming solvers.

Keywords: Combinatorial optimization; Combinatorial analysis; Evolutionary computations; Global optimization (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-40060-5_98

Ordering information: This item can be ordered from
http://www.springer.com/9783642400605

DOI: 10.1007/978-3-642-40060-5_98

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().