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Research Article

An Improved Direct Search Approach for Solving Mixed-Integer Nonlinear Programming Problems

Herman Mawengkang1*, Mangku M. Guno2, Dedy Hartama2, Arie S. Siregar2, Hikmah A. Adam2, Ommi Alfina2

1Graduate School of Mathematics, University of Sumatera Utara

2Graduate School of Computer Science, University of Sumatera Utara

*Corresponding Author:
Herman Mawengkang
Graduate School of Mathematics, University of Sumatera Utara
E-mail: [email protected]

Received date: January 2012; Revised date: March 2012; Accepted date: April 2012

Abstract

The special class of a nonlinear mathematical programming problem which is addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing non-basic variables from their bounds, combined with the “active constraint” method and the notion of super-basics, has been developed for efficiently tackling the problem. After solving the problem by ignoring the integrality requirements, this strategy is used to force the appropriate non-integer basic variables to move to their neighborhood integer points. A study of criteria for choosing a non-basic variable to work with in the integer zing strategy has also been made. Successful implementation of these algorithms was achieved on various test problems. The results show that the proposed integer zing strategy is promising in tackling certain classes of mixed integer nonlinear programming problems.

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