Jornal Global de Tecnologia e Otimização

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

Abstract

Herman Mawengkang 1 , Mangku M. Guno2 , Dedy Hartama2 , Arie S. Siregar2 , Hikmah A. Adam2 , Ommi Alfina2  

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.