An Improved Approach For Solving Mixed-Integer Nonlinear Programming Problems

This 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 nonbasic variables from their bounds, combined with the “active constraint” method and the notion of superbasics, 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 nonbasic variable to work with in the integerizing strategy has also been made. Successful implementation of these algorithms was achieved on various test problems. The results show that the proposed integerizing strategy is promising in tacking certain classes of mixed integer nonlinear programming problems.