The special nonlinear mathematical programming problem which isaddressed in this paper has a structure characterized by a subset ofvariables restricted to assume discrete values, which are linear andseperable from the continuous variables. The strategy of releasingnonbasic variables from their bounds, combined with the "activeconshaint" method and the notion of superbasics, has been developedfor efficiently tackling such a problem by ignoring the integralityrequirements, this strategy is used to force the appropriate non-integerbasic variables to move to their neighbourhood integer points. A studyof criteria for choosing a nonbasic variable to work with in theintegerizing shategy has also been made. Successful implementation ofthese algorithms was achieved on various test problems. The resultshow that the proposed integerizing strategy is promosing in tacklingcertain classes of mixed integer programming problems.