Many optimization problems are formulated as nonlinear mixed integer programming problems. Often practioners, as well as theoreticians, are interested in finding an Upper bound on the objective minimum as fast as possible. An upper bound can be found by locating an integer feasible solution first and then evaluating the corresponding value of the objective function. Given that an algorithm A exists which can generate integer feasible solutions, this paper suggests a heuristic so that the computational efforts are reduced in locating an integer feasible solution. Using the branch and bound procedures, this heuristic is tested on a number of test problems and the corresponding computational results are reported.