In　this　paper,　we　consider　the　box　constrained　nonlinear　integer　programming　problem.　We　present　an　auxiliary　function,　which　has　the　same　discrete　global　minimizers　as　the　problem.　The　minimization　of　the　function　using　a　discrete　local　search　method　can　escape　successfully　from　previously　converged　discrete　local　minimizers　by　taking　increasing　values　of　a　parameter.　We　propose　an　algorithm　to　find　a　global　minimizer　of　the　box　constrained　nonlinear　integer　programming　problem.　The　algorithm　minimizes　the　auxiliary　function　from　random　initial　points.　We　prove　that　the　algorithm　can　converge　asymptotically　with　probability　one.　Numerical　experiments　on　a　set　of　test　problems　show　that　the　algorithm　is　efficient　and　robust.　(c)　2008　Elsevier　B.V.　All　rights　reserved.