We　consider　in　this　paper　the　nonconvex　mixed-integer　nonlinear　programming　problem.　We　present　a　mixed　local　search　method　to　find　a　local　minimizer　of　an　unconstrained　nonconvex　mixed-integer　nonlinear　programming　problem.　Then　an　auxiliary　function　which　has　the　same　global　minimizers　and　the　same　global　minimal　value　as　the　original　problem　is　constructed.　Minimization　of　the　auxiliary　function　using　our　local　search　method　can　escape　successfully　from　previously　converged　local　minimizers　by　taking　increasing　values　of　parameters.　For　the　constrained　nonconvex　mixed-integer　nonlinear　programming　problem,　we　develop　a　penalty　based　method　to　convert　the　problem　into　an　unconstrained　one,　and　then　use　the　above　method　to　solve　the　later　problem.　Numerical　experiments　and　comparisons　on　a　set　of　MINLP　benchmark　problems　show　the　effectiveness　of　the　proposed　algorithm.　(C)　2011　Elsevier　Ltd.　All　rights　reserved.