This　paper　considers　the　nonlinearly　constrained　nonlinear　integer　programming　problem　over　a　bounded　box.　An　auxiliary　function　is　constructed　based　on　a　penalty　function.　By　increasing　the　value　of　a　parameter,　minimization　of　the　function　by　a　discrete　local　search　method　can　escape　successfully　from　a　previously　converged　discrete　local　minimizer.　An　algorithm　is　designed　based　on　minimizing　the　auxiliary　function　with　increasing　values　of　the　parameter.　Numerical　experiments　show　that　the　algorithm　is　robust　and　efficient.　©　2008　Elsevier　Ltd.　All　rights　reserved.