On the setof then-dimensional 0 – 1 vectors with at least ϱ positive components a semi-ordering is introduced. Each real valued functionf(x), defined on, withf(x) ≦f(y) forx<yis called 0 – 1 – ρ-monoton increasing. Combinatorial algorithms, presented by the authors for linear 0 – 1-programming, are extend to 0 – 1-programming problems with 0 – 1 – ρ-monoton increasing objective function and arbitrary restrictions.