The set of particular 0-1 optimization problems solvable in polynomial time has been extended. This becomes when the coefficients of the objective function belong to the set of superincreasing or superdecreasing types of sequence. We have defined special superincreasing sequences which we call the nearest up and nearest down to the sequence (
) of objective function coefficients. They are applied to calculate the upper and lower bound of optimal objective function value. When the problem needs to compute the minimum of objective function with the superdecreasing sequence (
), two cases are considered. Firstly, we have described a type of problem when optimal solution can be obtained directly using a polynomial procedure. The second case needs two phases to calculate an optimal solution. The second phase relies on improving a feasible solution. The complexities of all the presented procedures are given.