Ordered ranking machine learning techniques

I have the following problem. Suppose I have 100 groups of patterns. Group i has N_i patterns. The patterns have a ranking within each group. For group i the patterns are ranked in some order. The complete data set is composed of patterns that can be written as:

{x_j = (pattern_features, i), y_j=i_j},

where pattern_features are the pattern features, whatever they are, i is the group that contains the pattern, and i_j is the ranking of the pattern within group i.

What machine learning techniques exist to predict those rankings? The training samples should be pairs of pattern_features and rankings i_j.

Edit:

A metric for ranking should be for each group i

sum(abs(i_j-y_pred_j) for pattern j in group i)/N_i

where N_i is the maximum possible difference, i.e. in the case of a group of 2 items, the maximum possible difference is 2, which is obtained if item number 1 is ranked as 2, and item number 2 is ranked as 1. Similarly, in the case of a group of 3 items, the maximum possible difference is 4, which can be obtained for instance if item number 1 is ranked as 3, item number 2 is ranked as 2, and item number 3 is ranked as 1.