Let me give you an example of a variation on the normal subset-sum problem that I am trying to solve:Given a set S = {1,2,3,4,5,6,7,8,9} with the maximal capacity c0 <= 40. Furthermore we have 3 additional constraints on 3 different subsets of S:S1 = {2,3,4} with constraint c1 <= 5S2 = {3,4,5,6} with constraint c2 <= 12S3 = {7,8,9} with constraint c3 <= 25The objective is to find a subset of S such that the total sum of the included items is maximized without exceeding ANY given constraint (c0 - c4).Important:intersections are possible! (see S1 & S2)3 is just an example for the count of constraints - it could be considerably more!although the items of S are integer values in this example, it could also be positive real numbersQuestion: Does this particular subset-sum problem have a specific name and/or are there any papers/ literature reviews on this ?Addition:I want to clarify the meaning of the constraints by an example for a valid and an invalid selection: Valid solution = {2,3,7,8,9} since the total sum of this set and any subset is smaller than its constraintInvalid solution = {3,4,5,7,8,9} since the sum of S1 exceeds its constraint c1 ( 3 + 4 > 5)
Variation on the subset sum problem - constrained subsets
optimization;knapsack problems