The classical binary knapsack problem has numerous generalisations in relation to not only a capacity constraint but also an objective function. In 2006, two knapsack problems have coincidentally been proposed, both of which have an extension of the objective function paying the penalty. This...

This is a revised version of Iida [5]: We introduce a new type of problem that we shall call collapsing subset-sum problem, and present an algorithm to solve the problem. The problem is a special case of the collapsing knapsack problem, and the algorithm based on a depth-first branch-and-bound...