The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 0-1 knapsack set. One motivation for studying the submodular knapsack polytope is to address 0-1 programming problems with uncertain coefficients. Under various assumptions, a probabilistic constraint on 0-1 variables can be modeled as a submodular knapsack set....

The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 0-1 knapsack set. One motivation for studying the submodular knapsack polytope is to address 0-1 programming problems with uncertain coefficients. Under various assumptions, a probabilistic constraint on 0-1 variables can be modeled as a submodular knapsack set....

The 0/1 knapsack problem is a well known problem occurring in many real world problems. The problem is NP-Complete. The multiobjective 0/1 knapsack problem is a generalization of the 0/1 knapsack problem in which multiple knapsacks are considered. A new evolutionary algorithm for solving multiobjective 0/1 knapsack problem is proposed in this paper. This algorithm used a ε-dominance relation fo...

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under...

The knapsack problem (KP) is generalized to the case where items are partially ordered through a set of precedence relations. As in ordinary KPs, each item is associated with profit and weight, the knapsack has a fixed capacity, and the problem is to determine the set of items to be packed in the knapsack. However, each item can be accepted only when all the preceding items have been included i...