This paper deals with the collapsing knapsack problem. In the literature, to solve the problem, a method incorporating a reduction from the problem to the 0-1 knapsack problem has been proposed. In this paper we show an alternative reduction which produces coefficients smaller than those by the previous. rlOUS. The improvement makes it possible to solve the resulting 0-1 knapsack problem faster...

This paper presents hybrid algorithms for a variation of the Bounded Knapsack Problem which we call the Oregon Trail Knapsack. Our problem entails imposing a cost as well as a weight limit, constraining the values of types of items by means of a variety of value functions, and allowing the value of one item type to be dependent on the presence or absence of another type in the knapsack. These m...

In this paper, we address the online minimization knapsack problem, i. e., the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack. We study the removable model, where it is allowed to remove old items from the knapsack in order to accept a new item. We obtain the following results. (i) We propose an 8-competitive deterministic algorit...

In this note, we analyze a bilevel interdiction problem, where the follower’s program is a parametrized continuous knapsack. Based on the structure of the problem and an inverse optimization strategy, we propose for its solution an algorithm with worst-case complexity O(n). Keywords— Bilevel programming, Continuous knapsack problem, Polynomial time. 1 Model Recently, a number of papers have bee...

The deterministic knapsack problem is a well known and well studied NP-hard combinatorial optimization problem. It consists in filling a knapsack with items out of a given set such that the weight capacity of the knapsack is respected and the total reward maximized. For a review of references on the stochastic knapsack problem, stochastic gradient algorithms and branch-and-bound methods see [4]...

The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups. In this paper we deal with groups generated by Mealy automata—a class that is often used to study group-theoretical conjectures—and prove that the knapsack pr...

A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently. For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting. Surprisingly such inequalities have the simultaneous lifting property, and for small instances provide a sign...

In the classical deterministic knapsack problem, a knapsack of capacity C is given, together with K classes of objects. For every k = 1, . . . ,K, each object of the class k has a size bk and an associated reward rk. The objects can be placed into the knapsack as long as the sum of their sizes does not exceed the capacity C. The problem consists in placing the objects inside the knapsack so as ...

The Three-Dimensional Knapsack Packing Problem consists of finding the maximum profit for packing a subset of boxes in a larger box (packing box). The boxes to pack are rectangular but of different sizes. This problem is a variant of the Knapsack Problem and therefore its computational complexity is NP-Complete. This article shows a parallel genetic algorithm based on the Island Model and the N...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...