In this paper we introduce a new Packing problem, the Three-Dimensional Knapsack Problem with Balancing Constraints (3BKP), the extension of the ThreeDimensional Knapsack Problem (3KP) where additional constraints related to the packing center of mass are given. The 3BKP consists in orthogonally packing a subset of threedimensional weighted items into a knapsack in order to maximize the total p...

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms ar...

A lot of current research in DNA computing has been directed towards solving hard combinatorial problems. Among them Knapsack problem is one of the most common problems which have been studied intensively in the last decade attracting both theorists and practicians. Fractional Knapsack Problem is easily solvable by greedy strategy, but 0/1 Knapsack Problem is not possible to solve in this metho...

Studies on plant metabolites have attracted significant attention in recent years. Over the past 8 years, we have constructed a unique metabolite database, called KNApSAcK, that contains information on the relationships between metabolites and their expressing organism(s). In the present paper, we introduce KNApSAcK-3D, which contains the three-dimensional (3D) structures of all of the metaboli...

In this paper we study a particular version of the stochastic knapsack problem with normally distributed weights: the two-stage stochastic knapsack problem. In contrary to the single-stage knapsack problem, items can be added to or removed from the knapsack at the moment the actual weights come to be known (second stage). In addition, a probability constraint is introduced in the first stage in...

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...