In the d-dimensional knapsack problem given is a set of items, each having a d-dimensional size vector and a profit, and a d-dimensional bin. The goal is to select a subset of the items of maximum total profit such that the sum of all vectors is bounded by the bin capacity in each dimension. It is well known that, unless P = NP , there is no fully polynomial time approximation scheme for d-dime...

In this paper, as a main theorem, we prove that the decision version of the Frobenius problem is Σ2 -complete under Karp reductions. Given a finite set A of coprime positive integers, we call the greatest integer that cannot be represented as a nonnegative integer combination of A the Frobenius number, and we denote it as g(A). We call a problem of finding g(A) for a given A the Frobenius probl...

With the advent of novel mass spectrometry techniques such as Orbitrap MS, it is possible to determine the exact molecular formula of an unknown molecule solely from its isotope pattern. But for protein mass spectrometry, one is facing the problem that many peptides have exactly the same molecular formula even when ignoring the order of amino acids. In this work, we present an efficient method ...

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...

In this paper, we approximately solve the multiple-choice multi-dimensional knapsack problem. We propose an algorithm which is based upon reactive local search and where an explicit check for the repetition of configurations is added to the local search. The algorithm starts by an initial solution and improved by using a fast iterative procedure. Later, both deblocking and degrading procedures ...

We have previously developed an adaptation of the simulated annealing for multi-objective combinatorial optimization (MOCO) problems to construct an approximation of the e$cient set of such problem. In order to deal with large-scale problems, we transform this approach to propose an interactive procedure. The method is tested on the multi-objective knapsack problem and the multi-objective assig...

The Multi-Handler Knapsack Problem under Uncertainty (MHKPu) is a new stochastic knapsack problem where, given a set of items, characterized by volume and random profit, and a set of potential handlers, we want to find a subset of items which maximizes the expected total profit. The item profit is given by the sum of a deterministic profit plus a stochastic profit due to the random handling cos...

Optimization problems due to noisy data solved using stochastic programming or robust optimization approaches require the explicit characterization of an uncertainty set U that models the nature of the noise. Such approaches depend on the modeling of the uncertainty set and suffer from an erroneous estimation of the noise. In this paper, we introduce a framework that considers the uncertain dat...