Like for many NP-hard combinatorial optimization problems, both exact and heuristic algorithms have been developed for the MKP01. Existing exact algorithms are essentially based on the branch and bound method [11]. These algorithms are different one from another according to the way the upper bounds are obtained. For instance, in [11], Shih solves, exactly, each of the m single constrained, rel...

Preface This thesis is a result of my internship at the Centrum Wiskunde en Informatica (CWI). It is also an important part of my master study in Leiden University (UL). First of all, I want to give my special thanks to Chrétien Verhoef for all the daily advices and help from the beginning to the very end. I came to CWI with very little pre-knowledge about queueing theory and programming. His p...

Knapsack constraints are a key modeling structure in discrete optimization and form the core of many real-life problem formulations. Only recently, a cost-based filtering algorithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knapsack problem. In this paper, we provide an empirical evaluation of approximated consistency for K...

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...