Knapsack Problems

The development of computational complexity theory has led, in the last 15 years, to insights into the inherent difficulty of combinatorial optimization problems, but has also produced an undesirable side effect which can be summarized by the "equation" NP-hardness = intractability, thereby diminishing attention to the study of exact algorithms for NP-hard problems. This book presents exact and approximate algorithms for a number of important NP-hard problems in the field of integer linear programming, which are grouped under the term "knapsack". The reader will find not not only the "classical" knapsack problems (binary, bounded, unbounded, binary multiple), but also less familiar problems (subset-sum, change-making) or well-known problems which are not usually classified in the knapsack area (generalized assignment, bin-packing). The goal of the book is to fully develop an algorithmic approach without losing mathematical rigour. For each problem, the authors start by giving a mathematical model, discussing its relaxations and deriving procedures for the computation of bounds.
They then develop approximate algorithms, approximation schemes dynamic programming techniques and branch-and-bound algorithms.