A survey of effective heuristics and their application to a variety of knapsack problems

TLDR

Knapsack problems extend the classical KP by adding or modifying constraints and redefining objective functions. The paper introduces a family of knapsack problems, discusses their applications, and outlines promising research directions. The authors review successful techniques and hybrid approaches that combine exact methods and heuristics for solving these knapsack variants.

Abstract

We present a family of knapsack problems (KPs) while highlighting their particular applications. Though most of the problems are derived from the classical KP, the differences arise in the addition or modification of the constraints or in the way the objective function is defined. Appropriate techniques that were found to be successful in solving these problems are briefly reviewed. Hybrid methods that combine the strengths of different methods such as exact and heuristics are also briefly discussed. Some research avenues that we believe to be useful and challenging are also pointed out.