Christophe Wilbaut, Said Hanafi, Said Salhi; A survey of effective heuristics and their application to a variety of knapsack problems. IMA J Management Math 2008; 19 (3): 227-244. doi: 10.1093/imaman/dpn004
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.