Abstract Knapsack problem (KP) is a representative combinatorial optimization that aims to maximize the total profit by selecting subset of items under given constraints on weights. In this study, we analyze generalized version KP, which termed multidimensional knapsack (GMDKP). As opposed basic GMDKP allows multiple choices per item type weight constraints. Although several efficient algorithm...

Part II uses domination results in knapsack problems to assist in generating solutions more rapidly and with less work. In particular, domination results are used to: (1) generate smaller problems so that less work is needed to solve the problems, and (2) speed up solution by pruning the variable sets that must be examined. Three solution processes are examined in Part II. Domination resultS ar...

The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the followin...

We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a “typical” knapsack problem is drastically smaller than the integrality gap that occurs in a worst case scenario.

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem (MKP) are well known problems. Since KP, d-KP, and MKP are integer-valued problems defined on inputs of various informations, we study the fixed-parameter tra...