A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Core Problems in Knapsack Algorithms
Operations Research
Fast, effective heuristics for the 0-1 multi-dimensional knapsack problem
Computers and Operations Research
The core concept for the multidimensional knapsack problem
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm
International Journal of Bio-Inspired Computation
CORAL: An Exact Algorithm for the Multidimensional Knapsack Problem
INFORMS Journal on Computing
Kernel search for the capacitated facility location problem
Journal of Heuristics
Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems
Journal of Global Optimization
Hi-index | 0.01 |
In this paper we apply the kernel search framework to the solution of the strongly NP-hard multi-dimensional knapsack problem (MKP). Kernel search is a heuristic framework based on the identification of a restricted set of promising items (kernel) and on the exact solution of ILP sub-problems. Initially, the continuous relaxation of the MKP, solved on the complete set of available items, is used to identify the initial kernel. Then, a sequence of ILP sub-problems are solved, where each sub-problem is restricted to the present kernel and to a subset of other items. Each ILP sub-problem may find better solutions with respect to the previous one and identify further items to insert into the kernel. The kernel search was initially proposed to solve a complex portfolio optimization problem. In this paper we show that the method has general key features that make it appropriate to solve other combinatorial problems using binary variables to model the decisions to select or not items. We adapt the kernel search to the solution of MKP and show that the method is very effective and efficient with respect to known problem-specific approaches. Moreover, the best known values of some MKP benchmark problems from the MIPLIB library have been improved.