Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem
Management Science
Server-side coprocessor updating for mobile devices with FPGAs
Proceedings of the 18th annual ACM/SIGDA international symposium on Field programmable gate arrays
Local branching-based algorithms for the disjunctively constrained knapsack problem
Computers and Industrial Engineering
The Bin Packing Problem with Precedence Constraints
Operations Research
The Bin Packing Problem with Precedence Constraints
Operations Research
Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm
INFORMS Journal on Computing
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In this paper, we optimally solve the disjunctively constrained knapsack problem (DCKP), which is a variant of the standard knapsack problem with special disjunctive constraints. First, we develop a generic exact approach which can be considered as a three-phase procedure. The first phase tries to estimate a starting lower bound. The second phase applies a reduction procedure, combined with the lower bound, in order to fix some decision variables to the optimum. The third phase uses an exact branch and bound algorithm that identifies the optimal values of the free decision variables. Second, we design a specialized exact algorithm based upon a dichotomous search combined with a reduction procedure. Third and last, we propose a modified dichotomous search version which is based upon constructing an equivalent model to the DCKP, adding some dominating constraints, and injecting the so-called covering cut. We evaluate the performance of all versions of the algorithm and compare the obtained results to those of other exact algorithms of the literature. Encouraging results have been obtained.