12/17/2023 0 Comments Multi dimensional knapsack problemIn this note we settle both questions conclusively: we show that (a) Rkp is indeed NP -hard in the considered setting (and even in more restricted settings), and (b) there exists both a pseudopolynomial algorithm and a fully-polynomial time approximation scheme (i.e. The key results are an NP -hardness proof for a more general scenario than Rkp, and a 4.5-approximation for Rkp, raising the question of improvements for either result. 2 Previous work The 2D knapsack problem is NP hard (cf. A Sum-of-Ratios Multi-Dimensional-Knapsack Decomposition for DNN Resource Scheduling Abstract: In recent years, to sustain the resource-intensive computational needs for training deep neural networks (DNNs), it is widely accepted that exploiting the parallelism in large-scale computing clusters is critical for the efficient deployments of DNN. Measures such as fitness distance correlation and autocorrelation are applied to examine the landscapes associated with the tested genetic encodings. 11 2.3 Metode Penyelesaian Knapsack Problem Beberapa teknik atau metode telah digunakan untuk menyelesaikan persoalan Knapsack, diantaranya adalah Branch and Bound, Dynamic Programming, State Space Relaxations, Pre-prosecessing, GA dan sebagainya. Common mutation operators, such as bit-flip mutation, are employed to generate fitness landscapes. Multi-choice Multi-dimensional Knapsack Problem mmKP. After this the GA is subjected to a test using known benchmark instances, while at the end the paper is summarized. Five representations are investigated for the multidimensional knapsack problem. Then the genetic algorithm will be described. In this study, we analyze a generalized version of KP, which is termed as the generalized multidimensional knapsack problem (GMDKP). To this end, they started an investigation into its complexity and approximability. The next section provides an overview of the literature on the 2D knapsack problem. Knapsack problem (KP) is a representative combinatorial optimization problem that aims to maximize the total profit by selecting a subset of items under given constraints on the total weights. (Math Methods Oper Res 92(1):107–132, 2020) presented the Rectangular Knapsack Problem (Rkp) as a crucial subproblem in the study on the Cardinality-constrained Bi-objective Knapsack Problem (Cbkp).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |