Difference between Multiple Knapsack problem and Multidimensional Knapsack Problem What is the difference between Multiple Knapsack problem and Multidimensional Knapsack Problem? (http://en.wikipedia.org/wiki/List_of_knapsack_problems#Multiple_constraints) According to the literature, Multiple Knapsack problem has integrality gap of 2, what is the integrality gap for Multidimensional Knapsack Problem ?
In a multiple knapsack problem you pack a set of items into several (one-dimensional) knapsacks, whereas in the multidimentional knapsack problem you pack d-dimensional items into one d-dimensional knapsack. The multiple knapsack problem $\max\{\sum_i p_i x_i \mid \sum_i w_{ij}x_i \leq d_j, j=1,2,\ldots,m\}$ is a general 0-1 integer program restricted to positive coefficients. Its integrality gap is unbounded, since it includes the maximum independent set problem whose formulation $\max\{\sum_{v\in V} x_v\mid x_u+x_v\leq 1, \{u,v\}\in E\}$ on an undirected graph $G=(V,E)$ has integrality gap $|V|/2$.

You can find more information on these problems in chapters 9 and 10 of  Kellerer, Pferschy, and Pisinger, "Knapsack problems".