nonlinear knapsack problems (nkp) are the alternative formulation for the multiple-choice knapsack problems. a powerful approach for solving nkp is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

We present an algorithm for the penalized multiple choice knapsack problem (PMCKP), a combination of the more common penalized knapsack problem (PKP) and multiple choice knapsack problem (MCKP). Our approach is to converts a PMCKP into a PKP using a previously known transformation between MCKP and KP, and then solve the PKP greedily. For PMCKPs with well-behaved penalty functions, our algorithm...

We model the problem of bidding in ad auctions as a penalized multiple choice knapsack problem (PMCKP), a combination of the multiple choice knapsack problem (MCKP) and the penalized knapsack problem (PKP) [1]. We present two versions of PMCKP, GlobalPMCKP and LocalPMCKP, together with a greedy algorithm that solves the linear relaxation of a GlobalPMCKP optimally. We also develop a greedy heur...

Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...

it is shown in [1] that the optimal downlink radio resource allocation for non-realtime traffic in cellular cdma/tdma networks can be mapped to a multi-dimensional multiple-choice knapsack problem (mmkp) which is np-hard. in this correspondence we propose a heuristic algorithm with polynomial time complexity for this problem. numerical results indicate significant computational performance impr...

This paper treats the multiple-choice (continuous) knapsack problem P: n mi n mi maximize L .L cijxijsubjectto(l) I I aij x ij";b,(2)0,,;xij";1,i=I,2, i=l J=l i=l J=1 ... , n, j = 1,2, .... mi and (3) at most one of x il, x i2' ... , x im. is positive for i = 1,2, ., ., n, , where n, mi are positive integers and aij' Cij' bare nonnegative real numbers. Two approximate algorithms and an exact br...

In this paper the 0-1 Multiple-Choice Knapsack Problem (0-1 MCKP), a generalization of the classical 0-1 Knapsack problem, is addressed. We present a fast Fully Polynomial Time Approximation Scheme (FPTAS) for the 0-1 MCKP, which yields a better time bound than known algorithms. In particular it produces a (1+ ) approximate solution and runs in O(nm/ ) time, where n is the number of items and m...

Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...