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...

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...

We consider a budgeting problem where a speciied number of projects from some disjoint classes has to be selected such that the overall gain is largest possible, and such that the costs of the chosen projects do not exceed a xed upper limit. The problem has several application in government budgeting, planning, and as relaxation from other combinatorial problems. It is demonstrated that the pro...

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard that has many real-time applications. However, owing to its complexity, finding computationally efficient solutions for the MMKP remains challenging task. In this study, we propose Modified Artificial Bee Colony algorithm (MABC) solve MMKP. MABC employs surrogate relaxation, Hamming distance, and tabu list enha...

The multiple-choice multi-period knapsack problem sits in the interface of multiple choice programming and knapsack problems. Previous studies of this problem had attempted to find its optimal solution through the branch-and-bound procedure using special-ordered-sets. In this paper, we propose another solution approach based on the dynamic programming to locate its optimal solution through the ...