1. A new exact algorithm for concave knapsack problems with integer variables.
- Author
-
Wang, Fenlan
- Subjects
- *
ALGORITHMS , *KNAPSACK problems , *INTEGERS , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis - Abstract
Concave knapsack problems with integer variables have many applications in real life, and they are NP-hard. In this paper, an exact and efficient algorithm is presented for concave knapsack problems. The algorithm combines the contour cut with a special cut to improve the lower bound and reduce the duality gap gradually in the iterative process. The lower bound of the problem is obtained by solving a linear underestimation problem. A special cut is performed by exploiting the structures of the objective function and the feasible region of the primal problem. The optimal solution can be found in a finite number of iterations, and numerical experiments are also reported for two different types of concave objective functions. The computational results show the algorithm is efficient. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF