On approximation of the best case optimal value in interval linear programming
- 247 Downloads
Interval linear programming addresses problems with uncertain coefficients and the only information that we have is that the true values lie somewhere in the prescribed intervals. For the inequality constraint problem, computing the worst case scenario and the corresponding optimal value is an easy task, but the best case optimal value calculation is known to be NP-hard. In this paper, we discuss lower and upper bound approximation for the best case optimal value, and propose suitable methods for both of them. We also propose a not apriori exponential algorithm for computing the best case optimal value. The presented techniques are tested by randomly generated data, and also applied in a simple data classification problem.
KeywordsLinear programming Interval linear systems Interval analysis
The author was supported by the Czech Science Foundation Grant P402-13-10660S.
- 2.Hladík, M.: Interval linear programming: a survey. In: Z.A. Mann (ed.) Linear programming-new frontiers in theory and applications, chap. 2, pp. 85–120. Nova Science Publishers, New York (2012)Google Scholar
- 7.Allahdadi, M., Nehi, H.M.: The optimal solution set of the interval linear programming problems. Optim. Lett. To appear, doi: 10.1007/s11590-012-0530-4
- 10.Hladík, M.: How to determine basis stability in interval linear programming. Optim. Lett. To appear, doi: 10.1007/s11590-012-0589-y
- 11.Rohn, J.: A handbook of results on interval linear problems. technical report No. 1164, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague (2012)Google Scholar