Interval linear programming under transformations: optimal solutions and optimal value range

Optimal value range in interval linear programming

The optimal solution set of the interval linear programming problems

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the o...

On approximation of the best case optimal value in interval linear programming

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 discu...

Optimal Setting Sor Under Frequency Load Shedding Relays Using Mixed Integer Linear Programming

After occurrence of some disturbances in power system that causes the sever imbalance between generation power and electrical load, the power system frequency begins to decrease. To prevent power system frequency instability and stop the frequency decay below the power system allowable frequency limitation, load shedding schemes should be utilized by applying under frequency load shedding relay...

Pareto-optimal solutions in fuzzy multi-objective linear programming

The problem of solving multi-objective linear-programming problems, by assuming that the decision maker has fuzzy goals for each of the objective functions, is addressed. Several methods have been proposed in the literature in order to obtain fuzzyefficient solutions to fuzzy multi-objective programming problems. In this paper we show that, in the case that one of our goals is fully achieved, a...