5 Algorithms 8 5.1 Fourier-Motzkin Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 The Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Seidel’s Randomized Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.4 The Ellipsoid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.5 Using the Ellipsoid...

Sandpile group or Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. It is well known that these recurrent configurations can be characterized as optimal solution certain non-linear optimization problems. We show graph correspond to solutions some integer linear programs. More precisely, we present two new programming models, on...

multi-objective optimization is the simultaneous consideration of two or more objective functions that are completely or partially inconflict with each other. the optimality of such optimizations is largely defined through the pareto optimality. multiple objective integer linear programs (moilp) are special cases of multiple criteria decision making problems. numerous algorithms have been desig...

In this paper, we investigate a Transportation problem which is a special kind of linear programming in which profits; supply and demands are considered as Intuitionistic triangular fuzzy numbers. The crisp values of these Intuitionistic triangular fuzzy numbers are obtained by defuzzifying them and the problem is formulated into linear programming problem. The solution of the formulated proble...

 We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...