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How Well Do You Know Discrete Optimization and Integer Programming?

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How Well Do You Know Discrete Optimization and Integer Programming?

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Questions and Answers

Qu'est-ce que l'optimisation discrète ?

Elle implique des variables avec des valeurs continues.

Elle implique des variables avec des valeurs discrètes. (correct)

Elle implique des variables avec des valeurs aléatoires.

Elle implique des variables avec des valeurs nulles.

Qu'est-ce que le polyèdre d'un problème de programmation linéaire ?

C'est une forme géométrique abstraite

C'est une solution optimale

C'est un ensemble de points qui satisfont les contraintes du problème (correct)

C'est une fonction mathématique

Quelle est l'utilité des méthodes heuristiques dans la résolution de problèmes d'optimisation ?

Elles fournissent des solutions exactes.

Elles fournissent des solutions optimales.

Elles fournissent des solutions sous-optimales pour des instances importantes. (correct)

Elles ne sont pas utiles dans la résolution de problèmes d'optimisation.

Study Notes

Discrete optimization involves variables with discrete values.
The optimum integer solution may not be a vertex of the polyhedron.
If a linear programming problem has an integer optimum, it will also be the optimum for the linear programming problem with non-integer values.
The optimum of the LP is an upper bound (in maximization) or lower bound (in minimization) of the LPNE.
Rounding the LP optimum may not be the optimum for the integer problem and may not be feasible.
The polyhedron defined by constraints may not contain an integer solution.
Algebraic methods of LP do not work when variables must be integers.
There are efficient algorithms for solving simple problems with exact solutions.
For complex problems, there is no known efficient algorithm in the general case.
Heuristic methods may be used for sub-optimal solutions for large instances.

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Description

Do you want to test your knowledge on Discrete Optimization? Take this quiz and answer questions on topics such as LPNE, polyhedrons, algebraic methods, and more. Challenge yourself with questions on efficient algorithms and heuristic methods used for sub-optimal solutions. Sharpen your skills and improve your understanding of Discrete Optimization with this quiz.