1 / 13

Integer Programming Quiz: Key Concepts and Optimal Solutions Explained

This quiz focuses on fundamental aspects of integer programming (IP) and integer linear programming (ILP). It covers topics such as decision variables in optimization models, the feasible region in integer LPs, and the concept of LP relaxation. Questions include identifying optimal integer solutions from graphs, understanding the implications of LP relaxation, and effective handling techniques for ILPs using Solver. Test your comprehension of these critical concepts to enhance your understanding and application of integer optimization techniques.

derex
Télécharger la présentation

Integer Programming Quiz: Key Concepts and Optimal Solutions Explained

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 7 Integer Programming

  2. POP QUIZ #8 [5 points]

  3. POP QUIZ #8 • Integer Optimization models may require: • All of the decision variables to be integers • Some of the decision variables to be integers • Some of the decision variables to be binary (0 or 1) • Any of the above

  4. POP QUIZ #8 • The graph shows the feasible region in an Integer LP. Which point is the optimal integer solution? • Point A • Point B • Point C • Point D

  5. POP QUIZ #8 • What is the “LP relaxation” of an ILP? • A solution that ignores the integrality requirement • The nearest integer solution • The nearest integer solution that is also feasible • The optimal integer solution that is also feasible

  6. POP QUIZ #8 • How do we best handle ILPs using Solver? • Solver does not handle ILPs • By adding an integrality constraint • By manually rounding the LP solution to the nearest integer • By manually rounding the LP solution to the nearest optimal integer

  7. POP QUIZ #8 • In a Max LP relaxation problem, the Optimal Value: • Always provides an upper bound on the OV of the original ILP • Always provides a lower bound on the OV of the original ILP • Always coincides with the OV of the original ILP • Is an integer approximation of the OV of the original ILP

  8. Answers! √

  9. POP QUIZ #8 • Integer Optimization models may require: • All of the decision variables to be integers • Some of the decision variables to be integers • Some of the decision variables to be binary (0 or 1) • Any of the above √

  10. POP QUIZ #8 • The graph shows the feasible region in an Integer LP. Which point is the optimal integer solution? • Point A • Point B • Point C • Point D √

  11. POP QUIZ #8 • What is the “LP relaxation” of an ILP? • A solution that ignores the integrality requirement • The nearest integer solution • The nearest integer solution that is also feasible • The optimal integer solution that is also feasible √

  12. POP QUIZ #8 • How do we best handle ILPs using Solver? • Solver does not handle ILPs • By adding an integrality constraint • By manually rounding the LP solution to the nearest integer • By manually rounding the LP solution to the nearest optimal integer √

  13. POP QUIZ #8 • In a Max LP relaxation problem, the Optimal Value: • Always provides an upper bound on the OV of the original ILP • Always provides a lower bound on the OV of the original ILP • Always coincides with the OV of the original ILP • Is an integer approximation of the OV of the original ILP √

More Related