ISYE 6669 / ISYE 6669 Final Exam
(Latest Update )
Deterministic Optimization |
Questions & Answers | Grade A |
100% Correct - Georgia Tech
Question:
What is the general formulation for the set packing problem?
Answer:
Given weights w for binary variables x where each constraint contains a subset
of x. Maximize w given that each subset is disjoint.
Question:
What is the network flow supply constraint?
Answer:
Leaving flow - entering flow = supply
,Question:
What is so special about network flow problems when dealing with integers
and LP?
Answer:
If all supply and capacity data are integers, then every extreme point (ie BFS)
will be an integer. Thus the network flow problem can be solved using simplex
even though it is a Mixed Integer Linear Program (ie not Standard Form LP).
Question:
How do you relax an MILP? What are some properties of the relaxed LP?
Answer:
Turn the integer variables into continuous variables. If the LP relaxation is
infeasible, so is the MILP. If the LP has an optimal solution, the MILP may
still be infeasible or also have an optimal solution. If LP is unbounded, then
MILP is unbounded or infeasible. the relaxed optimal solution is always less
than or equal to the MILP optimal solution. If the optimal solution to the
relaxed problem is integral, then that is the optimal solution to the MILP.
, Question:
What is a stronger formulation for a MILP? What benefits do we get from
stronger formulations?
Answer:
A more restrictive set of constraints that contain the same feasible solutions.
This leads to better optimality gaps, better relaxation bounds, and sometimes
relaxation LP's with feasible solutions to the MILP.
Question:
How do we create a stronger formulation to a MILP?
Answer:
By adding new tightening inequalities, by tightening constraint coefficients to
current constraints, and by introducing new variables and constraints to
those variables.
Question:
What does a two stage stochastic problem consist of? What is the objective of
the problem?
Answer:
A here and now decision and a wait and see decision. Minimize production
cost and expected future cost
(Latest Update )
Deterministic Optimization |
Questions & Answers | Grade A |
100% Correct - Georgia Tech
Question:
What is the general formulation for the set packing problem?
Answer:
Given weights w for binary variables x where each constraint contains a subset
of x. Maximize w given that each subset is disjoint.
Question:
What is the network flow supply constraint?
Answer:
Leaving flow - entering flow = supply
,Question:
What is so special about network flow problems when dealing with integers
and LP?
Answer:
If all supply and capacity data are integers, then every extreme point (ie BFS)
will be an integer. Thus the network flow problem can be solved using simplex
even though it is a Mixed Integer Linear Program (ie not Standard Form LP).
Question:
How do you relax an MILP? What are some properties of the relaxed LP?
Answer:
Turn the integer variables into continuous variables. If the LP relaxation is
infeasible, so is the MILP. If the LP has an optimal solution, the MILP may
still be infeasible or also have an optimal solution. If LP is unbounded, then
MILP is unbounded or infeasible. the relaxed optimal solution is always less
than or equal to the MILP optimal solution. If the optimal solution to the
relaxed problem is integral, then that is the optimal solution to the MILP.
, Question:
What is a stronger formulation for a MILP? What benefits do we get from
stronger formulations?
Answer:
A more restrictive set of constraints that contain the same feasible solutions.
This leads to better optimality gaps, better relaxation bounds, and sometimes
relaxation LP's with feasible solutions to the MILP.
Question:
How do we create a stronger formulation to a MILP?
Answer:
By adding new tightening inequalities, by tightening constraint coefficients to
current constraints, and by introducing new variables and constraints to
those variables.
Question:
What does a two stage stochastic problem consist of? What is the objective of
the problem?
Answer:
A here and now decision and a wait and see decision. Minimize production
cost and expected future cost
