Multicriteria Optimization

Fall 2013

October 29, 2013: Class 7: Weighted Sum Method and Connectedness

In this class, we discuss the relationship between solutions found with the weighted sum method and properly efficient solutions. Further, we talk about criteria for having a connected nondominated set. Lastly, we show how to use Excel to solve a multicriteria optimization problem using the weighted sum method.

Details:
Quiz: Start at beginning
Background Set Information: Start around 2:40
Weighted Sum Method: Start around 5:45
Connectedness: Start around 21:20
Example in Excel: Start around 27:15

Goal Programmig

In this video, we go through a goal programming problem example. We take a problem with 3 different goals and weight any deviations from these goals appropriately. We then solve the problem in order to see which goals we can meet. Note: This video is from a previous class in case the extra commentary is not relevant.

Details:
Goal Programming Formulation: Start at beginning
Linear Programming Formulation and Deviations: Start at about 2:11
Solving with Excel: Start at about 11:50
Penalty Weights: Start at about 14:50

September 24, 2013: Class 3: Orders and Cones

In this class, we discuss ways to determine which solutions to multicriteria optimization problems are better than others based on different orders. Further, we prove that all orders compatible with scalar multiplication can be represented as a cone. Therefore, cones can be used to determine an ordering of solutions to multicriteria optimization problems.

Details:
Motivation: Start at beginning
Background Set Information: Start around 2:30
Orders: Start around 8:30
Cones: Start around 19:30
Key Takeaways/Information: Start around 39:45