Robust Optimization
We are living in a world with lots of uncertainties. Weather conditions, prices, and traffic jams are only a few uncertainties that we are encountering in our daily life. Societal and industrial parties are also facing uncertainties in demands, costs, and many more parameters on which their revenues are based. So, the important question is “how decision makers can take decisions while many of the decision parameters are uncertain?”
Praktische info:
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Leertraject
Programme
The goal of this course is to teach students how to answer this question using “robustness,” which is a concept that helps us to make decisions that are not vulnerable to changes in uncertain parameters. So, the first and the most important concept that will be taught in this course is Robustness in Optimization problems.
The course consists of 8 sessions of 2 hours. In these sessions we will cover 5 modules, each of which has its own objectives:
- Session 1: Covering a bit of pre-knowledge and Components 1-3
- Session 2: Components 4-5 and working out an exercise
- Session 3: Components 6-7 and working out two exercises
- Session 4: Component 8 and working out an exercise
- Session 5: Component 9 and working out an exercise
- Session 6: Components 10-11 and working out an exercise
- Session 7: Components 12 and working out an exercise
- Session 8: Component 13 and an introduction to RSOME (a Python package to solve robust optimization problems)
Module1: Introduction and Motivation
Component 1: Sources of Uncertainty
Learning goal:
- Understand the sources of uncertainty in problems
Component 2: Probability Theory and its Limitations
Learning goal:
- Understand the limitation of working with average valued
- Understand the limitation of working with chance constraints
Component 3: The Robust Optimization Paradigm
Learning goal:
- Understand the advantages of using RO
Module 2: Static Robust Optimization
Component 4: Robust Counterpart
Learning goal:
- Mathematically formulate RO
- Reformulate RC using linear programming duality
Component 5: Drawback of reformulation and enumeration
Learning goal:
- Understand the drawback of using the reformulation obtained by duality
- Use the vertex enumeration as an alternative technique
Component 6: Robust Facility Location
Learning goal:
- Construct the RC using a deterministic model
- Reformulate RC by analyzing the model
- Interprete the solution obtained from RC
Component 7: Selecting Parameters for Uncertainty Sets
Learning goal:
- Understand the effect of the uncertainty set is in the solution
- Select the parameters of an uncertainty set
Module 3: Adaptive Robust Optimization
Component 8: ARO formulation and its difference to SRO
Learning goal:
- Understand the concept of adaptivity
- Formulate adaptivity mathematically
- Understand the differences between adaptive and static RO
Component 9: Affinely Adaptive Robust Optimization
Learning goal:
- Understand the idea behind AARO
- Formulate AARO using ADR mathematically
Component 10: Finitely Adaptive Approach
Learning goal:
- Understand the idea behind FA
- Formulate FA mathematically
Component 11: Finite Scenario Approach
Learning goal:
- Understand the idea of FS
- Formulate FS mathematically
Module 4: Robust optimization with integer variables
Component 12: Partition and Bound Method for Two-Stage AMIO
Learning goal:
- Dealing with integer variables in SRO
- Dealing with the integrality of “here-and-now” decisions in ARO
- Dealing with the integrality of “wait-and-see” decisions in ARO
- Construct an iterative method using the Voronoi diagram
Module 5: Art of Modeling
Component 13: The Art of Robust and Adaptive Modeling
Learning goal:
- Understand the effects of modeling in the solution of RO
- Understand the reason behind the effects
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