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On Optimization Problems
Vahid Moosavi
Supervisor: Ludger Hovestadt
ITA, CAAD
August 2011
Categorization of Optimization Problems based
on two main factors
Features, Properties
(elements and relations)
and their Values
Desired Output Quality
(Desired output Value)
(desired Situation)
Number of …
Uncertainty
Vagueness
Features, Properties
(elements and relations)
and their Values
Desired Output Quality
(Desired output Value)
(desired Situation)
Unknown,
Disagreement
Known,
Agreement
Known,
Agreement
Unknown,
Disagreement
Number of …
Uncertainty
Vagueness
2
Features, Properties
(elements and relations)
and their Values
Desired Output Quality
(Desired output Value)
(desired Situation)
Unknown,
Disagreement
Known,
Agreement
Known,
Agreement
Unknown,
Disagreement
Number of …
Uncertainty
Vagueness
1
3
Infeasible
Space
1
Examples:
•Designing a precise! ruler
for drawing
•Gear Box Design
•A lot of classic Optimization
Problems:
•Knapsack Problem
•Blending Problem
•Classic Shortest path
Problem
Solution Methods:
•Classic Optimization
Methods (OR)
•Optimizing the target
(objective ) functions
subject to constraints
Class 1’s Characteristics:
•Clear Objective(s) , known Desired
output Value, known desired
Situation
•Clear operational system model
Examples:
•Real transportation
problems
•Communication Systems
and (Function
Approximation)
•Gene Expression problem
•Complex machining
process modeling
Solution Methods:
•Assume Clear system models
and then transforming it to class
1 problems
•Generalizing Classic
Optimization Methods (OR)
•Stochastic Optimization
•Model (mathematical )free
(Simulation based)
•Precise data modeling
•Feature selection and
remodeling
•Problem Restructuring
Semi-Solution Methods:
•System Understanding
and analysis
•System Dynamics
modeling
•Cognitive maps
•Simulation methods
2
Class 2’s Characteristics:
•Clear Objective(s) , known Desired output
Value , known desired Situation
•Unclear operational system model
•Large number of elements and properties
•Uncertain elements and relations
Examples:
•Messy (wicked)
problems
•Good health care
system
•Good City
•Good government
•Urban Sustainability
Solution Methods:
1. Assume Clear Objectives
and then transforming it
to class 2 problems
2. Try to model the
complex behaviors (e.g.
Agent based models in
movement of residents)
3. Problem Restructuring
4. Participatory and
collaborative design and
planning methods
5. City game and
mechanism design
6. Open source technology
Semi-Solution Methods:
•System Understanding and
analysis
•System Dynamics modeling
•Cognitive maps
•Simulation methods
•Policy analysis
3 Class 3’s Characteristics:
•Unclear Objective(s) , Unknown Desired Output
Value , Unknown desired Situation
•Unclear operational system model
•Large number of elements and properties
•Uncertain elements and relations
•Stakeholders (humans) are playing in the system
•Self-referential systems
Some times having a
solution doesn’t make
sense, because there
is no clear desired
outcomes in reality!!
Thank you
21 3
Centralized
model
Decentralized
model
Distributed
problem solving
Open Source
Centralized
model
Decentralized
model
Distributed
problem solving
Clear desired
Solution
Clear desired
Solution
(sometimes)
No Clear desired
Solution can be
defined
Directing the
system instead
of managing

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On Optimization Problems

  • 1. On Optimization Problems Vahid Moosavi Supervisor: Ludger Hovestadt ITA, CAAD August 2011
  • 2. Categorization of Optimization Problems based on two main factors
  • 3. Features, Properties (elements and relations) and their Values Desired Output Quality (Desired output Value) (desired Situation) Number of … Uncertainty Vagueness
  • 4. Features, Properties (elements and relations) and their Values Desired Output Quality (Desired output Value) (desired Situation) Unknown, Disagreement Known, Agreement Known, Agreement Unknown, Disagreement Number of … Uncertainty Vagueness
  • 5. 2 Features, Properties (elements and relations) and their Values Desired Output Quality (Desired output Value) (desired Situation) Unknown, Disagreement Known, Agreement Known, Agreement Unknown, Disagreement Number of … Uncertainty Vagueness 1 3 Infeasible Space
  • 6. 1 Examples: •Designing a precise! ruler for drawing •Gear Box Design •A lot of classic Optimization Problems: •Knapsack Problem •Blending Problem •Classic Shortest path Problem Solution Methods: •Classic Optimization Methods (OR) •Optimizing the target (objective ) functions subject to constraints Class 1’s Characteristics: •Clear Objective(s) , known Desired output Value, known desired Situation •Clear operational system model
  • 7. Examples: •Real transportation problems •Communication Systems and (Function Approximation) •Gene Expression problem •Complex machining process modeling Solution Methods: •Assume Clear system models and then transforming it to class 1 problems •Generalizing Classic Optimization Methods (OR) •Stochastic Optimization •Model (mathematical )free (Simulation based) •Precise data modeling •Feature selection and remodeling •Problem Restructuring Semi-Solution Methods: •System Understanding and analysis •System Dynamics modeling •Cognitive maps •Simulation methods 2 Class 2’s Characteristics: •Clear Objective(s) , known Desired output Value , known desired Situation •Unclear operational system model •Large number of elements and properties •Uncertain elements and relations
  • 8. Examples: •Messy (wicked) problems •Good health care system •Good City •Good government •Urban Sustainability Solution Methods: 1. Assume Clear Objectives and then transforming it to class 2 problems 2. Try to model the complex behaviors (e.g. Agent based models in movement of residents) 3. Problem Restructuring 4. Participatory and collaborative design and planning methods 5. City game and mechanism design 6. Open source technology Semi-Solution Methods: •System Understanding and analysis •System Dynamics modeling •Cognitive maps •Simulation methods •Policy analysis 3 Class 3’s Characteristics: •Unclear Objective(s) , Unknown Desired Output Value , Unknown desired Situation •Unclear operational system model •Large number of elements and properties •Uncertain elements and relations •Stakeholders (humans) are playing in the system •Self-referential systems Some times having a solution doesn’t make sense, because there is no clear desired outcomes in reality!!
  • 10. 21 3 Centralized model Decentralized model Distributed problem solving Open Source Centralized model Decentralized model Distributed problem solving Clear desired Solution Clear desired Solution (sometimes) No Clear desired Solution can be defined Directing the system instead of managing