On Optimization Problems

Vahid Moosavi

Supervisor: Ludger HovestadtITA, 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

2Class 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