Complex Systems, Networks and MDO in Design
Soundar KumaraPearce Chair Professor of Industrial Engineering
Professor of Computer Science & Engineering
The Pennsylvania State UniversityPresentation at the NSF Workshop on MDO
Fort Worth, TX; September 16, [email protected]
Complexity
� Two aspects of complexity –Variety to heterogeneity and connection.
� Distinction in the limit leads to disorder or chaos or entropy
� Connection (constraint) leads to order or negentropy
� Complexity can only exist if both neither perfect disorder nor perfect order
present – colloquially on the edge of chaos
� In order to have a complex system you need at least two parts connected together; distinct as well as interconnected – so when several parts are connected together we need to preserve the “emergent behavior.”
We need to modularize the interfaces – information, which in turn helps modularize functionality and possibly reduce diversity
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4
Multi-Agent Decision-Making Framework (with Drs. Simpson & Moon): Modeling Dimension
CommunicationCommunicationCommunicationCommunication
System System System System architecturearchitecturearchitecturearchitecture
TasksTasksTasksTasks
AgreementAgreementAgreementAgreement
MultiMultiMultiMulti----agent systemagent systemagent systemagent system Step 4: DecisionStep 4: DecisionStep 4: DecisionStep 4: Decision----MakingMakingMakingMaking
Step 1: Analysis Step 1: Analysis Step 1: Analysis Step 1: Analysis - Product dissection and a functional model
- Object-oriented concepts and a process model
Step 2: OntologyStep 2: OntologyStep 2: OntologyStep 2: Ontology - Techspecs Concept Ontology (product)
- Service ontology
Step 3: Module identificationStep 3: Module identificationStep 3: Module identificationStep 3: Module identification
- Fuzzy C-mean Clustering
- Association rule mining
- Classification
- Fuzzy set theory
- A negotiation mechanism
- A Bayesian game
AgentAgentAgentAgent----based Decisionbased Decisionbased Decisionbased Decision----MakingMakingMakingMaking
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Product Design and Multi-Agent System
� Product can be designed with modules and components
� Each module and component can be modeled as a self-interested agent
� A market-based mechanism can be applied to decision-making methods in dynamic and distributed environments
Product agentProduct agentProduct agentProduct agent
Module agentsModule agentsModule agentsModule agents
Component agentsComponent agentsComponent agentsComponent agents
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Market Mechanism Design
Platform agent
Module agents
Component agents
Combinatorial
auction
Market-based
negotiation
(Buyers/ Sellers)
Component agents(Sellers)
(Buyers)
Game theoretic
approach
Relationships among the Agents in a Market System
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System Architecture for Platform Design
Product1-Market
Agent 1
Negotiation
Customer
Needs
Customer Agent
Coordinator Agent
Manufacturing System
Product Agent
Module1 Agent
Market
Product1-Market
Agent 2 Platform Agent
Variant Design
Agent
Market Manager
Agent
Module2 Agent
Module3 Agent
Services Agent
Production Planning
Agent
Component
Agent 1
Component
Agent 2
Customer
Needs
Functional
Requirements Customer
Needs
Customer
Needs
Functional
Requirements
Functional
Requirements
Materials and Resources New or redesigned products
Company
Strategy
Game
Development SystemProcesses and Resources New or redesigned services
Products and Services Development System
Dynamic Multi-Agent System
Auction
Complex System Design
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Conceptual view of blended-wing-body control using agents [Kroo, 2005] – he calls the collection of agents as Collectives to reduce diversity
Information Dimension
� Can we represent the Design synthesis problem as a query retrieval process? Compose several services (disciplines, methodologies, components etc) in a
Web Service Information Modeling framework ?
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What is a web service?
Google map, Yahoo map, MapQuest
EBay, Amazon
Online BankingOnline education
Consumer goodsPeople
Function
Crowd SourcingProduction plan/ design/Web service composition
W1: getHospital
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Web Service Composition (WSC)W1: getHospital
W2: getBlood
Initial
Goal
Input :
W3: askDeliveryOutput :
Input :
Output :
Input :
Output :a: PatientInfo b: BloodType
c: BloodAmount
d: TargetTime
a: PatientInfo
e: HospitalAddress
b: BloodTypec: BloodAmount
f: BloodBankAddress
f: BloodBankAddress
d: TargetTimee: HospitalAddress
e: HospitalAddress
g: DeliveryConfirmation
g: DeliveryConfirmation
W4: getDirectionInput :
Output :g’: SourceAddressf’: DestinationAddress
j: EstimatedDeliveryDateTimek: Direction
Hospitals
Blood banks
Transportation companies
f: BloodBankAddress
W6: getRestaurantInput :
Output :n: HotelAddressm: FoodTaste
o: RestaruantAddressp: TelephoneNumber
W5: getHospitalWithBankInput :
Output :
a: PatientInfo
f: BloodBankAddress
b: BloodType
e: HospitalAddress
g: DeliveryConfirmation
c: BloodAmount
Problem Definition
Find a plan for a request:
Given:(1) Web Service Descriptions (WSDL file)
(2) Semantic Ontology (OWL file)
Aim: ( , )g v e
Maximize Utility( )U G
( , , )G V E Q QoS of a service: (price $11,
lead time: 2 business days, reliability 0.8)
Concept: Time Instant: 10 am on Tuesday
Departure time
Proposed methods
(2)MCGP model (3)DP model(1)Network model
compromised solution
functionality and QoS;
the optimal plan;
Real time
uncertainty
the optimal plan;
Preprocess of service networ
ks
Network Mining;
Fast;
Web Service Composition
Three types of models
Two solving method for MCP
3x2=6
Web service compositionFind the clusters, and bridges. (This can help the system to judge the effects of a catastrophe upon some queries in the network.)
Analyze the distancebetween the services. (We can use the information for service computing)
Analyze the network dynamics. (identify the hidden/ indirect information from the network)
Calculate the centrality for services. (This can help the system to find out the important services.)
Betweeness Centrality: How many path that this node is on
Degree centrality
•LiYing Cui, Soundar Kumara and Reka Albert, “Complex Networks: An Engineering View”, IEEE
Circuits & Systems Magazine, Issue 3, Vol. 10, 2010, pp10-25.
Problem Definition
Identify the hidden information from the service network.
Given:(1) web service descriptions (WSDL file)
(2) Semantic Ontology (OWL file)
Objective:
Method:Networks
Nodes: Web Services,
Arcs: Information flow (among concepts and web services)
Network Modeling
Departure timeDeparture time
Return timeReturn time
Person’s namePerson’s name
Book flight ticket
Departure time from SCDeparture time from SC
Arrival time at DCArrival time at DC
Departure time from DCDeparture time from DC
Arrival time at SCArrival time at SC
Book a hotel
Rent a car
Concepts
Concept: Time
Network model�(� +�)×(� +�)
= �11 … �1�… ⋱ … ��1 … ����(� +1)1 … �(� +1)�… ⋱ …�(� +�)1 … �(�+�)�
�
�1(� +1) … �1(� +�)… ⋱ …�� (� +1) … ��(� +�)�(� +1)(� +1) … �(� +1)(� +�)… ⋱ …�(� +�)(� +1) … �(� +�)(� +�)
In M: ��� = 0, � = 1,2, … , (� + �); ��� = 0, � = � + 1, … , � + �; � = � + 1, … , � + � ,
S-S: service composition
C-C: semantic
•LiYing Cui, Soundar Kumara and Reka Albert, “Complex Networks: An Engineering View”, IEEE Circuits & Systems
Magazine, Issue 3, Vol. 10, 2010, pp10-25.
•Li Ying Cui, Soundar Kumara, John Jung-Woon Yoo, and Fatih Cavdur, " Large-Scale Network Decomposition and Mathematical Programming Based Web Service Composition," pp511-514, 2009; in the proceedings of IEEE Conference on Commerce and Enterprise Computing, 2009
S-C: Output
C-S: Input
StartEntire initial network Initial service network Initial semantic network
Nodes:Yellow : web servicesGreen: parameters
Edges:Pink: semantic links
Blue: parameter to web service (input)Black: web service to parameter (output)
Green: web service web service
80 nodes, 104 edgesC-C: p=0.01
C-S, and S-C: p=0.04Selfloops:0
Components: 16
t=7
Initial network t=180 nodes, 104 edges
C-C: p=0.01C-S, and S-C: p=0.04
Selfloops:0Components: 16
80 nodes, 260 edgesC-C: 0.06-0.23S-S: 0.03-0.14
Overall:0.02-0.99Selfloops:6
Components: 16
Centrality(a) Complete graph (t=1) (b) Complete graph (t=7)
80 nodes, 260 edgesC-C: 0.06-0.23S-S: 0.03-0.14
Overall:0.02-0.99Selfloops:6
Components: 16
80 nodes, 104 edgesC-C: p=0.01
C-S, and S-C: p=0.04Selfloops:0
Components: 16
Interaction dimension
� When the components/processes interact with
each other we can capture the communication in
a graph
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Change in approachComplex network
Individual properties: Degree, neighbors, edge weights
Statistical properties: Degree distribution, average path length
Box of gas
Individual properties: Position and velocity
Statistical properties: Pressure, temperature
nRTPV =
One mole = 6.022 * 1023 atoms
Motivation
Design Parameters-Cost: < $400
-Weight: < 1.5kg-Color: Blue
-Length: < 20cm-Width: < 16cm-Height: < 1cm
CPUSupplier #
1CPU
Supplier #2 HDD
Supplier #1
HDDSupplier #
2
Mother B/D
Supplier #2
Global DesignRepository
MemorySupplier #
1Memory
Supplier #2Korea
JapanChina
Thailand
TaiwanIndia
USAMexico
OEM (USA)
Motivation : Customers’ Various, Changing Preferences
(Mass Customization Trend)
Motivation : Shorter Product
Development Life Cycle
Product Design Supporting Tools
Product DesignOntology
Machine-Readable Component Representation
Mother B/D
Supplier #1
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Motivation : Numerous Newly-Introduce
d Components
Motivation : Increasing Global Collaboration
P1P1
P3P3
P2P2P5
P4
P6
P1P1
P3P3
P2P2
P5
(a) Modularization
(b) Interface-Oriented Modular Product Design
Interface-BInterface-B
Interface-CInterface-CInterface-EInterface-E
Interface-DInterface-D
P6
P4
Interface-AInterface-A
Interface-BInterface-B
Interface-CInterface-C
Modularization
Modularization
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Interface-BInterface-B
Interface-CInterface-C
Interface-AInterface-A
Module Description
= functions
= geometric information
= input = output
U.Missouri-RollaDigital Design
Repository
Module Description Language
(MDL) 30
System Architecture
MDLs
Bootstrap
Query
Execution
DesignRequest(query)
CPLEXILP
Solver
ProductDesignResult
Query Processing
Execution Engine
Solution Generation
ILP Formulation Generation
CPUSupplier #
1CPU
Supplier #2 HDD
Supplier #1
HDDSupplier #
2
Mother B/D
Supplier #2
MemorySupplier #
1Memory
Supplier #2Korea
JapanChina
Thailand
TaiwanIndiaUSA
Mexico
Mother B/D
Supplier #1
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Detection of Communities (= Modules)� Criteria: High reliability (Supreet et al. 2009 –working
paper)
• Maximize internal connection
• Minimize external connection
Hub
Bridge
Community
Handling Complexity
� Complexity arises due to diversity and connections
� Modeling the MDO environment using Multi Agent Paradigm
� Web Services concept as an information implementation mechanism
� Complex Network Modeling for analyzing
interactions
Work in these will help handling compexity and controlling emergence 36
Networks in modularity (Sosa et al., 2007)
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A Network Approach to Define Modularity of Components in Complex Products S
Network of Information Flows
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Network of Information Flows Between Tasks of an OperatingSystem Development Process [Braha and Bar-Yam, 2007]
This Product Development task network consists of 1,245 directed information flows between 466 development tasks. Each task is assigned to one or more actors (“design teams” or “engineers”) who are responsible for it.
Publications – complex networks
� Cui, Liying, Kumara, S., and Reka Albert, Complex Networks: An Engineering View,, IEEE Circuits and Systems, September 2010
� Usha Nandini Raghavan, Réka Albert and Soundar Kumara, Near linear time algorithm to detect community structures in large-scale networks, Phys. Rev. E 76, 036106 (2007)
� H. P. Thadakamalla, R. Albert and S. R. T. KumaraSearch in spatial scale free networks, New Journal of Physics 9, 190 (2007)
� H. P. Thadakamalla, S. R. T. Kumara, and R. Albert, Complexity and Large-scale Networks, Chapter 11 in Operations Research and Management Science Handbookedited by A. R. Ravindran, CRC press, 2007.
� Hari P. Thadakamalla, Réka Albert and Soundar Kumara Search in weighted complex networks, Phys. Rev. E 72 , 066128 (2005)
� Hari P. Thadakamalla, Usha N. Raghavan, Soundar Kumara and Réka Albert Survivability of Multiagent-Based Supply Networks: A Topological Perspective IEEE Intelligent Systems, Volume 19 , issue 5, pp 24-31 (2004)
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