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, 2010skumara@psu.edu

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

2

Complex Systems - Dimensions

� Modeling Dimension

� Information Dimension

� Interaction Dimension

3

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

5

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

6

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

7

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 ?

9

Examples of Web Services

10

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

Propagation

t =2t =3 t =4

t =5 t =6 t =7

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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The Internet

By K. C. Claffy, http://www.nd.edu/~networks/gallery.

htm

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Social Networks

Science co-authorship network, from the Max Planck Institute

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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

Application to Modular Product Design

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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Product Dissection

Assembly Diagram

Design Structure Matrix (DSM)

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

Work in Design Literature

� Already there are evidences of this being feasible

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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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Change Propagation (Giffin et al., 2009)

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