the concept of problem complexity
TRANSCRIPT
The concept of problem complexity
Alejandro SaladoStevens Institute of Technology
A) Anyone born in Hoboken?
B) Anyone born elsewhere?
C) Anyone unborn?
Choose your preferred concept
Constraints: fixed budget and schedule
A very SIMPLE system
Performance = 1.00
A very COMPLEX system
Performance = 1.00
What is a COMPLEX system?
Emergence
Dynamic loops
Interconnectivity
Number of parts
InteractionDisorder Unexpected
Diversity
Exercise 1:
Draw the most COMPLEX figure you can imagine
Time: 2 s
Hint: loops, crossings, corners, randomness...
Exercise 2:
Draw the SIMPLEST figure you can imagine
Time: 2 s
Hint: a straight line
What happened?
A SIMPLE system was DIFFICULT to develop
A COMPLEX system was EASY to develop
What is a COMPLEX system?
ACADEMIAProperty of a model
Based on system elements
INDUSTRYDifficulty to developBased on system / project properties
Needs a system architecture Does NOT help in mitigating/reducing complexity
Why MEASURING complexity?
1. Understand system behavior
2. Design for some -ilities
3. Estimate development effort
Science drive
Design drive
Decision drive
System complexity
FUNCTIONAL PHYSICAL ORGANIZAT.
Interdependence between system
functions
Interdependence between system
components
Interdependence between
organizations
System complexity
SYSTEM PROJECT ENVIRON.
System of interest
The system developing the system
Where the system
operates
COGNITION
Understanding of people
interacting with system
*Sheard and Mostashari, extracting 39 factors from more than 300 definitions
One more thought
Which one is more complex?
A standard car batteryA standard laptop
battery, but with 100 h autonomy
Does the problem definition induce complexity?
Do requirements influence system complexity?
Can we anticipate a complexity bound?
Perhaps a complexity SPECTRUM?
System complexity
Problem complexity
Organiz. complexity
Functional complexity
Structural complexity
Some correlations / overlaps already measured
Need a common unit of measurement
How to MEASURE system complexity?
SCIENCE DESIGN ESTIMATION
DisorderBehavior
InterconnectednessParametric cost
estimators
π»=ββπ=1
π
ππ β πππ2 (ππ) πΆ=πΆ1+πΆ2 βπΆ3N parts, N I/Fs, N reqs,
materials...
πΉ :πΆπβπΈ
The power of joint ENTROPY
πΆ (πΆ1β―πΆπ)=ββπ1
β―βπππ (π1β―ππ )β πππ π [π (π1β―ππ ) ]
πΆ (πΆ1β―πΆπ)β₯πππ₯ (πΆπ)
πΆ (πΆ1β―πΆπ)β€βππΆπ
Property 1.
Property 2.
... And therefore
Effort to reduce FUNCTIONAL/STRUCTURAL complexity may be limited/jeopardized by
how the PROJECT is organized or the REQUIREMENTS to be fulfilled!
MATHEMATICAL justification if joint entropy can be applied
Problem Complexity
A function of the SIZE of the solution space
Design space
CS1 CS2
*CS: compliant space
Problem Complexity
A function of AMOUNT of requirements and CONFLICTS between them
DSM?Flawed
Problem Complexity
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π» ππ π
Inspired on COSYSMO (Valerdi, 2008)
Problem Complexity
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π» ππ π
Calibration factor
Size of requirement set Conflicting requirements
Problem Complexity
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π» ππ π
Functional requirementRelative weight
Diseconomies of scale*
Problem Complexity
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π» ππ π
Amount of conflicting requirements *
Diseconomies of scale*
Problem Complexity
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π ππ» π
NOT IN THIS PAPER!
Heuristics to identify conflicting requirements
H1β₯ 2 phases of matter
H4Competing for
resources
H3Opposing directions
laws of physics
H2Opposing directions
laws of society
Case StudyID Requirement (fuzzy)
R1 Standard driving functionality
R2 4x wheel traction
R3 Big trunk
R4 Airbag
R5 Auto parking
R6 Auto breaking
R7 High speed & acceleration
R8 High autonomy
Requirement de-scoping
Industry benchmarkVs.
Conflict-based
Problem complexityVs.
Expert judgment
Case Study: BenchmarkID Requirement (fuzzy)
R1 Standard driving functionality
R2 4x wheel traction
R3 Big trunk
R4 Airbag
R5 Auto parking
R6 Auto breaking
R7 High speed & acceleration
R8 High autonomy
COSYSMO assessment based on industry experts
Dinh
1
2
1
1
3
3
2
2
De-scoped
Yes
Yes
Case Study: Conflict basedID Requirement (fuzzy)
R1 Standard driving functionality
R2 4x wheel traction
R3 Big trunk
R4 Airbag
R5 Auto parking
R6 Auto breaking
R7 High speed & acceleration
R8 High autonomy
Sensitivity based on (notional) problem complexity metric
Dinh
1
2
1
1
3
3
2
2
De-scoped
Yes
rf
X
X
X
X
X
H3
+mass
-mass/+energy
-mass/-energy
Case Study: Comparative analysis
Element
Problem complexity
Resulting functionality
Resulting performance
Relative complexity subject matter expert
Dinh de-scoped requirements
Based on industry experts
Benchmark
58.61
3/5
3/3
β
3
Conflict-based
33.22
5/5
2/3
β
1
Contributions
System complexity
Problem complexity
Organiz. complexity
Functional complexity
Structural complexity
πΆ (πΆ1β―πΆπ)=ββπ1
β―βπππ (π1β―ππ )β πππ π [π (π1β―ππ ) ]
πΆπ=πΎ β(βπ=1π
ππ βπ π π)πΈ
ββπ=1
π
π» ππ π
Left for the future
VALIDATE heuristics based on subject matter expert
Perform RELATIVE calibration of problem complexity
Perform ABSOLUTE calibration of problem complexity
Further investigate IMPLICATIONS of joint entropy
TOPIC TITLE:THE CONCEPT OF PROBLEM COMPLEXITY
Alejandro SaladoStevens Institute of [email protected]+49 176 321 31458