1. TOWARDS FOUR-LAYER FRAMEWORK OF COMBINATORIAL PROBLEMS
Mark Sh. Levin
Inst. for Inform. Transmission Problems, Russian Acad. of Sci.
PLAN:
1.Decision cycle (problem, model, algorithm, computing, decisions)
2.Four-layer Framework:
*basic combinatorial problems/models
*composite models
*typical composite solving schemes
*application frameworks
3.Illustrations
4.Conclusion
1-st IEEE Int. Workshop on Engineering Open Complex Systems EOCS-MCP’2008
32nd Annual IEEE COMPSAC’2008, Turku, Finland, July 28, 2008

2. Multi-layer framework
Basic Glance
Multi-layer
systems
Multi-layer
computer
Multi-layer
communication
network
Multi-layer framework
of combinatorial
problems

3. DECISION CYCLE & Support Components
Frame of problems/
mathematical models
Library
of problems/models
Applied modular
problem(s)
Algorithms
Selected/designed
solving scheme(s)
Man-machine
procedures
DECISION(S)
Solving process
(e.g., computing)

4. Library of typical applications (examples, case studies)
My experience: Decision Support System COMBI-PC ( )
Library of typical applications
(examples, case studies)
Basic (typical) solving schemes
Algorithms & procedures for processing/transformation
of graph structures (binary relations)
Data
(alternatives, criteria, estimates,
preferences as binary relations/graphs)

5. Four-layer Framework
Layer 4: Domain-oriented frameworks
Modular
design of
software
Informa-
tion
retrieval
Design of
marke-
ting
strategy
Design/
planning of
testing
Planning of
mainte-
nance
Planning of
medical
treatment
Improve-
ment of
network
Evolution of
require-
ments
ETC
Layer 3: Basic (typical) solving framework
Hierarchical
morpho-
logical
design
System
upgrade/
improve-
ment
System
evolution/
forecasting
Four-stage
composite
framework
Multistage
design
ETC
Layer 2: Composite models/procedures
Multi-
criteria
knapsack
Multicriteria
multiple
choice
problem
Multi-
criteria
assignment/
allocation
Morpholo-
gical
clique
(synthesis)
Design of hierarchy
(clustering,
multicriteria
spanning)
ETC
Layer 1: Basic problems/models
Multicriteria
ranking
Knapsack
problem
Multiple
choice
problem
Cluste-
ring
Assignment/
allocation
Span-
ning
tree
Steiner
tree
problem
Shortest
path
problem
ETC

6. I.Extension of each framework layer: 1.1.New applications
Conclusion as future research directions
I.Extension of each framework layer:
1.1.New applications
1.2.New components (modules) at each layer of framework:
*modification of the models, e.g., under uncertainty
(stochastic models, fuzzy set based models),
*new composite modules
(e.g., multicriteria spanning problems,
covering problems)
*new typical composite solving schemes
II.Study and design of methods for selection and
combination/composition of components (modules)
as models, algorithms/procedures, etc.
III.Implementation of the four-layer framework