TOWARDS FOUR-LAYER FRAMEWORK OF COMBINATORIAL PROBLEMS

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TOWARDS FOUR-LAYER FRAMEWORK OF COMBINATORIAL
PROBLEMS
Mark Sh. Levin Inst. for Inform. Transmission
Problems, Russian Acad. of Sci. Email
mslevin_at_acm.org Http//www.mslevin.iitp.ru
/
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-MCP2008 32nd Annual IEEE
COMPSAC2008, Turku, Finland, July 28, 2008
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Basic Glance
Multi-layer systems
Multi-layer computer
Multi-layer communication network
Multi-layer framework of combinatorial problems
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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)
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My experience Decision Support System COMBI-PC
(1986-1991)
Library of typical applications (examples, case
studies)
Basic (typical) solving schemes
Algorithms procedures for processing/transformat
ion of graph structures (binary relations)
Data (alternatives, criteria, estimates,
preferences as binary relations/graphs)
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Four-layer Framework
Layer 4 Domain-oriented frameworks
Design/ planning of testing
Modular design of software
Informa- tion retrieval
Design of marke- ting strategy
Planning of mainte- nance
Planning of medical treatment
Improve- ment of network
Evolution of require- ments
ETC
Layer 3 Basic (typical) solving framework
Four-stage composite framework
Hierarchical morpho- logical design
System upgrade/ improve- ment
System evolution/ forecasting
Multistage design
ETC
Layer 2 Composite models/procedures
Design of hierarchy (clustering, multicriteria
spanning)
Morpholo- gical clique (synthesis)
Multi- criteria knapsack
Multicriteria multiple choice problem
Multi- criteria assignment/ allocation
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
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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