TOWARDS FOUR-LAYER FRAMEWORK OF COMBINATORIAL PROBLEMS Mark Sh. Levin Inst. for Inform. Transmission Problems, Russian Acad. of Sci. Email: mslevin@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-MCP’2008 32nd Annual IEEE COMPSAC’2008, Turku, Finland, July 28, 2008

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

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)

Library of typical applications (examples, case studies) My experience: Decision Support System COMBI-PC (1986-1991) 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)

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

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