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A core Course on Modeling

A core Course on Modeling. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.24. formulate purpose. define. identify entities. choose relations. conceptualize. obtain values. formalize relations. formalize. operate model.

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A core Course on Modeling

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.24

  2. formulate purpose define identify entities choose relations conceptualize obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude Executionphase: operate model

  3. Cat.-II –spaceanddominance Revisitoptimization with multiple criteria: Problems with lumpingpenalties Q=iwiqi • what are the values of wi (trial and error)? • don’taddthingsthatshouldn’tbeadded. •  look foralternative approach, usingdominance

  4. Cat.-II –spaceanddominance • Assume cat.-II quantities are ordinals: • Everyaxis in cat.-II space is ordered; • concept C1dominatesC2 • iff, forall cat.-II quantitiesqi, C1.qi is betterthan C2.qi; • ‘Beingbetter’ maymean ‘<‘ (e.g., waste) or ‘>’ (e.g., profit); http://www.morguefile.com/archive/display/765894

  5. Cat.-II –spaceanddominance A.f1<C.f1 and A.f2<C.f2, so Adominates C A.f2<B.f2 and B.f1<A.f1, so B and A don’tdominateeachother f1 shouldbeminimal (e.g., costs) B.f1<C.f1 and B.f2<C.f2, so B dominates C f2 shouldbeminimal (e.g., waste)

  6. Cat.-II –spaceanddominance Only non-dominatedsolutions are relevant  dominanceallowspruningcat.-I space; http://www.morguefile.com/archive/display/50363

  7. Cat.-II –spaceanddominance Only non-dominatedsolutions are relevant  dominanceallowspruningcat.-I space; QUIZ http://www.morguefile.com/archive/display/50363 Why does cat.-I spaceneedstobepruned?

  8. Cat.-II –spaceanddominance Only non-dominatedsolutions are relevant  dominanceallowspruningcat.-I space; Nr. non-dominatedsolutions is smaller with more cat.-II quantities http://www.morguefile.com/archive/display/50363

  9. Cat.-II –spaceanddominance Only non-dominatedsolutions are relevant  dominanceallowspruningcat.-I space; Nr. non-dominatedsolutions is smaller with more cat.-II quantities http://www.morguefile.com/archive/display/50363 QUIZ Why do we have fewer non-dominatedsolutions with more cat.-II quantities?

  10. Cat.-II –spaceanddominance Only non-dominatedsolutions are relevant  dominanceallowspruningcat.-I space; Nr. non-dominatedsolutions is smaller with more cat.-II quantitiesnr. of cat.-II quantitiesshouldbesmall (otherwisethere are few dominatedsolutions). http://www.morguefile.com/archive/display/50363

  11. Trade-offsand the Pareto front In cat.-II space, dominatedareas are half-infiniteregionsboundedbyiso-coordinatelines/planes; Solutionsfalling in one of these regions are dominatedandcanbeignored in cat.-I-spaceexploration; Non-dominatedsolutions form the Pareto front.

  12. Trade-offsand the Pareto front D • Cat.-II quantities f1 and f2 bothneedtobeminimal. A and B are non-dominated, C is dominated. Of A and B, none dominates the other.

  13. Trade-offsand the Pareto front D • Cat.-II quantities f1 and f2 bothneedtobeminimal. Solution D woulddominateallothersolutions – ifitwouldexist.

  14. Trade-offsand the Pareto front Relevance of Pareto-front: • itbounds the achievable part of cat.-II space; • solutions not on the Pareto front canbediscarded.

  15. Trade-offsand the Pareto front Relevance of Pareto-front: • itexistsforany model function, although in generalitcanonlybeapproximatedby sampling the collectionof solutions.

  16. Trade-offsand the Pareto front Relevance of Pareto-front: • itdefinestwodirections in cat.-II space:

  17. direction of absolute improvement Trade-offsand the Pareto front http://cdn.morguefile.com/imageData/public/files/a/alvimann/preview/fldr_2010_03_23/file3831269347533.jpg Relevance of Pareto-front: • itdefinestwodirections in cat.-II space: the direction of absolute improvement / deterioration,

  18. direction of absolute deterioration Trade-offsand the Pareto front http://cdn.morguefile.com/imageData/public/files/a/alvimann/preview/fldr_2010_03_23/file3831269347533.jpg Relevance of Pareto-front: • itdefinestwodirections in cat.-II space: the direction of absolute improvement / deterioration,

  19. tangent to the pareto-front: trade-offs Trade-offsand the Pareto front http://cdn.morguefile.com/imageData/public/files/a/alvimann/preview/fldr_2010_03_23/file3831269347533.jpg Relevance of Pareto-front: • itdefinestwodirections in cat.-II space: the direction of absolute improvement / deterioration, and the planeperpendiculartothisdirectionwhich is tangent to the Pareto front, whichrepresentstrade-offsbetween cat.-II quantities.

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