Practical Robust Optimization - an introduction - - LNMB

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AARC shows often very good behaviour (Ben-Tal et al., 2004):Unc.ty (%) Opt(ARC) Opt(AARC) Opt(RC)10 13531.8 13531.8 (+0.0%) 15033.4 (+11.1%)20 15063.5 15063.5 (+0.0%) 18066.7 (+19.9%)30 16595.3 16595.3 (+0.0%) 21100.0 (+27.1%)40 18127.0 18127.0 (+0.0%) 24300.0 (+34.1%)50 19658.7 19658.7 (+0.0%) 27500.0 (+39.9%)60 21190.5 21190.5 (+0.0%) 30700.0 (+44.9%)70 22722.2 22722.2 (+0.0%) 33960.0 (+49.5%)F A C U L T Y O F E C O N O M I C S A N D B U S I N E S S A D M I N I S T R A T I O N42 / 53
whereZ 1 ⊂ Z 2 .Example:Globalized robust counterpart(a+Bζ) T x ≤ β +αdist(ζ,Z 1 ) ∀ζ ∈ Z 2 ,■ Z 1 = {ζ : ‖ζ‖ 2 ≤ ρ 1 }, Z 2 = {ζ : ‖ζ‖ ∞ ≤ ρ 2 },ρ 1 ≤ ρ 2 .■ dist(ζ,Z 1 ) = min ζ′ ∈Z 1‖ζ −ζ ′ ‖ 2 .Globalized <strong>Robust</strong> Counterpart (GRC):{a T x+ρ 2 ‖v‖ 1 +ρ 1 ‖B T x−v‖ 2 ≤ β‖B T x−v‖ 2 ≤ αThis is a system of conic quadratic constraints.F A C U L T Y O F E C O N O M I C S A N D B U S I N E S S A D M I N I S T R A T I O N43 / 53
Page 2 and 3: Overview■Motivation for Robust Op
Page 4 and 5: What sets great optimization apart?
Page 6 and 7: Flaw of using nominal valuesOptimiz
Page 8 and 9: Flaw of using nominal valuesConstra
Page 10 and 11: Flaw of using nominal valuesOptimiz
Page 12 and 13: Flaw of using nominal valuesā T x
Page 14 and 15: Flaw of using nominal valuesAmong 9
Page 16 and 17: Why RO can make a difference ...Ext
Page 18 and 19: BookImportant chapters: Preface, Ch
Page 20 and 21: Relation with Stochastic Programmin
Page 22 and 23: Introduction to robust linear optim
Page 24 and 25: Tractable robust counterparts(a+Bζ
Page 26 and 27: RC for ball uncertaintyThis is equi
Page 28 and 29: Budget uncertainty regionOften used
Page 30 and 31: Planning of Air Traffic Controllers
Page 32 and 33: Planning of Air Traffic Controllers
Page 34 and 35: Safe approximation of chance constr
Page 36 and 37: Bridge that was not robust ...F A C
Page 38 and 39: Multistage problemsSome of the deci
Page 40 and 41: Linear Decision Rule(ARC) (a+Bζ) T
Page 44 and 45: Advantage of Globalized Robust Coun
Page 46 and 47: Example 2:(RP) |x 1 −ζ|+|x 2 −
Page 48 and 49: General remarks■■■■■RC re
Page 50 and 51: Application areas of ROHundreds of
Page 52 and 53: Application: Cancer treatment■ Tr

Practical Robust Optimization - an introduction - - LNMB

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