Ch12 The Art of Modelling with Spreadsheet

8/20/2019 Ch12 The Art of Modelling with Spreadsheet

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MANAGEMENT

SCIENCEThe Art of Modeling with Spreadsheets

STEPHEN G. POWELL

ENNETH !. "AE!

Co#pati$le with Anal%ti& Sol'er Platfor#(O)!TH E*ITION

CHAPTE! +, POWE!POINT

NON-SMOOTH MO*ELS


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INTRODUCTION (CONT)D*

• This method conducts a systematic search!ith random elements' comparing thesolutions encountered along the !ay and

retaining the better ones"• The best solution it +nds may not be optimal'

although it may be a very good solution"

• This type o$ procedure is called a heuristic

procedure' meaning that it is a systematicprocedure $or identi$ying good solutions' butnot guaranteed optimal solutions"

Chapter +, Cop%right ,/+0 1ohn Wile% 2Sons3 In&.

0


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,E-TURES O, T.E E/O0UTION-R1 SO0/ER

• The evolutionary solver is designed to mimic the processo$ biological evolution in certain !ays"

• The algorithm proceeds through a series o$ stages' !hichare analogous to generations in a biological population"

In each generation the approach considers not a singlesolution' but a pop4lation o$ perhaps 23 or 34 solutions"

• Ne! members are introduced to this population througha process that mimics mating in that o5spring solutionscombine the traits o$ their parent solutions"

• Occasional #4tations occur in the $orm o$ ofspringsolutions !ith some random characteristics that do notcome $rom their parents"


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,E-TURES O, T.E E/O0UTION-R1 SO0/ER(CONT)D*


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• The 55+tness)) o$ each member o$ the population isdetermined by the value o$ its ob#ective $unction"

• 6embers o$ the population that are less +t (have arelatively !orse value o$ the ob#ective $unction* are

removed $rom the population by a process that mimicsnatural sele&tion"

• This process o$ selection propels the population to!ardbetter levels o$ +tness (better values o$ the ob#ective$unction*"

•

The procedure stops !hen there is evidence that thepopulation is no longer improving (or i$ one o$ the user7designated stopping conditions is met*"

• 8hen it stops' the procedure displays the bes tmembero$ the +nal population as the solution"


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T.E EN9INE T-% ,OR T.EE/O0UTION-R1 SO0/ER


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T.E -D/ERTISIN9 %UD9ET :RO%0E6

• The decision variables in this problem are the;uarterly e


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-D/ERTISIN9 %UD9ET 6ODE0 8IT. UNITCOST T-%0E


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O:TI6-0 -00OC-TION ,RO6 T.E NON0INE-RSO0/ER


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O:TI6-0 -00OC-TION ,RO6 T.E E/O0UTION-R1SO0/ER


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RESU0TS O, USIN9 E/O0UTION-R1 SO0/ER

• The evolutionary solver +nds a solution !ith a pro+t o$ =>?'3@A'!hich is B percent higher than the base case and 23 percenthigher than the solution $ound by the nonlinear solver"

• The advertising e


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T.E C-:IT-0 %UD9ETIN9 :RO%0E6

• -lthough the evolutionary solver can !or&!ith constraints' it is less ecient !henconstraints are present' and per$ormance

tends to deteriorate as the number o$constraints increases"

• Rather than imposing an e


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8ORFS.EET ,OR T.E 6ODI,IED 6-RR COR:OR-TIONEG-6:0E


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RESU0TS O, RUNNIN9 E/O0UTION-R1 SO0/ERON T.IS 6ODE0


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• - solution o$ =3 million' !hich is better than the optimum inthe base case"

• I$ the previous run stopped because o$ convergence' !e shoulde


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SU66-R1

• The evolutionary solver contains an algorithm thatcomplements the nonlinear solver' the linear solver' and theinteger solver"

• Evolutionary solver can o$ten +nd good' near7optimal solutionsto very dicult problems' and it may be the only efective

procedure !hen there is a nonsmooth ob#ective $unction"

• The evolutionary solver !or&s !ith a set o$ specialiedparameters"

• :ractice and e


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COPYRIGHT © 2013 JOHN WILEY & SONS, INC.

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Ch12 The Art of Modelling with Spreadsheet