Download - 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"
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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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