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1→b/2representstheeasthalf,b/2+1→brepresentsthewesthalf;Nisthetotalnumberoflocationsinwarehouse.ThewidthofthecounterisD1,D1等于1meteranditsdepthisD3,D3等于0.5meter;ThewidthofthechannelisD2,D2等于1meter;theWidthofthemainchannelisD4,D4等于2meter.

Whenanytwolocationsofpiandpjdistributeinthesamelaneway(xi等于xj),theshortestdistancebetweenthemis:

dij等于zi-zj×D1,{(1≤zi≤b/2,1≤zj≤b/2)or(b/2

Whenthetwolocationsarenotdistributedinthesamelaneway(xi≠xj),canbedividedintothefollowingthreecircumstances:

Whenyi等于yj等于1:

dij等于zi+zj×D1+xi-xj×D2+2D3,(1≤zi≤b/4,1≤zj≤b/4)30-zi-zj×D1+xi-xj×D2+2D3,(b/4

Whenyi等于yj等于0:

dij等于zi+zj-30×D1+xi-xj×D2+2D3,(b/2

Whenyi≠yj:

dij等于zi-zj×D1+xi-xj×D2+2D3+D4,{(1≤zj≤b/2,b/2

ThedistancefromI/Opointtoanylocationis:

d0i等于(b/2-zi)×D1+(xi-1)×D2+2D3+D4/2,(xi∈{1,...,a},1≤zi≤b/2)(zi-b/2)×D1+(xi-1)×D2+2D3+D4/2,(xi∈{1,...,a},b/2
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Theobjectivefunctionofcalculatingthetotaldistanceis:

D等于mindij×xij+d1O+dNO(1)

Intheformulaabove:dijindicatesthedistancebetweenanytwolocations(locationiandlocationj)inthewarehouse;d1,O(ordN,O)indicatesthedistancefromthefirst(orthelast)pickingmoditytotheI/Opoint.Because,pickerssetofffromtheI/Opoint,whentheyfinishtheirtaskstheyhavetodeliverthegoodstotheI/Opoint.


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Theconstraintconditionsare:

xij等于1,(i≠j;j等于1,2,...N)(2)

xij等于1,(i≠j;i等于1,2,...N)(3)

Intheformulasabove:xijandxjiaredecisionvariables,ifthepickergofromlocationiandlocationj,xij等于1orelsexij等于0;xijandxijindicatethetotalfrequencyoflocationitolocationjandlocationjtolocationi.Whenbiningtheformulasof(2)and(3)makeanindicationofthereisonlyonewaybetweeniandjlocations,sopickersmaynotmakearepeatedpicking.2Algorithmicprocesses

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1)Therequiredinformation:Makeastatisticforallthelocationsofpickinggoods,designaprograminordertocalculatetheshortestdistancesbetweenanytwogo

关于MultiplePeoplePickingAssignmentandRoutingOptimizationBasedonGeneticAlgorithm的电大毕业论文范文
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ods.Setupthedistancematrixwhichisrepresentedbyatwo-dimensionalarrayintheprogram.

2)Coding:nindicatesthetotallocationnumberofthepickinggoods.Encodeallthepickinglocationswith0,1,...,n-1(eachpickinglocationhasauniquenumber).

3)Initialization:Generateminitializedarraysinthemethodofarrangingthenlocationnumberrandomly(mindicatesthenumberofthereservedindividualsineachgeneration).

4)Alternative:Whenanewgenerationemergences,abandonthedisadvantageswiththeprobabilityofpsandthenreplacetheinferiorgroupwiththeoptimalindividuals.

5)Cross:Withthecrossoverprobabilitypcselectstheindividualsfromthecurrentgeneration,andthendividedalltheselectedindividualsintotwogroupsasthetwomalesofthenextgeneration.Namethemasparent1andparent2.Selectacrossoverpointrandomlyforeachpairoftheparent.Thecrossingprocessisdesignedasfollows:

father1:0,1,2,3|4,5,6,7,8,9father2:5,6,4,3|2,1,0,8,7,9?圯son1:0,1,2,3|*,*,*,*,*,*son2:5,6,4,3|*,*,*,*,*,*

?圯son1:0,1,2,3|5,6,4,8,7,9son2:5,6,4,3|0,1,2,7,8,9

Asshownabove“|”indicatesthecrosspoint;the“*”partduplicatesfromfirstelementofanotherparenttothelastone,extracttheelementswhicharedifferentfromtheformerones.

6)Variation:Withthemutationratepmselectstheindividualsfromthecurrentgeneration,anddeterminetwomutationpointsrandomlyforeachindividual(selectedasthecrossingpoint),exchangethetwoelementsatthemutationpoints,aftertheprocessofvariation,newindividualsappear.Inordertoavoidprematureconvergence,whentheevolutionnumberislargeenoughthemutationratepmwillbeincreased.

7)CalculateObjectivefunctionvalue:anyindividual,e.g.0,1,2,3,4,5,6,7,8,9,*,*,*******,canbedividedintoMone-dimensionalarraysbytheneverrepeatedM-1randomseparationpoints(M≤n).“|”representtheseparationpoints,e.g.0,1,2,3|4,5,6,7,8|9,*,*,*|******...(thenumberofpickersisM,thisstepaimtoassigntasksfortheMpickers).Inthiswaywecansplitanone-dimensionalarrayintochunksofnewarraysas[0,1,2,3],[4,5,6,7,8],[9,*,*,*],...thentakethebiggestobjectivefunctionvalueofthenewarraysastheoriginal’s.8)Select:accordingtotheobjectivefunctionvalue,sortallindividualsofeachgenerationandrese

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