An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities

23 Pages·2016·4.28 MB·English

sensors
Article
An Improved Simulated Annealing Technique for
Enhanced Mobility in Smart Cities
HayderAmer1,*,NaveedSalman1,MatthewHawes1,MoumenaChaqfeh2,
LyudmilaMihaylova1andMartinMayfield3
1 DepartmentofAutomaticControlandSystemsEngineering,UniversityofSheffield,SheffieldS13JD,UK;
n.salman@sheffield.ac.uk(N.S.);m.hawes@sheffield.ac.uk(M.H.);l.s.mihaylova@sheffield.ac.uk(L.M.)
2 CollegeofInformationTechnology,UAEUniversity,AlAin15551,UnitedArabEmirates;
[email protected]
3 DepartmentofCivilandStructuralEngineering,UniversityofSheffield,SheffieldS13JD,UK;
martin.mayfield@sheffield.ac.uk
* Correspondence:hmamer1@sheffield.ac.uk;Tel.:[phone]
AcademicEditors:AndreaZanellaandToktamMahmoodi
Received:24April2016;Accepted:24June2016;Published:30June2016
Abstract: Vehiculartrafficcongestionisasignificantproblemthatarisesinmanycities. Thisisdueto
theincreasingnumberofvehiclesthataredrivingoncityroadsoflimitedcapacity. Thevehicular
congestion significantly impacts travel distance, travel time, fuel consumption and air pollution.
Avoidanceoftrafficcongestionandprovidingdriverswithoptimalpathsarenottrivialtasks. The
keycontributionofthisworkconsistsofthedevelopedapproachfordynamiccalculationofoptimal
trafficroutes. Twoattributes(theaveragetravelspeedofthetrafficandtheroads’length)areutilized
bytheproposedmethodtofindtheoptimalpaths. Theaveragetravelspeedvaluescanbeobtained
fromthesensorsdeployedinsmartcitiesandcommunicatedtovehiclesviatheInternetofVehicles
androadsidecommunicationunits. Theperformanceoftheproposedalgorithmiscomparedtothree
otheralgorithms: thesimulatedannealingweightedsum, thesimulatedannealingtechniquefor
orderpreferencebysimilaritytotheidealsolutionandtheDijkstraalgorithm. Theweightedsum
andtechniquefororderpreferencebysimilaritytotheidealsolutionmethodsareusedtoformulate
differentattributesinthesimulatedannealingcostfunction. AccordingtotheSheffieldscenario,
simulationresultsshowthattheimprovedsimulatedannealingtechniquefororderpreferenceby
similaritytotheidealsolutionmethodimprovesthetrafficperformanceinthepresenceofcongestion
by an overall average of 19.22% in terms of travel time, fuel consumption and CO emissions as
2
comparedtootheralgorithms;also,similarperformancepatternswereachievedfortheBirmingham
testscenario.
Keywords: traffic congestion; Internet of Vehicles; Internet of Things; simulated annealing;
multi-objectiveoptimisation;vehiclere-routing
1. Introduction
Theexplosivegrowthoftheglobaleconomyhasledtoanexpansionofcities. Therehasbeen
anincreaseinthepopulationmassand,therefore,anincreaseinthenumberofvehiclesdrivingon
cityroadnetworksoflimitedcapacity. Thishaspromptedanextremeincreaseoftrafficcongestion,
roadaccidentsandairpollution. Somestudieshaverevealedthat30%ofCO emissionsaredueto
2
inefficientvehiclemanagement[1]. Thishasresultedinsignificanteconomicandproductivitylosses,
makingimprovementofmobilityakeychallengewithinsmartcities. Solvingsuchaproblemcanbe
aidedbyinformationobtainedviasensorsdeployedaspartofsmartcityinitiatives,whichthenhave
tobecommunicatedtovehicles/driverstoallowthemtomakeadecisionwithregardstoalternative
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routes. Oncesuchadecisionhadbeenmade,itwouldalsobefeasibletoeventuallyseeinformation
regardingplannedroutestobecommunicatedbackfromthevehiclestothesmartcityinfrastructure.
Suchinformationcan thenbeusedto predictthe numberofvehiclesat each intersectionwithina
smartcity,whichinturncouldbeusedtoadaptthesequencesoftrafficlightstoallowamoreoverall
optimaltrafficflowforthecityasawhole. Afurtherexampleofhowthiscanbeusedwithinsmart
citieswouldberelatedtoreducingtheconcentrationsofairpollutionwithinthecity. Thiswouldbe
achievedbyredirectingheavilypollutingvehiclesawayfromareaswithhighpollutionlevels.
Asaresult,therehasbeenasignificantbodyofresearchdealingwiththealgorithmstoreduce
traffic jams. The Dijkstra [2] and the A* algorithms [3] are the two most common path planning
algorithms. Otherstudiesconcentrateontheintegrationofswarmintelligencealgorithms,suchas
artificialantcolonyalgorithms[4],geneticandsimulatedannealingalgorithms[5]. However,most
oftherecentlydevelopedalgorithmsaregenerallydesignedforstaticgraphs. Theyarenotdesigned
to be employed for dynamic path planning in a real-time traffic environment. This is due to the
unpredictabletrafficconditionsthatmightoccurinthedynamicenvironment.
Recently,hybridsystemshavebeensuggestedtointegratealgorithmsineachgrouptocreate
avigorousintegratedsolutiontoovercomeanydrawbacksorobstructionsoneachsingleapproach;
forexample,thehybridgeneticalgorithmusingDijkstra’sheuristicmulti-objectiveoptimizationfor
dynamicrouteplanningwiththepredictedtrafficinareal-worldroadnetwork[6].
Thereisasignificantincreaseindevelopingefficientsolutionsforimprovedmobilityinintelligent
transportationsystems(ITS)[7]. Findingtheoptimalnavigationroute,fromasourcetoadestination,
withinareasonabletimeisthekeytask. Differentcostfunctionscanbeapplied, suchasattaining
theminimumtraveldistance(TD),minimumtraveltime(TT)orminimumfuelconsumption. ITSis
comprisedofabroadrangeofwirelesscommunication-basedinformation,controlandtechnologies.
When combined with the transportation system infrastructure and in vehicles themselves, this
technologyhelpstomanagetrafficflow,reducetrafficjams,enhanceroadsafety,providealternative
routestocommuters,reducefuelconsumption,time,moneyandvehicleemissionsincongestedurban
areas[8].
AnefficientapproachcanbedevelopedwiththeaidoftheInternetofThings(IoT).TheIoTis
anenvisagedcommunicationsystemthatallowsvariousdevices,suchaswirelesssensornetworks
(WSN),mobilephones,mobilephonemasts,actuatorsandnear-fieldcommunicationdevices(NFC),
to communicate and collaborate with each other to complete a common goal [9]. The Internet of
Vehicles (IoV), a natural offshoot of the IoT, foresees all future vehicles to be connected, sharing
informationrelatedtosafety,convenienceandinfotainment. Vehicletovehicle(V2V)andvehicleto
infrastructure(V2I)communicationsystemsaretwosubsetofIoV.TheV2Vcommunicationsystem
allowstwovehiclestointeractdirectlywithoutrelyingonfixedinfrastructure. Onthecontrary,theV2I
communicationsystemallowsvehiclestocommunicatewithroadsideunits(RSU),suchassensors,
traffic light controllers, intelligent signals, mobile phone masts, etc., which are installed as part of
thesmartcityconcept[10]. V2VandV2Ihavebeenwidelyutilizedtoresolvevariouscomplications
relatedtotransportationinsmartcities,inwhichthemostsignificantproblemisthetrafficcongestion.
IoVsystemscansignificantlyimprovetrafficsafetyandconvenienceinsmartcities,byproviding
driverswithtimelyinformationaboutroadconditionsandtravelsituations. Existingsolutionstothe
trafficcongestionproblembyutilizingvehicularcommunicationrelyeitheronV2Vcommunication
aloneorbothV2VandV2Icommunications. However,therearestillsomeLimitations,whichcanbe
summarizedasfollows:
1. A large portion of the previous or current vehicle routing algorithms attempt to identify the
minimumTDorTT.Generally,theycannotattainanactivetrade-off.
2. Utilizing just individual traffic information or a single cost function for the vehicle routing
problemisnotsatisfactory. Differentnavigationcriteriashouldbeconsideredtofindtheoptimal
pathofthedriver. Thiswillhelpdriverstohavedifferentnavigationoptions,whichcanbethe
fastestroute,theleastcongested,theleastfuelconsumptionandtheleastairpollution.
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Thispaperpresentsandevaluatesanewmulti-objectiveimprovedsimulatedannealingtechnique
fororderpreferencebysimilaritytotheidealsolution(ISATOPSIS)algorithmforcongestionavoidance
basedonanIoVcommunicationsystem. ThemainobjectiveinISATOPSISistoprovidevariousroute
decisionsaccordingtodifferentobjectivesinordertomeetthediversenavigationrequirementsof
drivers;forexample,theminimumTT,TD,fuelconsumptionoratrade-offofallconditions. Inthis
paper,twootheralgorithmshavebeenimplemented: simulatedannealingweightedsum(SAWS)and
thesimulatedannealingtechniquefororderpreferencebysimilaritytotheidealsolution(SATOPSIS)
forcompressionpurposes. ThecostfunctionofSAWShasbeenformulatedusingtheweightedsum
method. ThecostfunctionofSATOPSISandISATOPSIShasbeenformulatedusingthemulti-attribute
decisionmaking(MADM)method,whichiscalledthetechniquefororderpreferencebysimilarityto
theidealsolution(TOPSIS)method[11]. TheresultsoftheproposedalgorithmISATOPSIShavebeen
comparedtotheshortestpathDijkstraalgorithm(DA),SAWSandSATOPSIS.
Theremainderofthepaperisorganizedasfollows: InSection2,aliteraturereviewofrelated
workispresented. ThedetailsofSAWS,SATOPSISandISATOPSISaregiveninSection3. InSection4,
aperformanceevaluationisprovided. Finally,conclusionsaredrawninSection5.
2. RelatedWork
Numerous studies have been published on IoV as part of IoT to find a solution to the traffic
congestionprobleminordertoreducetheTD,TTandfuelconsumption. Inthissection,adiscussion
andreviewoftheseroutingalgorithmsisgiven.
In [12], the algorithm aims to send geo-broadcast messages in V2V and V2I communications.
The algorithm used an event-driven message instead of a beacon message sent periodically.
Thismessageistransmittedtoallvehiclesthatarewithinaspecificrangetoprovidethedriverwith
informationabouttrafficconditions. However,thisapproachfocusesonlyonprovidinginformationto
othervehicleswithoutanymechanismtoavoidthecongestedarea.
In[13],theauthorsemployV2Vcommunicationwithmessagesperiodicallysentbetweenvehicles.
Theyproposeatechniquecalledcontent-orientedcommunication(COC)tosolvetrafficcongestion.
Withthismethod,thevehicleevaluatestheroadtrafficdensityfrommessagesreceivedfromother
vehiclesandperiodicallysendsthesedatatothefurthestvehicleswithincommunicationrange. Asa
result,vehiclesobtaintrafficdensityinformationfordifferentlocationsanddetectcongestionlevelsby
comparingtheroadtrafficdensitycalculatedwithaveragetrafficdensityvaluesfortheroadsegment.
However,thisworkdidnotproposeamechanismtoavoidtrafficjams.
In [14], a new Dijkstra algorithm was proposed. This algorithm encompasses new inputs for
vehicle path planning, along with a reactive planner to update the selected path according to the
requiredroutechanges. Ageneralclassificationofvehicleroutingalgorithmsandevaluationmetrics
insmartcitiesisalsopresented. However,thisisdonewithoutanyperformanceevaluation.
In [15], the authors evaluate four algorithms: static Dijkstra, static A*, dynamic Dijkstra and
dynamicA*. Theevaluatedalgorithmshavebeenappliedinthreedifferenttestscenarios(citycentre,
suburbanandrural). Accordingtotheperformanceevaluation,theauthorsrecommendtheA*-based
algorithmsasthebestroutingalgorithmsinthedifferingroadenvironments. However,thedrawback
ofthesealgorithmsisthattheyutilizeonlyasingleobjectivewhenfindingthealternativepaths,which
leadstothetransferofthecongestiontootherroads.
In[16],theauthorsproposeanalgorithmcalledcooperativetrafficcongestiondetection(CoTEC),
whichusesfuzzylogiccontrolwithtwoinputs(thespeedandthedensityofvehicles)andoneoutput
(congestionlevel). Thisalgorithmusescooperativeawarenessmessages(CAM)orbeaconmessages,
sentperiodicallytoothervehiclestellingthemtoavoidthecongestedarea. Inaddition,itdetectsthe
congestionbyusinganexternalmetriccalledthelevelofservice(LOS)developedbySkycomp. This
involvestheclassificationofcongestionlevelsfromaerialsurveysofhighways. Onceobtained,this
informationisthencombinedwithdatafromorganizations,suchaslocalauthorities. Asaresult,the
performanceofthealgorithmisheavilydependentontheaccuracyofthedatafromtheseexternal
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organizations. Additionally, no mechanism is provided for drivers to find the optimal route for
theirjourney.
In[17],acentralizedframeworkisproposedtoobtainreal-timecoordinatesofvehiclesandtheir
directionandvelocity,whichcanbeusedtodeterminetrafficcongestionlevels. Whencongestionis
detected,vehiclesclosebyarere-routedusingtwoalgorithms. Thefirstalgorithm,dynamicshortest
path(DSP),allocatestoeachvehicletheshortestpath(smallestTT)toreachtheirdestination. However,
the drawback of the first algorithm is the probability of transferring the congestion to other areas.
Therefore,thesecondalgorithm,randommultipathKshortestpaths(RKSP),determinestheKshortest
paths for each vehicle and randomly allocates the vehicle to one of them. As a result of using K
alternativepaths,itispossibletoensurethatthecongestionisnotjusttransferredtoadifferentroad.
However, thedrawbackofthisalgorithmisthatthechoiceofroutesisarbitraryandusesasingle
objectivefunction.
In [18], the authors propose an ant-based congestion avoidance system (AVCAS). AVCAS
integratestheaveragetravelspeedpredictionwithsegmentationofacitymaptodetectandreduce
thecongestion. ItcollectsthetrafficinformationfromV2VcommunicationsandRSUtoforecastthe
averagespeedoftheroads. Then,itusesaweightedsummethodtoformulatethecostfunctionforthe
roads,wheretheweightshavebeencalculatedbytrialanderror. However,thisalgorithmstillchooses
theshortestpathswhenre-routingthevehiclestoavoidthecongestion. Asaresult,thistransfersthe
congestiontoanewroad.
In[19],theauthorsdescribeadistributedreal-timeV2Vcongestionevasiontechnique.Congestion
levelsaredetectedandvehiclesre-routedusingcongestionmessagescalledrequest/receivemessages
(insteadofbeaconmessages). Whenavehiclereachesanintersectionandcanselectfromdifferent
paths,itsendsacongestionrequestpackettoallneighbouringvehicleswithinitscommunicationrange
toobtainthetrafficstatusinformation. Thismessageencompassesalistofroadsthatformpotential
pathstotheirdestination. Thevehiclewillselectitsnextpotentialroutebasedonthereceivedtraffic
data. Acongestionresponsemessageistransmittedonlywhenacongestionrequestisreceived. Ifthe
congestionrequestmessageisreceivedtwice,thevehiclewillnotsendaresponsemessage,andthe
congestionmessagewillbediscardedfromthedatabaseofthereceivingvehicle. Thisensuresthatno
redundantinformationistransmitted. Otherwise,thevehiclewillbroadcasttheresponsemessage,
which includes data about the congested roads available at the receiver. The vehicle that receives
the congestion message request will select the road that has the minimum travel time. However,
thismethodhastwodrawbacks. Firstly,itincludesahighdelaytimeduetosendingthetrafficdata.
Secondly,theauthorshavenotconsideredthehighprobabilityandconsequencesoflostpacketsina
builtuparea.
In[20],theauthorssuggestanITSbasedonRSUsinordertoavoidtrafficcongestion. Thissystem
istriggeredonlywhenanaccidentoccurs. Thevehiclesinvolvedstarttotransmitalertmessageswith
thelocationoftheaccidenttotheothervehicleswithintheirtransmissionrange. Everyvehiclethat
hasreceivedanalertmessagechecksifitisnearanaffectedarea. Ifitisfarfromtheaccidentpoint,the
vehiclewilldeletethereceivedmessage. However,ifthevehicleisneartheaccidentpoint,itchecks
itsroutetoestablishwhetheritisaffectedbytheaccidentornot. Atthisstage,anewroutecanbe
calculatedandassignedtothevehicle. However,thedrawbackofthismethodisthatthere-routingis
donebasedoneitherastaticDAorA*algorithm. Thiswouldtransferthecongestionfromoneareato
another. Inaddition,thissystemdoesnotconsiderthetrafficcongestionthatoccursduetothehigh
vehicledensitiesinagivenarea.
Recently, in [21,22], the authors proposed two systems called geographical accident aware
of reducing urban congestion (GARUDA) and a solution using cooperative re-routing to prevent
congestionandimprovetrafficcondition(SCORPION)basedontheITSandIoV.TheGARUDAisa
decentralizedsystem,anditoffersanewpathtothedriversconsideringallcarsandavailableroutes
intheregionnearesttoanaccident. TheSCORPIONisacentralizedsystemthatcollectsthetraffic
data from RSU, and it uses the concept of fuzzy logic to predict congested roads. However, both
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systemsproposethere-routingbasedonstaticDijkstraorA*algorithmsand,thus,willhavethesame
shortcomingasin[15],i.e.,thepossibilityofmovingcongestiontoanewarea.
Otherstudieshavereviewedthemostrelevantalgorithmstocalculatetherouteinthevehicle
route problem (VRP), such as in [2–4,6] and [23]. In [23], a modified version of ACO is proposed
inordertoreducethetraveltimeforvehiclesonthemove. Themodifiedantcolonyoptimization
(MACO) is a variation of the classical ACO in which the idea of an ant colony has been reversed.
Insteadofattractingthevehiclestowardroadsthathavehighpheromonelevels,theMACOalgorithm
routesanddispersesthetraffictowardpathswithlowerpheromonevaluestoavoidthecongestion.
However,thecostfunctionofthisalgorithmisverysimilartotheclassicalDijkstraalgorithm.
Hence,thenoveltyofthisworkisthedevelopeddynamicmulti-objectiveoptimizationalgorithm,
whichcombinessimulatedannealing(SA)withtheMADMTOPSIScostfunctiontoprovidethedriver
with optimal paths. In addition, the proposed algorithm utilizes real-time data using IoV, unlike
otherworks,wherethestaticalDAorA*isusedtore-routethevehiclesandleadstothetransferof
congestionontootherroads. OurproposedapproachisalsobetterthantheACO-basedmethodsas
theACOcanbecomestuckinlocaloptimasolutions(ratherthantheglobalsolution). Thisisbecause
oftheACOupdatingthepheromonebasedonthecurrentoptimalroute[24].
Theproposedalgorithmhasfourfeatures:
1. ISATOPSISallowstransitionfromagoodsolutiontoaworsesolutionunderastrictcondition.
Thisallowsthealgorithmtofindtheglobaloptimalsolutionandavoidbecomingstuckinlocal
optimalsolutions.
2. ISATOPSIScanworkfordynamicpathplanningbycollectingreal-timetrafficdatafromIoVand
efficientlyfindingalternativeroutesforthedriver.
3. ISATOPSIScanoptimizemorethanonecriteriausingtheMADMTOPSISmethod,whichallows
alternativeroutestobejudgedondifferentcriteria.
4. ISATOPSIS periodically detects and avoids congestion by selecting the paths that have the
minimum traffic, CO emissions, fuel consumption, as well as travel time. This is due to
2
combiningdifferentnavigationattributesinthecostfunction.
3. SystemDescription
IoVconsistsoftwocomponents: V2VandV2Icommunication. TheV2Vsystemisanon-board
WSN,whichisinstalledinthevehiclesthemselves. Thesensorsallowthevehiclestosendandreceive
information,suchasspeed,locationanddirection[10]. TheV2Isystemisaroadsideunitnetwork
comprisingsomeoftheinfrastructurerelatedtosmartcities,e.g.,trafficsensorsdeployedalongthe
roadsandatintersections.
Inthispaper,bothsystemshavebeenusedwiththe“hello”protocol[25]orbeaconmessages,
whichfocusontacklingtheproblemofmonitoring,trafficandreducingcongestion. Figure1showsthe
V2VandV2Iarchitectures. Inthisprotocol,eachvehiclewillhaveanoverviewoftheaveragespeed
anddensityofvehiclesontheroadnetwork. Thisallowsthemtochoosetheoptimalpathtoreachtheir
destination. Inthissection,wedescribeourproposedsystembyspecifyingthedatadissemination
methodology,theroadnetworkmodel,simulatedannealingofSAWSandSATOPSISandanimproved
simulatedannealingTOPSISalgorithm.
3.1. DataDissemination
Thedatahave beentransmittedusingbeacon messages, andthe proposedprotocolworksas
follows: thevehiclestransmittheiraveragevelocityand“roadId”totheirneighbouringRSUsthrough
beaconmessages. EachRSUholdsadatastructurecontainingtheaveragespeeds,roadIdsandroads
lengthofallvehicleswithinitstransmissionrange. Theaveragespeedsarefoundfromthespeed
measurementsoverthepreviousfiveseconds(onemeasurementasecond). Iftheaveragespeedis
lessthanorequaltoavelocitythresholdpredeterminedbythedesigner,thecongestiondetectionis
initiated,inwhichcongestedroadsareidentified. TheRSUwillthenverifywhetherornottobroadcast
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thedatafromreceivingbeaconmessages. ThedatawillbeusediftheRSUdoesnotreceiveaduplicate
messagewiththesameroadId. WhenevertheRSUreceivesanewbeacon,itupdatesitsdatastructure
andbroadcaststhedatatovehicleswithinitstransmissionrange. Asaresult,congestedroadscanbe
excludedfromthemapandanewroutecalculatedattheapplicationlayerofV2Vcommunication
usingtheISATOPSISalgorithm.

Ro ad Side Unit (RSU)
Vehicle on-board sensors

Figure1.InternetofVehicles(IoV)roadnetworkinfrastructure.

3.2. RoadNetwork

The road network can be modelled as a directed graph G = (N,E), where N corresponds to

theintersections(nodes)andE = {e ,e ,...,e}correspondstotheroadsegments(edges). Theroad
1 2 i
matrix Acanbeformulatedasfollows: supposee achintersectioncontainsnroads;eachoftheroads
containsthejattributevalueintheroadnetwork:
C C
L S
 
A r r
1 11 12
A r r 
2 21 22 
.  . . 
A = ..  .. ..  (1)
 
 
A r r
n n1 n2 
w w
1 2
Thenormalizedroadmatrixhasbeenobtainedusingthefollowingequation:
x
kj
rkj = (cid:115) where k =1,...,n; j =1,2 (2)
n
∑(x )2
kj
k=1
wherer = {r |k = 1,...,n; j = 1,2} arethenormalizedperformancevaluesofeachC andC ,
kj L S
respectively. X = {x |k =1,...,n; j =1,2}denotesthesetofperformancevaluesofeachC andC ,
kj L S
respectively. w = {w | j =1,2}denotesthesetofweights;V = {v ,v ,...,v }isthesetofvehicles;
j 1 2 j
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andA = {A |k =1,...,n}arethealternativeroadsforeachvehicleinV.Everyvehiclev periodically
k j
sends a message msg thatcontains {roadId ,averagespeed ,position ,route ,destination } to the
j j j j j j
neighbouringRSUs.
Twoparametershavebeenusedinouroptimization:
1. Road length C = {r |k = 1,...,n; j = 1} represents the normalized length in a directed
L kj
graphGforeachalternativein A.
2. AveragevelocityC = {r |k = 1,...,n; j = 2}representsthenormalizedaveragespeedof
S kj
eachvehicleatacertainperiodin A.
3.3. SimulatedAnnealingofSAWSandSATOPSIS
SAisanoptimizationapproachfirstproposedby[26]thatimitatestheprocessofannealingin
mineralogy. Itallowstransferencefromagivensolutiontoaworsesolutionunderstrictconditions.
Thisallowsthealgorithmamutationtomovefromlocalminimaormaximatowardstheglobaloptima.
SAbeginswithasetofrandomly-chosensolutions. Eachiterationproducesanewsolutionofthe
statevector,whichisfoundbasedonthecostfunction. Anewsolutionwithahighcostisaccepted
immediately. However,asolutionwithalowercostthanthepreviousonecanbeacceptedwitha
transitionprobability. Inthiswork, K randompathshavebeengeneratedfrommatrix A. Figure2
showshowthepathsaregenerated.
Initial path

P = {𝒓 , 𝒓 , ……, 𝒓 }
𝒔 𝟏 𝒅
Randomly select a road
𝒓 from road matrix A
𝒊
No Is the path
P is feasible
Yes
Delete the 𝒓 from A
𝒊
Is the
No
destination
reached?
Yes
Return P and repeat the process
until the desired number of
paths are achieved
Figure2.Theprocedureofgeneratingarandompath.
SAhasbeenusedwithtwodifferentcostfunctions(theweightedsumandTOPSISmethods)to
selecttheoptimalpathfromtheKrandompaths. Everyv inV hasasetofalternativepathsfromR ,
j k
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whereR isamatrixofKrandompathsgeneratedfrom A. EverypathinR containsthenumberof
k k
roads A ,andthecostfunctionofeachpathhasbeencomputedasthesumofthecostsofallofthe
k
roadsitcontains.
Algorithm1describestheprocedureofchoosingapathfromKrandompaths,whereX isthe
c
current solution, which is generated randomly from A. T is the temperature parameter, which is
moderately decremented with time. The constant α is the cooling rate used to gradually decrease
thevalueofT. Whenthetemperatureparameterhasaveryhighvalue,i.e.,T → ∞,anewpathX
n
isselectedrandomlyfrom R . Thecostfunctionisevaluatedfor X (N(X ))andcomparedtothe
k n n
previousvalueofthecostfunction(C(X )). Ifthecostfunctionishigherthanthepreviousvalue,then
c
thesolutionisaccepted. Evenifthenewsolutionisnotappropriate(meaningthecostofthenew
solutionislessthanorequaltothecurrentsolution),itisacceptedwithsomeacceptanceprobability.
Thishelpstoexpandthesearchandavoidslocaloptima. WhenTapproacheszero,pathswithahigh
costhaveahighprobabilityofbeingaccepted.
The SAWS and SATOPSIS find up to three alternatives for vehicles that have the same
source/destination. Whentheoptimalpathsarefound,theyareorderedbasedonthecostfunction.
The vehicles that have the same source/destination are distributed on these three optimal paths.
Thiswillensurethevehiclesaresharedbetweenthepathsandensuresthetrafficloadisbalancedon
themap.
Algorithm1Thesimulatedannealingalgorithmforenhancingmobility.
1: Xc = Xc0 Initialrandomsolution
2: T = T0Aninitialtemperature
3: α=Coolingrate
4: sb =Currentbestsolution
5: sb ←Xc
6: WhileT > Tm whereTm istheminimumtemperature
7: GeneratearandomneighboursolutionXn fromRk
8: IfN(Xn)>C(Xc)
9: MovetoXn
10: Acceptchangesb ←Xn
11: ElseIfN(Xn)≤C(Xc)Then
12: MovetoXn withtransitionprobability
13: Pt =1/1+exp(C(Xc),N(Xn),T)
14: Endif
15: T = αT
16: Endwhile(ifT < Tm)
17: Returnsb
3.4. AnImprovedSimulatedAnnealingTOPSISAlgorithm
In this section, SA has been implemented for dynamic path planning using the TOPSIS cost
functionmethod. Thedecision-makingprocessoftheproposedapproachisconstructedasfollows:
3.4.1. Off-LineComputationofPathPlanning
SAbeginswithoff-lineroutecalculation,inwhicheveryv inV hasasetofroadsfrom Aand
j
everyroad A in AhasacostfunctionformulatedusingTOPSISmethod. Thealgorithmdescriptionof
k
theSAisoutlinedinAlgorithm1,exceptStep1,whereX isthecurrentsearchsolutionoraninitial
c
feasiblepath,whichisanoptimalpathfrom R . Whenthetemperatureparameterhasaveryhigh
k
valuethenewsearchsolution,X inStep7isconstructedbasedonX asfollows:
n c
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1. An initial optimal path Xc = {rs,r1,...,ri,ri+1,...,rl−1,rl,rd} where ri means the i-th
roadsegment.
2. Theperturbation(seeFigure3)consistsofthefollowingthreesteps.
(a) Tworoadsr andr ,calledbaseroads,arechosenrandomlyintheX path.
i l c
(b) Apathisconstructed,usingr asanoriginandr asadestination.
i l
(c) ThepathXc = {rs,r1,...,ri,ri+1,...,rl−1,rl,rd}isreplacedby(ri,ri+´1,...,rl−´1)togivea
newpathXn = {rs,r1,...,ri,ri+´1,...,rl−´1,rl,rd}.
3. Checkthefeasibilityofthenewpath.

4. Ifitsnotfeasible,thenrepeattheprocess. Otherwise,useSAasinAlgorithm1andcomparethe

costofthenewpathtothepreviouspath.

𝒓𝒊 𝒓𝒊′+𝟏 ..…….… 𝒓𝒍′−𝟏 𝒓𝒍

𝒓𝒔 𝒓𝟏 ..…… 𝒓𝒊 𝒓𝒊+𝟏 ..…….… 𝒓𝒍−𝟏 𝒓𝒍 ..…… 𝒓𝒅

Figure3.TheprocedureforconstructinganewpathXnbasedonaninitialpathXc.
3.4.2. On-LineComputationofPathPlanning
Start Journey

Initial optimal path from
source to destination

Drive on current path
Reach an Intersection
Is there
an Yes
update?
No Does this
Follow the same No update effect
path the current
path?
Yes
A. Disclose the congested
Is the roads
No destination B. Discard the congested
reached? roads from the map
C. Calculate a new optimal
route using ISATOPSIS
Yes
End Journey
Figure4.Flowchartofthesimulatedannealing(SA)congestionavoidancemechanism.
Asdiscussedintheoff-linecomputationsection,thevehiclesusetheroutegeneratedbyoff-line
pathplanningtotravelthroughthecity;theon-linepathplanningisthentriggeredtoautomatically
computeanalternativeroutewhencongestionisdetectedasfollows: Whenthevehiclereachesan
intersection and enters the RSU transmission range, it will receive updated data with the table of
congestedroads. Then,thevehicleevaluatesitscurrentroute. Iftheevaluationshowsthatthecurrent
Sensors2016,16,1013 10of23
routehasnotbeenaffectedbytheupdateddata,thevehiclewillkeeptravellingalongthecurrent
route. Otherwise,ifthevehicleislikelytoenteracongestedroad,SAwillbeactivatedandreloaded
withtheupdatedsearchspace. Theupdatedsearchspacecontainsthecurrentstatusofthevehicle,
itscurrentlocationandthenewcostoftheroadsegments. Thealternativeroutewillbecomputed
fromtheupdatedsearchspacetoallowthevehicletotravelfromitscurrentlocationtothedestination.
Figure4showstheprocedureofthecongestionavoidanceusingISATOPSIS.
3.5. CalculatetheWeightsofSAWS,SATOPSISandISATOPSIS
Inthispaper,thestandarddeviation(SDV)methodisusedtodeterminetheweightsofmultiple
objectives. TheweightintheMADMproblemreflectstherelativeimportanceofthevariousobjectives.
Theweightsofthedifferentcriteriahavebeennormalizedtotransformthedifferentscalesandunits
intocommonmeasurableunitsusing:
r − min r
kj kj
(cid:48) 0≤j≤m
R = (3)
kj max r − min r
kj kj
0≤j≤m 0≤j≤m
(cid:48) (cid:48)
whereM = (R )m×nisthematrixafterrangenormalizationandmaxrkjandminrkjarethemaximum
andtheminimumvaluesofthecriterion(j)inC andC ,respectively.
L S
(cid:48)
R ∈ [0,1] k =1,...,n; j =1,2
kj
SDV is the standard deviation that is calculated independently for every j-th criterion using the
j
(cid:48) (cid:48)
normalizedmatrix M = (R )m×n asshownin(4):
(cid:115)
SDV = 1 ∑n (R(cid:48) −R¯ )2 (4)
j n kj j
k=1
where:
R¯ = 1 ∑n R(cid:48) (5)
j n kj
k=1
andR¯ isthemeanofthevaluesofthej-thcriterioninC andC afternormalizationandj =1,2.
j L S
FromEquation(4),theweight(w )ofthecriterion(j)inroadmatrix Acanbedefinedas:
j
SDV
j
w = (6)
j
2
∑
SDV
j
j=1
3.6. SimulatedAnnealingWeightedSumMethod
A multi-objective problem is often solved by combining the multiple objectives into one
single-objectivescalarfunction.Thisapproachisingeneralknownastheweighted-sumorscalarization
method. Inthispaper,thecostfunctionofthesimulatedannealinghasbeenformulatedusingthe
weightedsummethodasbelow:
f =Max{w C +w C } (7a)
1 L 2 S
n
∑
C = r (7b)
L k1
k=1
n
∑
C = r (7c)
S k2
k=1