A Review of Genetic Algorithm Approaches for Wildfire Spread Prediction Calibration

  Ci a ion: Pe ei a, J.; Mendes, J.; Júnio , J.S.S.; Viegas, C.; Paulo, J.R. A Re iew o Gene ic Algo i hm App oaches o Wild i e Sp ead P edic ion Calib a ion. Ma hema ics 2022,10, 300. h ps://doi.o g/ 10.3390/ma h10030300 Academic Edi o : Ioannis G. Tsoulos Recei ed: 16 Decembe 2021 Accep ed: 13 Janua y 2022 Published: 19 Janua y 2022 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). ma hema ics Re iew A Re iew o Gene ic Algo i hm App oaches o Wild i e Sp ead P edic ion Calib a ion Jo ge Pe ei a 1, Jé ôme Mendes 1,* , Jo ge S. S. Júnio 1, Ca los Viegas 2and João Rui o Paulo 1 1Depa men o Elec ical and Compu e Enginee ing, Ins i u e o Sys ems and Robo ics, Uni e si y o Coimb a, Pólo II, 3030-290 Coimb a, Po ugal; jo ge.pe ei a@is .uc.p (J.P.); jo ge.sil ei a@is .uc.p (J.S.S.J.); jpaulo@is .uc.p (J.R.P.) 2Associa ion o he De elopmen o Indus ial Ae odynamics, Uni e si y o Coimb a, 3030-289 Coimb a, Po ugal; [email p o ec ed] *Co espondence: je mendes@is .uc.p Abs ac : Wild i es a e complex na u al e en s ha cause signi ican en i onmen al and p ope y damage, as well as human losses, e e y yea h oughou he wo ld. In o de o aid in hei man- agemen and mi iga e hei impac , e o s ha e been di ec ed owa ds de eloping decision suppo sys ems ha can p edic wild i e p opaga ion. Mos o he a ailable ools o wild i e sp ead p e- dic ion a e based on he Ro he mel model ha , apa om being ela i ely complex and compu ing demanding, depends on se e al inpu pa ame e s conce ning he local uels, wind o opog aphy, which a e di icul o ob ain wi h a minimum esolu ion and deg ee o accu acy. These ac o s a e leading causes o he de ia ions be ween he p edic ed i e p opaga ion and he eal i e p opaga ion. In his sense, his pape conduc s a li e a u e e iew on op imiza ion me hodologies o wild i e sp ead p edic ion based on he use o e olu iona y algo i hms o inpu pa ame e se calib a ion. In he p esen li e a u e e iew, i was obse ed ha he cu en li e a u e on wild i e sp ead p edic ion calib a ion is mos ly ocused on me hodologies based on gene ic algo i hms (GAs). Inline wi h his end, his pape p esen s an applica ion o gene ic algo i hms o he calib a ion o a se o he Ro he mel model’s inpu pa ame e s, namely: su ace-a ea- o- olume a io, uel bed dep h, uel mois u e, and mid lame wind speed. The GA was alida ed on 37 eal da ase s ob ained h ough expe imen al p esc ibed i es in con olled condi ions. Keywo ds: wild i e; wild i e sp ead p edic ion; calib a ion; gene ic algo i hm; e olu iona y algo i hms 1. In oduc ion Wild i es a e one o na u e’s mos dange ous haza ds and, in he las ew yea s, hei impac has been inc easing signi ican ly, as epo ed by he Eu opean Commission’s 20 h issue o he annual wild i e epo [ 1 – 3 ]. This epo , om 2019, shows a o al bu ned a ea o 789,730 (ha) egis e ed o 40 coun ies om Eu ope, he Middle Eas , and No h A ica. This numbe is nea ly ou imes la ge han he eco ds o he p e ious yea (2018). Wild i es can impac ecosys ems by des oying na u al habi a s, esou ces, and wildli e. Fu he mo e, hey cause signi ican damage o socie y, being esponsible o nume ous a ali ies, acciden s, inju ies, heal h p oblems, and he des uc ion o human in as uc u es. These damages bea a signi ican economic impac , no only due o he i e damage bu also he la ge in es men s in p e en ion, p epa edness, i e supp ession and eco e y e o s [ 4 ]. I is essen ial o di ec e o s owa ds unde s anding he beha io o wild i es and imp o ing hei managemen . In his sense, knowledge o how wild i es p opaga e is c i ical, allowing he p edic ion o whe e he i e will be and aking he app op ia e measu es o mi iga e i s impac . Theo e ical, empi ical and semiempi ical models ha e been de eloped o p edic he wild i e beha io [ 5 ]. The semiempi ical Ro he mel model [ 6 ] is he mos widely used model o wild i e sp ead p edic ion [ 5 ], pa icula ly in Medi e anean Eu opean coun ies [ 7 ], being he co e o some o he mos ci ed i e simula o s such as FARSITE [ 8 ] Ma hema ics 2022,10, 300. h ps://doi.o g/10.3390/ma h10030300 h ps://www.mdpi.com/jou nal/ma hema ics Ma hema ics 2022,10, 300 2 o 19 and FIRESTATION [ 9 ]. The Ro he mel model uses se e al inpu pa ame e s ela ed o he a ailable o es uels, such as ees, g ass o bushes (su ace-a ea- o- olume a io, heigh and mois u e con en ), he e ain con igu a ion (slope), and a mosphe ic condi ions (wind speed and di ec ion). The quali y o he i e sp ead p edic ion depends on he quali y o he p opaga ion model, and on he accu acy o he inpu pa ame e s [ 10 ]. The p esen wo k ocuses on he la e cause o unce ain y in wild i e sp ead p edic ions. As a ma e o ac , while some a iables emain cons an h oughou he whole i e e en o can be ob ained wi h a high deg ee o accu acy (e.g., e ain slope), o he a iables may change due o i e and canno be ob ained wi h enough empo al o spa ial esolu ion (e.g., uel cha ac e is ics and wind speed/di ec ion). This unce ain y in he inpu pa ame e s esul s in conside able de ia ions be ween he p edic ed and he eal i e sp ead. In o de o imp o e he i e sp ead simula ions/p edic ions, i is essen ial o deal wi h his unce ain y in he Ro he mel model inpu pa ame e s. In an e o o ind he accu a e inpu pa ame e s alues o he wild i e p edic ion, some me hodologies based on E olu iona y Algo i hms (EAs) ha e been p oposed o calib a e he Ro he mel model [ 11 ]. EAs, such as gene ic algo i hms (GA), an colony op imiza ion (ACO), and pa icle swa m op imiza ion (PSO), ha e p o en hei e ec i eness o op imiza ion/calib a ion p oblems [12–14]. In his pape , we p esen a e iew o gene ic algo i hm app oaches o wild i e sp ead p edic ion calib a ion. The main con ibu ions o he pape a e: • A li e a u e e iew ocused on wild i e sp ead p edic ion calib a ion using GAs is pe - o med. The GA was chosen as a echnique o he calib a ion due o i s p edominance in esea ch wo ks ha used EAs o calib a e he wild i e sp ead p edic ion model; • Based on he p esen ed li e a u e e iew, in a didac ic way, wild i e sp ead calib a ion using gene ic algo i hm is desc ibed, in which a speci ic GA amewo k o Ro he mel model calib a ion is p esen ed. Mo eo e , he pa ame e s o be calib a ed a e dis- cussed, namely he su ace-a ea- o- olume a io ( σ ), uel bed dep h ( δ ), uel mois u e (M ), and mid lame wind speed (U); • The ac ual easibili y o using GAs o he calib a ion o he Ro he mel model o wild i e sp ead p edic ion is explo ed/s udied on 37 eal da ase s. The esul s show a signi ican e o educ ion in he wild i e sp ead p edic ion, i.e., om 95% o 10%. This pape is o ganized as ollows. Sec ion 2con ains a desc ip ion o he Ro he mel model, as well as an insigh in o he cu en s a e o he a ega ding me hods o wild i e sp ead p edic ion using gene ic algo i hms. In Sec ion 3, GAs a e e ised, and he me hod used in his pape o calib a e he Ro he mel model is p esen ed. In Sec ion 4, he esul s o he p oposed calib a ion a e p esen ed and analyzed. Finally, Sec ion 5p esen s he inal conclusions. 2. Li e a u e Re iew o Wild i e Sp ead P edic ion Calib a ion Gene ic algo i hms a e he mos adop ed echnique o calib a ion o he Ro he mel model’s inpu pa ame e s. Due o he impo ance o his subjec o wild i e sp ead p edic ion, and due o he numbe o la es de elopmen s in his pa icula ield, a li e a u e e iew o he mos ele an wo k in his a ea is undamen al. The sea ch p ocess o he p esen ed li e a u e e iew was pe o med by using he Sci- ence Di ec and IEEE Xplo e da abases and de ining he ollowing sea ch keywo ds: (“ i e sp ead” OR “ i e p edic ion” OR “ i e a e o sp ead” OR “Ro he mel model”) AND (“ge- ne ic algo i hm” OR “e olu iona y algo i hm” OR “calib a ion” OR “ uning”). The yea s conside ed o he sea ch we e om 2000 un il 2021. Addi ionally, he e e ences o he selec ed pape s we e also analyzed and se ed as a sou ce o inding new pape s. The li e a u e e iew a ionale o a icle selec ion was based on he ollowing c i e ia: • Accep ance 1. The a icle uses he Ro he mel model o a Ro he mel model-based simula o o i e p opaga ion p edic ion/simula ion; Ma hema ics 2022,10, 300 3 o 19 2. The a icle uses e olu iona y algo i hms o Ro he mel model calib a ion; 3. The a icle ocuses on imp o ing he p edic ion esul s o i s execu ion ime. • Rejec ion 1. The a icle’s me hod o i e p opaga ion p edic ion is no based on he Ro he mel model; 2. The a icle implemen s calib a ion echniques o he han e olu iona y algo i hms. Based on his p ocess, 15 pape s we e ob ained. 2.1. Ro he mel Model The Ro he mel model, p oposed in [ 6 ], es ima es a Ra e O Sp ead R o a i e on , gi en by R=IRξ(1+φw+φs) ρbεQig , (1) which is measu ed in uni s o dis ance pe uni o ime ( [m/s] o [ /min] ), and i ep esen s he linea eloci y o a i e, in a gi en di ec ion and se o condi ions. The equa ions o he associa ed ac o s in (1)IR(ρp,σ,δ,w0,ST,h,Mx,M ,Se),ξ(σ,ρp,w0,δ),φw(ρp,w0,δ,σ,U), φs(ρp , w0 , δ , anφ) , ρb(w0 , δ) , ε(σ) , and Qig(M ) depend on se e al inpu pa ame e s and a e gi en by: IR=Γ0wnhηMηS(2) Γ0=Γ0 maxβ βop A expA1− − β βop  (3) A=133σ−0.7913 (4) β=ρb ρp(5) ρb=w0 δ(6) Γ0 max =σ1.5 (495 +0.0594σ1.5)(7) βop =3.348σ−0.8189 (8) wn=w0(1−ST)(9) ηM=1− −2.59 M+5.11( M)2− −3.52( M)3(10) M=M Mx (max =1.0)(11) ηS=0.174S−0.19 e(max =1.0)(12) ξ=exp[(0.792 +0.681σ0.5)(β+0.1)] (192 +0.2595σ)(13) φw=CUBβ βop −E (14) C=7.47exp(−0.133σ0.55)(15) B=0.02526σ0.54 (16) E=0.715exp(−3.59 ×10−4σ)(17) φS=5.275β−0.3( anφ)2(18) ε=exp−138 σ(19) Qig =250 +1116M (20) whe e he desc ip ion o he espec i e pa ame e s is p esen ed in Table 1. Ma hema ics 2022,10, 300 4 o 19 Table 1. Iden i ica ion o he pa ame e s in Equa ions (2)–(20) [6,15]. Pa ame e Desc ip ion IRReac ion in ensi y (B u/ 2min) Γ0Op imum eac ion eloci y (min−1) βPacking a io ρbO en-d y bulk densi y (lb/ 3) Γ0 max Maximum eac ion eloci y (min−1) βop Op imum packing a io wnNe uel load (lb/ 2) ηMMois u e damping coe icien ηSMine al damping coe icien ξP opaga ing lux a io φwWind ac o φSSlope ac o εE ec i e hea ing numbe Qig Hea o p eigni ion (B u/lb) The inpu pa ame e s o he Ro he mel model (1) can be sepa a ed in o h ee ca ego ies: uel p ope ies, opog aphy and wind p ope ies. The uel p ope ies a e hea con en ( h ), mine al con en ( ST ( o al) and Se (e ec i e)), o en-d y pa icle densi y ( ρp ), o en-d y uel load ( w0 ), su ace-a ea- o- olume a io ( σ ), uel bed dep h ( δ ), dead uel mois u e o ex inc ion ( Mx ) and uel mois u e ( M ). Topog aphy is ep esen ed by slope s eepness ( an φ ), and wind p ope ies co espond o he mid lame wind speed ( U ). A deepe insigh in o he Ro he mel model can be seen in [6,15]. 2.2. The Need o a Fi e Sp ead Model Calib a ion Figu e 1p esen s a gene al illus a ion o wild i e sp ead p edic ion, which consis s in eeding a i e simula o wi h a se o inpu pa ame e s ha aim o ep esen he ini ial eal i e condi ions, a 0 . The esul o he i e simula o , i.e., he simula ed wild i e pe ime e , a 1 , should ma ch he p opaga ion o he eal wild i e, i.e., he eal wild i e pe ime e [ 16 ]. Howe e , he inpu pa ame e s a e ela ed o he en i onmen al condi ions, e.g., uel, wea he , and e ain cha ac e is ics as desc ibed in Sec ion 2.1, and ob aining hem becomes a di icul ask in o de o p o ide an accu a e p edic ion. Time Real i e igni ion Real wild i e pe ime e Real i e da a Simula ed wild i e pe ime e Fi e simula o Inpu pa ame e s Figu e 1. Illus a ion o i e sp ead p edic ion using only one se o non-calib a ed inpu pa ame e s. Adap ed om [17]. In mo e de ail, some inpu pa ame e s can be di ec ly measu ed, such as e ain slope, which can also be ob ained based on p e ious opog aphical in o ma ion. Howe e , o he pa ame e s, such as uel-speci ic pa ame e s, equi e de ailed knowledge abou he local ege a ion, which migh no be a ailable. Some inpu pa ame e s, such as uel mois u e, a e calcula ed using models based on me eo ological da a [18], while wind ield maps a e Ma hema ics 2022,10, 300 5 o 19 es ima ed based on poin obse a ions om he a ailable me eo ological s a ions close o he i e loca ion. These es ima ions in oduce a g ea amoun o e o in he p edic ion. In e ms o beha io change, cha ac e is ics such as he e ain slope and he ype o ege a ion in a ce ain egion a e cons an in ime and space, while o he s, such as wind speed and di ec ion, ha e e y sudden a ia ions du ing he wild i e [ 10 ]. The e o e, inding a se o inpu pa ame e s ha p oduces accu a e esul s solely based on p e ious knowledge abou he wild i e loca ion and wea he condi ions is a challenging ask. Due o he unce ain y and he consequen inaccu acy in wild i e sp ead simula ion, he e is a need o calib a e he inpu pa ame e s. 2.3. Wild i e Sp ead Calib a ion Li e a u e O e iew The Ro he mel model is he mos used and ecognized i e sp ead p edic ion model, se ing as he base o se e al i e simula o s (FARSITE [ 8 ] and FIRESTATION [ 9 ]). Resea ch wo ks ha deal wi h Ro he mel model calib a ion and wild i e sp ead p edic ion mos ly use gene ic algo i hms. Ini ially, wo ks such as [ 19 , 20 ] ha e p o ed he pe o mance o gene ic algo i hms by compa ing hem agains o he op imiza ion echniques and wi h implemen a ion in a pa allel wo-s age p edic ion amewo k. Mo e ecen ly, o he wo ks such as [ 17 , 21 ] aim o imp o e he calib a ion by me ging he algo i hms wi h o he ools ha complemen hei pe o mance, such as he S a is ical Sys em o Fo es Fi e Man- agemen ( S2F2M ) and WildFi e Analys (WFA) (a componen o he Tecnosyl a Inciden Managemen so wa e sui e designed o di ec ly suppo mul i-agency wild- i e inciden managemen ). Gi en ha he quali y o gene ic algo i hms was p o en ea ly, wo ks e ol ed in o di ec ing e o s o imp o e hei pe o mance. One o he a eas explo ed o imp o e he pe o mance o gene ic algo i hms is pa allel compu ing. Se e al wo ks used pa allel implemen a ions o gene ic algo i hms o educe calib a ion ime. In gene al, hese s a egies consis ed o implemen ing a simula o ’s in insic unc ions in pa allel and alloca ing mo e p ocessing co es o indi iduals (elemen s o a popula ion ha ep esen one possible solu ion o he p oblem) wi h longe p edic ed execu ion imes. In he ollowing sec ions, he main wo ks dealing wi h his opic a e p o ided, p o id- ing a pe spec i e o he philosophy cu en ly being pu sued in his esea ch ield. 2.4. Wild i e Sp ead Calib a ion Li e a u e Using Gene ic Algo i hms Gene ic algo i hms ha e been used o ind he se o inpu pa ame e s ha be e adjus s he wild i e sp ead model p edic ions o he eal obse a ions. In o he wo ds, op imizing he model using a amewo k o wild i e sp ead p edic ion uning. The au ho s in [ 20 ] in oduced a amewo k, illus a ed in Figu e 2, ha consis s o wo s ages: a calib a ion s age and a p edic ion s age. A e he igni ion, he calib a ion s age s a s, a 0 . Se s o Ro he mel’s inpu pa ame e s a e gene a ed (using an op imiza ion app oach). Each se o inpu pa ame e s is e alua ed, a ins an o ime 1 , by compa ing he simula o p edic ion wi h he eal obse ed i e da a o ha ime ins ance. The op imal se o inpu pa ame e s is he one ha minimizes he de ia ion be ween he p edic ed and he eal i e pe ime e . This p ocess is epea ed se e al imes o un il a ce ain solu ion c i e ion is eached. In he p edic ion s age, assuming ha en i onmen al condi ions emain cons an , he esul ing op imal se o pa ame e s om he calib a ion s age is used as inpu o he i e simula o o p edic he i e sp ead a e e y ins an o ime i ( i∈N ). He e, he p edic ion s age is simila o he classical me hod/ amewo k ( Figu e 1 ), excep ha now a uned se o inpu pa ame e s is used. Ma hema ics 2022,10, 300 6 o 19 Time Real i e igni ion Real wild i e pe ime e Real i e da a Inpu pa ame e s Simula ed wild i e pe ime e Feedback Bes se o pa ame e s Real wild i e pe ime e Simula ed wild i e pe ime e Fi e simula o Fi e simula o Figu e 2. Two-s age me hod o i e sp ead p edic ion, adap ed om [17]. Du ing he calib a ion s age, he goal is o ind an op imal solu ion o he inpu pa ame e s. In a gene ic way, he op imiza ion p oblem can be de ined as: x∗=a g min x∈S F(x), (21) whe e F(x) ep esen s he unc ion o be minimized (by an op imiza ion algo i hm, such as GA), x ep esen s he inpu pa ame e s ec o , S is he espec i e sea ch space, and x∗ ep esen s he inpu pa ame e s ha minimize F(x) . A usual unc ion o be op imized in wild i e sp ead calib a ion is he di e ence be ween he eal wild i e a e o sp ead (measu ed om he eal- ime wild i e da a) and he p edic ed a e o sp ead (ob ained by he Ro he mel model), o he di e ence be ween he eal and he p edic ed bu ned a ea. The goal is o ind he se o inpu pa ame e s x o (21) ha mos accu a ely p edic s he eal i e p opaga ion. The majo i y o he wo ks om he cu en s a e o he a on wild i e sp ead p edic ion a e based on he p e iously p esen ed Two-S age amewo k (Figu e 2). Ea ly wo ks, such as [ 19 , 20 ], ha e p oposed e olu iona y algo i hms as echniques ha could be used o ind an op imal se o inpu pa ame e s o a i e simula o . Gene ic algo i hms a e included in he g oup o e olu iona y algo i hms and hey a e he dominan op imiza ion echnique o inpu pa ame e calib a ion. In [ 20 ], ollowing he p esen a ion o he wo-s age amewo k, a sensi i i y analysis was ca ied ou in o de o e alua e how he indi idual a ia ion o each Ro he mel inpu pa ame e ac oss i s ange o possible alues a ec s he model ou pu : he bigge he sensi i i y o one pa ame e , he mo e i a ec s he model’s ou pu . Based on he sensi i i y esul s, an expe imen al s udy was conduc ed o con i m ha calib a ing pa ame e s wi h la ge sensi i i ies and ixing he o he s educes he GA’s sea ch space and accele a es he op imiza ion ime. The esul s showed ha , a e 1000 gene a ions, he scena ios in which only 6 inpu pa ame e s we e calib a ed achie ed an imp o emen in he objec i e unc ion (XOR a ea be ween he eal and simula ed bu ned a eas) o app oxima ely 33.3% (one hi d) in ela ion o he scena io in which 10 inpu pa ame e s we e calib a ed. This educ ion also ma ches he educ ion in GA’s sea ch space om one scena io o he o he . In [ 19 ], he gene ic algo i hm’s pe o mance is es ed agains h ee o he algo i hms: Random Sea ch, Tabu Sea ch and Simula ed Annealing. The es s we e ca ied ou by com- pa ing he simula ed i e line based on he se s o pa ame e s gene a ed by he algo i hms agains a i e line ob ained by se ing known alues o all he inpu s and unning he ISS es simula o o 45 min. Each algo i hm was execu ed 10 imes up o 1000 i e a ions. The i e lines we e compa ed using he Hausdo dis ance H (22), which measu es he deg ee o misma ch be ween wo se s o poin s F1 and F2 , ep esen ing he i e line simula ed based on he op imized pa ame e s and he i e line gene a ed wi h known inpu pa ame e s o compa ison. H(22) is gi en by H(F1,F2) = max(h(F1,F2),h(F2,F1)), (22) Ma hema ics 2022,10, 300 7 o 19 whe e h(F1 , F2) and h(F2 , F1) ep esen s he Hausdo dis ance be ween wo se s o poin s F1 and F2 a a speci ic poin in F2 and F1 , espec i ely (see [ 19 ] o mo e de ails). The esul s show ha simula ed annealing, abu sea ch and gene ic algo i hms p esen ed simila esul s a e he 500 h gene a ion. In [ 16 ], a dynamic da a-d i en gene ic algo i hm was p oposed o une he i e sim- ula o ’s inpu pa ame e s based on he eal i e beha io . The simula o used was i eLib and, h ough e e se enginee ing, i was possible o ob ain equa ions o wind alues (wind speed and di ec ion). These equa ions a e ed wi h e ain slope wi h he posi ion ( x , y ) o he i e on wi h he maximum a e o sp ead. The ob ained wind speed and di ec ion alues we e used o s ee he sea ch o an op imal inpu pa ame e se ca ied ou by he gene ic algo i hm. A e wa ds, in [ 22 ], he same esea ch g oup p oposed a new calib a ion s ee ing me hod as an imp o emen o he p e ious s a egy. Since his was highly dependen on he unde lying simula o , he new app oach consis ed o gene a ing a da abase wi h i e e olu ion in o ma ion om bo h eal and simula ed (syn he ic) i es. Fo he calib a ion s age, a dynamic da a-d i en gene ic algo i hm (DDDGA) was p oposed o de ine he bes wind di ec ion and wind speed alues, by sea ching he da abase o p e ious i es ha we e simila in e ms o a e o sp ead, slope and uel model o he eal obse ed i e sp ead, and using wind alues om hose i es o s ee he gene ic algo i hm’s sea ch. The au ho s in [ 17 ] in oduced a sys em called SAPIFE (Spanish ac onym o Adap- i e Sys em o Fi e P edic ion Based in S a is ical-E olu i e S a egies) which is based on he wo-s age i e sp ead p edic ion amewo k wi h a gene ic algo i hm implemen ed du ing he calib a ion s age. Howe e , in SAPIFE, he gene ic algo i hm is coupled wi h ano he me hod called he S a is ical Sys em o Fo es Fi e Managemen ( S2F2M ) [ 23 ]. This new me hod ecei es a ce ain popula ion om he GA and analyzes almos all possible in- pu pa ame e combina ions om all indi iduals in he popula ion. F om his analysis, S2F2M e alua es he p obabili y o each map cell o be bu ned o no and gene a es a p obabilis ic map. Then, based on hese p obabili ies, he numbe o possible scena ios (pa- ame e combina ions be ween di e en indi iduals) is educed, dec easing he calib a ion ime equi ed. In [ 24 ], he wo me hods in oduced in [ 16 , 22 ] we e compa ed. The me hod in oduced in [ 16 ] is named as he “analy ical me hod” and, as was desc ibed abo e, is based on he in e sion o a i e simula o . The me hod in oduced in [ 22 ] is named as he “compu a ional me hod” and elies on a da abase wi h in o ma ion om pas i es. Bo h o hese me hods use ongoing i e p opaga ion da a o ob ain wind speed and di ec ion alues and use hem o s ee he gene ic algo i hm’s sea ch. Two se s o es s we e ca ied ou : i s , he wo-s age amewo k was es ed agains he classical wild i e sp ead p edic ion me hod, which uses a single se o inpu pa ame e s in oduced in he i e simula o . This es used da a om pas i es and con i med ha he wo-s age amewo k wi h a gene ic algo i hm p o ides be e esul s han he classical p edic ion wi hou inpu pa ame e calib a ion. Then, he second se o es s compa ed he use o a simple non-guided gene ic algo i hm agains gene ic algo i hms wi h di e en con igu a ions o he p oposed s ee ing s a egies. The guided gene ic algo i hm wi h he compu a ional and analy ical me hods ob ained simila esul s and imp o ed p edic ion quali y o e he non-guided gene ic algo i hm. The wo k de eloped by [ 10 ] is also based on he wo-s age p edic ion amewo k wi h a gene ic algo i hm and in oduces an app oach o educing he p edic ion e o s caused by he a iabili y o wind pa ame e s (wind speed and di ec ion). Du ing he calib a ion s age, wind pa ame e s a e no calib a ed; ins ead, eal wind measu emen s om he i e loca ion a e aken in pe iodic sub-in e als. These measu emen s a e used as inpu s o he i e simula o in he ecu ing simula ions. A e wa ds, du ing he p edic ion s age, a nume ical wea he p edic ion (NWP) model [ 25 ] is used o pe iodically es ima e he wind pa ame e s be ween sub-in e als o he p edic ion s age. The es ima ed wind pa ame e s a e in oduced in he simula o and a e upda ed a each sub-in e al. The p edic ion esul is ob ained using he eal wind measu emen s and he calib a ed pa ame e s, which a e mois u e con en s and ege a ion ea u es. The es esul s showed ha , when he wind Ma hema ics 2022,10, 300 8 o 19 condi ions a e s able, he basic wo-s age amewo k wi h a gene ic algo i hm p o ides sa is ac o y esul s, in compa ison wi h he new me hod o using measu ed and es ima ed wind alues (p edic ion e o o 0.4 s. 0.29, espec i ely). Howe e , when he wind condi- ions a e mo e dynamic, he esul s ob ained by he in oduced me hod a e signi ican ly be e compa ed o he basic wo-s age amewo k wi h a gene ic algo i hm (p edic ion e o o 0.19 s. 0.58 m, espec i ely). In [ 26 ], a calib a ion o he uel models wi hin he Ro he mel’s i e sp ead p edic ion model was ca ied ou h ough he use o gene ic algo i hms. The GA’s indi iduals consis ed o he ollowing Ro he mel uel pa ame e s: o en-d y uel load ( w0 ), su ace-a ea- o- olume a io ( σ ), uel bed dep h ( δ ), uel mois u e o ex inc ion ( Mx ), and hea con en ( h ). Two es s we e pe o med o e alua e he p oposed GA me hod. The i s es consis ed o using GAs o he uel model calib a ion me hod, wi h he suppo o wo wo ks [ 27 , 28 ] (g ass and sh ub uels, espec i ely) ha p o ided da ase s o obse ed a e o sp ead R and o he inpu pa ame e s’ da a ( uel mois u e, wind speed and slope s eepness). The GA was pe o med wi h 9999 maximum i e a ions, 100 indi iduals, mu a ion p obabili y and eli ism ac o equal o 0.1 and 0.05, espec i ely, and he uel inpu pa ame e s calib a ed based on he pa ame e anges gi en by he pape s. Each indi idual was e alua ed using he Roo Mean Squa e E o (RMSE) be ween he obse ed and p edic ed a e o sp ead R . The second es consis ed o implemen ing he GA o calib a ing a uel model o a ype o ege a ion (Calluna hea h). Nine p esc ibed i e expe imen s we e ca ied ou in d y Calluna hea hland ege a ion and R , i e wea he (1 h uels mois u e, li e woody uel mois u e and wind speed) and e ain da a (igni ion line leng h, i e plo size and slope) we e eco ded om each expe imen . F om he nine i e expe imen s, ou we e conside ed o GA calib a ion and i e we e conside ed o alida ion. The calib a ion expe imen s da a we e used o un he GA and calib a e he uel pa ame e s, simila ly o he i s es . Then, p edic ed a e o sp ead R alues we e calcula ed using di e en uel models: GA calib a ed uel pa ame e s, he S anda d Fuel Model which p o ided he smalle RMSE when compa ing p edic ed s. obse ed R , a cus om uel model o Calluna ege a ion and a “cus om uel model pa ame e ized wi h modal alues om uels in en o ied in each i e expe imen ”. An addi ional p edic ion o he a e o sp ead R was ob ained by a Ro he mel model e o mula ion implemen ed in he Fuel Cha ac e is ics Classi ica ion Sys em (FCCS) [ 29 ]. Fo he alida ion expe imen s da a, he calib a ed GA uel pa ame e s esul ed in he lowes RMSE be ween p edic ed and obse ed a e o sp ead R, in compa ison o he al e na i e models. The s udy in [ 21 ] p esen s a dynamic da a-d i en gene ic algo i hm and in oduces a new app oach o p edic ing i e p opaga ion based on Wild i e Analys (WFA) [ 30 ]. The pape desc ibes he wo-s age p edic ion amewo k wi h a gene ic algo i hm, whe e he i e p opaga ion is simula ed using he FARSITE i e simula o [ 8 ], and he i ness unc ion co esponds o he symme ic di e ence be ween p edic ed and bu ned a eas ob ained by: Di e ence =UnionCells − −In e sec ionCells RealCells − −Ini Cells , (23) whe e UnionCells ep esen s he sum o he numbe o cells ha we e bu ned in he p e- dic ed a ea and he eal a ea, In e sec ionCells is he numbe o cells bu ned simul aneously in he p edic ed a ea and he eal a ea, RealCells is he inal numbe o cells bu ned in he eal a ea, and Ini Cells is he s a ing numbe o cells bu ned in he eal i e a ea. The newly in oduced app oach uses WildFi e Analys (WFA) and seeks he bes R (Ra e o Sp ead) adjus men ac o s, minimizing he e o be ween simula ed i e and he eal i e da a. Bo h he FARSITE i e simula o and Wild i e Analys use he Ro he mel model. A e wa ds, he wo-s age amewo k wi h he gene ic algo i hm and Wild i e Analys a e coupled oge he by o e lapping hei p edic ed i e sp ead maps. In o de o es he wo-s age amewo k and Wild i e Analys , expe imen s we e ca ied ou wi h da a om a eal i e ha occu ed in Ca dona, Ca alonia, Spain in 2005. The esul s show ha bo h me hods adap o d as ic changes in he i e cha ac e is ics. Ma hema ics 2022,10, 300 9 o 19 In [ 31 ], he wo-s age amewo k was conside ed o educe inpu pa ame e unce - ain y and p edic i e sp ead. Howe e , when he wild i e is la ge, wind canno be conside ed uni o m h oughou he whole wild i e a ea. So, his wo k in oduced a wind ield model (WindNinja), being ep esen ed by a cell map, o accoun o his a ia ion. In essence, du ing he calib a ion phase, he ob ained me eo ological wind pa ame e s a e used o calcula e he wind ield o each scena io gene a ed by he gene ic algo i hm. Then, ha ing each indi idual’s wind ield, he co esponding i e p opaga ion map is calcula ed and he e o unc ion is e alua ed. Finally, in [ 32 ], a s a is ical s udy was ca ied ou o cha ac e ize he gene ic algo i hm in he calib a ion phase o he wo-s age p edic ion me hod. The cha ac e iza ion e e s o es ima ing which GA pa ame e con igu a ion esul s in a be e calib a ion wi hin he imposed ime es ic ions. A s a is ical s udy was conduc ed based on he esul s o a gene ic algo i hm calib a ion on a simula ed i e-hou i e ob ained using FARSITE as he i e sp ead simula o . The esul s om his s udy we e maximum adjus men e o s which ha e di e en deg ees o gua an ee depending on he numbe o gene a ions ha he GA i e a es. These esul s a e impo an in unde s anding he comp omise be ween he algo i hm’s execu ion ime (numbe o gene a ions) and he adjus men e o , which is la ge when he algo i hm i e a es ewe gene a ions. 2.5. Calib a ion h ough Pa allel Compu ing Th oughou Sec ion 2.4, se e al wo ks ega ding i e sp ead p edic ion using gene ic algo i hms we e desc ibed. Despi e hei ocus being on imp o ing p edic ion accu acy, some wo ks ha e p oposed/adap ed a Mas e /Wo ke pa adigm (Figu e 3) in o de o educe he calib a ion and p edic ion imes. Mas e Gene a ed popula ion Gene ic algo i hm ... Fi e Simula o Wo ke 1 E o calcula ion Fi e Simula o Wo ke 2 E o calcula ion Fi e Simula o Wo ke N E o calcula ion Figu e 3. Gene ic algo i hm using he Mas e /Wo ke pa adigm, adap ed om [33]. GAs, as wi h any e olu iona y algo i hm, equi e he execu ion o a se o indi idual simula ions h ough se e al i e a ions, which can be e y ime-consuming, and gi en he u gency and need o accu acy associa ed wi h wild i e sp ead p edic ion in eal- ime, i is impo an o educe he execu ion ime o he calib a ion phase while main aining app op ia e accu acy. One way o achie e his is h ough he pa allel implemen a ion o he i e sp ead simula o used o he GA indi iduals’ simula ion. The au ho s in [ 34 ] p esen ed a echnique based on he pa alleliza ion o bo h he GA (used in he wo-s age i e p edic ion amewo k) and he FARSITE i e simula o . Fo he i s expe imen s, wi h i e simula ions o 20 s, he esul s showed an imp o emen in GA execu ion ime o eaching he same e o (15%) when using mo e co es pe indi idual. Ma hema ics 2022,10, 300 16 o 19 is 0.9510 (95%). Wi h GA calib a ion, he mean e o is 0.0603 (6.03%). This shows he impo ance o inpu pa ame e s calib a ion, as seen in he li e a u e. 0 20 40 60 80 100 Gene a ions, g 0.0 0.5 1.0 RFinal E o (a) 2 4 6 8 10 12 14 16 18 20 Gene a ions, g 0.0 0.5 1.0 RFinal E o (b) Figu e 5. E olu ion o he 30- un a e age o he bes i ness alues o e e y calib a ed da ase . ( a ) E olu ion o he 30- un a e age o he bes i ness alues o 100 gene a ions. ( b ) E olu ion o he 30- un a e age o he bes i ness alues o 20 gene a ions. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Da ase 0.0 0.5 1.0 Rela i e E o Non-calib a ed Ro he mel GA-calib a ed Figu e 6. Rela i e e o be ween he p edic ed and obse ed a e o sp ead R o non calib a ed s. calib a ed inpu pa ame e s. 5. Conclusions Due o he physical complexi y o wild i es, hei p edic ion models equi e he de - ini ion o se e al inpu pa ame e s. Howe e , some o hem a e e y di icul o ob ain accu a ely o , due o hei na u e, p esen signi ican a ia ions o e a sho pe iod o ime, due o wea he o i e-d i en dynamics (e.g., uel and wind p ope ies). The e o e, he use o op imiza ion me hodologies—speci ically, gene ic algo i hms— o calib a e he model and o o e come inpu pa ame e unce ain y has shown o be a alid s a egy o ob ain accu a e p edic ion esul s. This s a egy will pa e he way o imp o ed i e sp ead simula o s, capable o adap ing o he pa icula and cons an ly e ol ing condi ions o Ma hema ics 2022,10, 300 17 o 19 each loca ion, p oducing i al da a o he decision make s and po en ially mi iga ing he impac o wild i es. In his wo k, a li e a u e e iew o esea ch wo ks on i e sp ead p edic ion using gene ic algo i hms was p esen ed, showing ha gene ic algo i hms a e he mos well- accep ed me hodology o his applica ion, being well-sui ed echniques o Ro he mel model calib a ion. Mo e ecen ly, some wo ks ocused on coupling gene ic algo i hms wi h o he me hods o imp o e he p edic ion quali y. Howe e , due o he na u e o gene ic algo i hms and he complexi y o he model, he calib a ion p ocess can be e y compu a- ionally demanding. The e o e, o he wo ks also explo e he possibili y o educing gene ic algo i hms’ execu ion ime by using pa allel compu ing and co e-alloca ion echniques. Fu he mo e, in his wo k, a calib a ion o he Ro he mel model using a gene ic algo i hm implemen a ion was ca ied ou on eal da ase s. The calib a ion was pe o med on ou inpu pa ame e s: σ (su ace-a ea- o- olume a io), δ ( uel bed dep h), M ( uel mois u e) and U (mid lame wind speed). The esul s o he i e sp ead p edic ion using he calib a ed model we e compa ed o he i e sp ead p edic ion wi hou calib a ion. The esul s showed ha calib a ion imp o es p edic ion quali y by 93.66%. As u u e wo k, based on he li e a u e e iew, we in end o ex end he p edic ion o he domain o a wo-dimensional g id in o de o imp o e he model’s applicabili y o eal i e si ua ions, whe e cells ep esen a squa ed a ea o he e ain h ough which i e p opaga es. This will esul in he p edic ion o eal i e beha io in he o m o a map o bu ned cells o e ime. Fu he mo e, he pa allel implemen a ion o a gene ic algo i hm o he calib a ion o he wo-dimensional Ro he mel model based on he wo-s age amewo k should be conside ed, which is alida ed by he e iew pe o med in his pape . Las ly, he amewo k should be es ed and applied on da a ob ained h ough p esc ibed i es. Au ho Con ibu ions: Concep ualiza ion, me hodology, o mal analysis: J.P. and J.M.; w i ing— o iginal d a p epa a ion: J.P., so wa e, J.P. and J.S.S.J.; alida ion, w i ing— e iew and edi ing, J.M., C.V. and J.R.P. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was ca ied ou unde he p ojec IMFi e–In elligen Managemen o Wild i es, e . PCIF/SSI/0151/2018, and was ully unded by na ional unds h ough he Minis y o Science, Technology and Highe Educa ion. Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. 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