Better medical efficiency by means of hospital bed management optimization - a comparison of artificial intelligence techniques

1 Be e Medical E iciency by means o Hospi al Bed Managemen Op imiza ion – a Compa ison o A i icial In elligence Techniques A onso Lobo1, Agos inho Ba bosa2, Tiago Guima ães1, João Lopes1, Hugo Peixo o1, Manuel Filipe San os1 1 Cen o ALGORITMI, Uni e si y o Minho, 4800-058 Guima ães, Po ugal 2 Cen o Hospi ala do Tâmega e Sousa, 4564-007, Pena iel, Po ugal [email protected] , [email p o ec ed] saude.p , [email p o ec ed], [email p o ec ed], [email p o ec ed], [email p o ec ed] Abs ac . The combina ion o he phenomenon o o e c owding wi h ine icien managemen o esou ces is a majo obs acle o he good pe o mance o hospi al uni s and consequen ly he deg ada ion o he medical se ice p o ided. This pape p o ides an analysis o unde s and he co ela ion be ween poo bed alloca ion and hospi al pe o mance. The lack o an e icien esou ce planning among he a ious medical special ies can nega i ely impac he quali y o se ice. Fou di e en echniques we e compa ed o ealize which is be e sui ed o op imizing he alloca ion o beds in Hospi al uni s. Hill Climbing and he Gene ic Algo i hm s ood ou he o he s, he la e p esen ing g ea e consis ency and a sho e compu a ion ime. When es ed wi h eal da a om Cen o Hospi ala do Tâmega e Sousa, a ained a o al o 0 w ongly alloca ed pa ien s agains 92 when compa ed wi h o me me hods. This ansla es in o be e pa ien se ice, educed wai ing ime and s a wo kload, which means inc eased pe o mance in all adjacen medical issues. Keywo ds: A i icial In elligence, Mode n Op imiza ion, Hospi al Bed Managemen , Medical E iciency. 1 INTRODUCTION Nowadays, mo e and mo e da a ega ding hospi als and all he su ounding a ea in he heal h sec o a e becoming a ailable o us. This means an inc easingly acili a ed use o a i icial in elligence echniques o seek a signi ican imp o emen in he e iciency o hese se ices, om componen op imiza ion o e icien managemen o esou ces in he hospi al uni s, con ibu ing in a signi ican way o mone a y cos educ ion[1] The app oach pe o med in his ype o p oblem is called p esc ip i e analysis. I is an analysis wi h he pu pose o esponding o eal decisions ega ding he planning o esou ces in he hospi al uni s as well as he alloca ion o ce ain medica ions depending on he con ex , always aiming o each he bes possible solu ion [2]. This s udy is cen e ed on he de elopmen and compa ison o Machine Lea ning Op imiza ion Algo i hms (MLOA), o in elligen and e icien managemen o beds in he di e en special ies o a hospi al, co esponding in he bes possible way o he needs o he hospi al as a whole. The applica ion o hese algo i hms is becoming mo e and mo e ele an as we a e wi nessing a global aging o he popula ion which causes he low o pa ien s o be g ea e and he p essu e on heal h se ices o inc ease. The esul o his p essu e, wi hou p ope planning, is an ine icien managemen and o ganiza ion o hospi al uni s, alling sho o hei needs and an inc ease in ope a ing cos s [3]. Adop ing op imiza ion algo i hms o answe hese ques ions and ob ain he bes possible planning has been one o he bes answe s o his ype o p oblem, ep esen ing an inc ease in 2 pe o mance in se ice deli e y and ope a ion o hospi al uni s [4]. In he ealiza ion o his p ojec as ollowed he app oaches o Design Science Resea ch. 2 BACKGROUND 2.1 Resou ces Planning in Hospi al Se ings A good planning o esou ces in heal h ca e uni s o gua an ee an adequa e esponse and pe o mance o hei needs is becoming inc easingly di icul and he e o e i becomes mo e pe inen o ind ways o ob ain a be e use and op imiza ion o esou ces h ough success ul planning and managemen . The main obs acle o a good o ganiza ion and managemen o esou ces in a hospi al is due o he cu en phenomenon o o e c owding coupled wi h an ine icien managemen o esou ces, inc easingly accen ua ing he unde u iliza ion o hem, i.e. he low o pa ien s is oo high o he esponse ha hospi als can gi e, educing he esponse capaci y and consequen o e c owding [5]. Acco ding o a s udy conduc ed a he Uni e si y o Cali o nia, he main easons o his O e c owding a e concen a ed in he high olume o pa ien s, he complexi y o ela ed medical issues, delays in he p o ision o se ices and mainly in he poo managemen and alloca ion o beds in hospi als being his ac o conside ed as he one ha ep esen s mo e weigh o he p oblem in ques ion [6]. The inadequa e alloca ion o beds is due, besides he lack o a ailable beds, o an ine icien managemen o esou ces which causes a nega i e di e en ial be ween he needs p esen ed and he esponse capaci y. This means ha e en in scena ios whe e he esou ces can mee he needs, occu s a subop imal use o hem esul ing in loss o pe o mance, causing delays and cancella ion o admissions and su ge ies, ea ly ans e s o pa ien s and accumula ion o cos s[7]. To his end, i is impo an o ind a o m o model o o ganiza ion based on wo main a iables: he occupancy o beds and he o ecas ing o pa ien low, in o de o ob ain an e icien managemen o esou ces ha allows he p ope unc ioning o hospi al ins i u ions being able o p o ide adequa e ca e o hei pa ien s o ensu e a esponse capaci y app op ia e o he needs [5, 6]. 2.2 Rela ed Wo k The planning and managemen o esou ces in hospi al uni s ep esen a need and a pe inen conce n in ou days. We a e he e o e wi nessing a sys ema ic a emp o ind he bes possible solu ion ha allows us o espond e ec i ely o he p oblem o o e c owding using mo e e icien managemen o means. The e a e se e al s udies p oposing solu ions and showing impo an cha ac e is ics o be conside ed o achie e he desi ed success. One way o p omo e e icien esou ce managemen in hospi als is he use o he Ma ko model. The Ma ko model, o s a egy, is a ma hema ical queuing model in ending o p edic and imp o e he wai ing ime o pa ien s o se ice. This app oach was he a ge o a s udy published in Heal hca e Enginee ing, whe e he ocus was op imizing a model in o de o ob ain g ea e e iciency in bed alloca ion. This model was based on se e al indica o s such as he a e age numbe o pa ien s, bed u iliza ion a e, pa ien s op a e, and pa ien a e age wai ing ime. Simula ions and se e al expe imen s conduc ed wi h his model showed a signi ican imp o emen in esou ce alloca ion and o e all pa ien sa is ac ion [8]. I was made in 2022 a s udy wi h he in en o p edic ing pa ien Leng h O S ay (LOS) h ough machine lea ning models and inpu da a ega ding medical eco ds and demog aphic in o ma ion o pa ien s in he in e nal medicine special y o a hospi al in Po ugal. The au ho s ollowed wo scena ios: one ha p edic s he LOS a he ime o admission; and ano he ha upda es he p edic ion du ing he hospi aliza ion p ocess. They compa ed ou machine lea ning algo i hms: decision ee, andom o es , k-nea es neighbo s and g adien boos ing. They ound ha g adien boos ing pe o ms he bes , achie ing an accu acy o abou 96%. They also ound ha including da a abou he pa ien 's heal h elec onic eco d, such as exams, lab esul s, 3 medica ions and su ge ies, imp o es he p edic i e capaci y o he model. They concluded ha hei model can help heal h p o essionals plan and manage hospi al esou ces mo e e icien ly and imp o e he quali y o ca e o pa ien s [9] In 2020, In B azil in Minas Ge ais he use o op imiza ion algo i hms, mo e speci ically a gene ic algo i hm, was also he a ge o s udy o imp o e he alloca ion o beds in hospi als in he egion, p o ing, despi e an inc ease o 13% in ope a ing cos s, a educ ion up o 1/30 o he e usal pa ien a e [10]. Following he applica ion o MLOA, mo e speci ically he gene ic algo i hm, a s udy was conduc ed a Tous Hospi al in Teh a based on pa ien low da a, a s udy aimed a op imizing he use o human esou ces in he hospi al in ques ion. The objec i e was o ind a solu ion ha ep esen ed he minimum op imal numbe o s a equi ed o mee he needs o he hospi al, hus leading o a educ ion in was e, ope a ing cos s and an inc ease in he e iciency and e ec i eness o he se ice p o ided, h ough a be e dis ibu ion o s a hou s. In he applica ion o his algo i hm, he i ness unc ion, a cons i uen unc ion o he algo i hm, whose pu pose is o a ibu e a ce ain sco e o a ce ain solu ion o he p oblem, ook in o conside a ion pa ame e s such as he employee's sala y, he numbe o pa ien s seen on a e age pe employee and he a ailable wo k shi s. I was hen, a e 500 gene a ions, ound a solu ion o s a hou ly alloca ion in which only 69 employees we e needed compa ed o he 108 ac i es in unc ion daily in he hospi al, o gi e he same o be e esponse o he needs p esen ed [11]. When i comes o compa ing op imiza ion algo i hms wi h each o he , a s udy was conduc ed a he Fukuoka Ins i u e in Japan, o e alua e he pe o mance o algo i hms such as Hill Climbing, Simula ed Annealing and Gene ic Algo i hm o op imal alloca ion o ou e s in o de o p omo e be e co e age and connec ion condi ions o Local A ea Ne wo ks. F om his s udy esul ed an ad an age o Hill Climbing and Simula ed Annealing, showing o each he desi ed esul s as e [12]. Following he pe o mance compa ison be ween he algo i hms, a s udy was conduc ed in o de o unde s and he beha io o he Hill Climbing and Gene ic algo i hms o digi al p edis o ion model sizing. F om his s udy i was concluded ha he gene ic algo i hm is dependen on he inpu pa ame e s, and ha he la ge he popula ion size, he be e he esul s, which also means a p opo ional inc ease in execu ion ime. The Hill Climbing algo i hm, on he o he hand, does no depend on he inpu pa ame e s and can p esen i sel wi h a sho e execu ion ime due o he inc ease in he popula ion size o he gene ic algo i hm. As o he pe o mance compa ison ega ding he quali y o he solu ion ob ained, he gene ic algo i hm eached he op imal solu ion mo e o en, while he hill climbing also p esen ed local op imal solu ions, i.e., solu ions close o he bes possible solu ion, bu no being so [13]. In he big pic u e we can obse e se e al di e en ways o y o achie e a mo e e icien managemen o esou ces in hospi als. In mos o he s udies ega ding he alloca ion o beds and esou ces in hospi al uni s, ac o s such as he Leng h O S ay (LOS) and he Occupa ion Ra e a e highligh ed. The applica ion o MLOA o sol e his ype o p oblems has been s udied and i s beha io is also obse ed, no only in alloca ion p oblems ela ed o he Hospi al indus y bu also in he applica ion o se e al ypes o con ex s. In his s udy he ocus will be on he applica ion o ou di e en machine lea ning op imiza ion algo i hms wi h he objec i e o ob aining an op imal solu ion o he dis ibu ion o beds by he di e en special ies o he hospi al, a oiding o e c owding. They will hen be compa ed and concluded which one p esen s he g ea es impac and signi ican imp o emen in he ma e o medical issues. 3 MATERIALS AND METHODS 3.1 Me hodologies The documen was de eloped acco ding o he Design Science Resea ch me hodology, a me hodology wi h he objec i e o c ea ing a amewo k o help sol e and in es iga e p oblems. In his amewo k a i ac s ha gene a e new knowledge a e gene a ed and analyzed. This me hodology is composed o six dis inc phases: P oblem Iden i ica ion and Mo i a ion(1), De ining he Objec i es o he solu ion(2), Design and De elopmen (3), Demons a ion(4), E alua ion(5) and Communica ion(6) [14]. 4 3.2 Tools and Algo i hms The de elopmen o his p ojec was all based on he Py hon language and i s espec i e lib a ies (NumPy, Pandas, Ma plo lib, Ma h, Da eTime). The de elopmen pla o m was Google's Colab. The algo i hms used a e Machine Lea ning Op imiza ion Algo i hms, highligh ing, Random Sea ch, Hill Climbing, Simula ed Annealing, and Gene ic/E olu iona y Algo i hm. 3.3 Da a Se s The da ase s used a e ela ed o pa ien low a he Cen o Hospi ala do Tâmega e Sousa (CHTS) and i s espec i e special ies, o a pe iod co esponding o 4 yea s. This da ase con ained in o ma ion such as, admissions, discha ges, espec i e days and imes, numbe o special y beds, which pa ien s we e alloca ed o each special y and which pa ien s we e he esponsible o each special y, and also con ained in o ma ion abou which days he pa ien was hospi alized in se ice, in a pa icula special y 4 Expe imen s The ollowing sec ion desc ibes he expe imen s in all hei phases. 4.1 P oblem Fo mula ion The aim is o imp o e he misalloca ion o pa ien s in di e en special ies due o poo managemen and planning o esou ces, speci ically beds. The ine iciency on managemen leads o an unde u iliza ion o esou ces and a consequen inc ease in o e c owding. The p oposed challenge was o ob ain an op imal solu ion o planning and dis ibu ing beds in he di e en special ies o he hospi al, conside ing: Max_bed - The o al numbe o beds in a hospi al; Special ies – All he 36 special ies in he Hospi al; Beds_needed – Numbe o beds needed on a ce ain day o each special y; Bed_a ailable – Numbe o beds a ailable/emp y in each special y; I is impo an o men ion ha he model solu ion o his p oblem would always ha e o comply wi h wo es ic ions: i) The sum o beds o be alloca ed in each special y on a gi en day, by he applied algo i hm, should ne e exceed he maximum limi o a ailable beds o be used; ii) The maximum numbe o beds o be alloca ed o a gi en special y should ne e exceed he numbe o needs p esen ed, hus a oiding he unde use o esou ces. 4.2 Da a P o ided The da ase p o ided o he s udy co esponded o he low o pa ien s in he CHTS o e a pe iod o 4 yea s (2019-2022) and i had he ini ial dimension o 708492 ows x 15 columns. Table 1 shows he a ious sou ces p o ided and a b ie desc ip ion o hem. Table 1. Da a Sou ces Da a Sou ces Desc ip ion Admissions Inpa ien s Da a ega ding he admission o pa ien s o he Hospi al, hei special ies, da es, and imes. 5 Discha ges Inpa i en s Da a iden ical o hose o pa ien ’s admission o he hospi al, bu e e ing o he discha ges. Pa i en s Alloca ion Da a ega ding he special y whe e a ce ain pa ien was alloca ed. Special ies A da a se ha con ained all he in o ma ion ega ding he hospi al's special ies. Beds Real da a ega ding he numbe o beds exis ing in he hospi al, in each special y, and abou he ype o bed in ques ion. I was possible o ob ain daily in o ma ion abou admissions, discha ges, pa ien ans e s and he days on which hey we e unde admission o each special y. I was also possible o de e mine ha he maximum numbe o beds a ailable in he hospi al was 551 beds. 4.3 Da a P epa a ion In he da a p epa a ion phase o la e use in he op imiza ion models, all da a wi h cons uc ion e o s o Null o NaN alues we e i s iden i ied. Nex , ele an da a o he analysis o bed alloca ion, epea ed o edundan a ibu es we e iden i ied. To a be e impac unde s anding and p oblem sol ing, an impo an ans o ma ion was pe o med dis inguishing wo classes o inpa ien s: • physical pa ien s - pa ien s physically admi ed o he se ice esponsible o hei ea men ; • esponsible pa ien s - pa ien s who a e physically hospi alized in se ices o he han hose ha ea hem. These wo classes co espond o co ec and inco ec bed dis ibu ion, espec i ely. A co ec bed alloca ion ma ching he daily needs o each special y would maximize physical pa ien s and minimize esponsible ones. A e hese changes he da ase was ans o med in o a ime se ies, mo ing he da e a ibu e o index and di ided in o 36 di e en sub-da ase s each co esponding o a speci ic special y. Is hen possible, o a gi en day, o know he low o pa ien s, wha he s a us o he occupa ion o beds is and how many supplemen a y beds a e necessa y o supply he eal needs o he special y. 4.4 Domain and Fi ness Func ion Be o e applying MLOA algo i hms, i is necessa y o de ine: i) he solu ion space o he p oblem; ii) how solu ions will be ep esen ed; iii) how o de ine he cons ain s; and i ) how o e alua e he e iciency o he p esen ed solu ions. I is he e o e impe a i e o de ine he p oblem domain and he objec i e unc ion. The p oblem domain de ines how he solu ion se will be ep esen ed gi en he p oblem cons ain s. The domain co esponds o he minimum and maximum numbe o beds a ailable in each special y so ha he solu ion is always possible in he space o he p oblem since i doesn' exceed he maximum numbe o beds needed o he day. In o de o op imize he algo i hms' pe o mance and dec ease he p obabili y o unde u iliza ion o esou ces, a "dynamic domain" was c ea ed depending on he day in ques ion. Con a y o wha is usually unde s ood as a ixed a iable in he p oblem, in his p oblem he domain may a y acco ding o he daily needs o he di e en special ies o he hospi al. In o he wo ds, o each day, he domain could a y be ween 0 and he numbe o pa ien s unde he esponsibili y o each special y. The solu ion was ep esen ed in an a ay o 1 dimension, wi h 36 elemen s, each 6 co esponding o an in ege numbe o beds o alloca e in a gi en special y o he day in ques ion. The i ness unc ion o objec i e unc ion has as i s main objec i e o e alua e a se o solu ions. This unc ion assigns a ce ain sco e o he solu ion o be e alua ed aking in o a accoun a se o condi ions speci ic o he con ex o he p oblem. The goal is o minimize o maximize he sco e. P esen ed in Pseudocode 1, he i ness unc ion ies o maximize he numbe o co ec bed assignmen s knowing he daily Speciali y while minimizing he numbe o emp y on unused beds. This leads o maximizing he numbe o pa ien s co ec ly assigned o a bed, i.e. maximizing physical pa ien s o a he han esponsible pa ien s. 1. Fi ness Func ion Pseudo Code sa is ac ion = 0 solu ion = solu ion inpu max_bed = 551 I sum(solu ion) > max beds hen sa is ac ion = -100 Fo each special y in solu ion do I beds_needed == beds in solu ion and beds a ailable == 0 hen sa is ac ion += 2 Else i beds_needed == beds in solu ion and beds a ailable > 0 hen sa is ac ion += 1 Else i beds_needed no equal o beds in solu ion: sa is ac ion -= |beds_in_solu ion – beds_needed| * 0.1 End I End Fo Re u n sa is ac ion 4.5 Op imiza ion Techniques Fo op imizing he alloca ion o beds o pa ien s, ou di e en Op imiza ion Algo i hms we e compa ed in o de o unde s and which one would ep esen a be e pe o mance. The con igu a ion o he algo i hms was adap ed o ake he da e in one o he pa ame e s, since i is an inpu a iable in he i ness unc ion and essen ial o de ine he daily domain o he p oblem. The algo i hms ha we e conside ed in his s udy a e p esen ed below. • Random Sea ch (RS) A me hod based on he andom sea ch o solu ions du ing a ce ain numbe o ounds. No e ha he g ea e he numbe o ounds he mo e likely i is ha a be e solu ion will eme ge, inc easing in he same way he compu a ion ime [15]. 2. RS Pseudo Code ound = 0 bes _sa is ac ion = 0 bes solu ion TO NULL 7 While ound < ounds solu ion = andom solu ion be ween he domain alues sa is ac ion = i ness unc ion(da e, solu ion) I sa is ac ion > bes _sa is ac ion hen bes _sa is ac ion = sa is ac ion bes solu ion = solu ion End I ound ++ End While Re u n bes solu ion • Hill Climbing (HC) Hill Climbing is a local sea ch algo i hm, based on inc emen s and dec emen s o he gene a ed solu ions, called "neighbo s", s a ing wi h an ini ial andom o p e iously p o ided solu ion wi hin he domain. In i s execu ion, each gene a ed neighbo is analyzed and e alua ed h ough he i ness unc ion as o i s quali y, and i one o he neighbo s gene a ed in he i e a ion p esen s a be e esul , i becomes he cu en solu ion. The algo i hm con inues un il he e is no possibili y o imp o emen in he solu ions. This algo i hm ends o ind local op imal solu ions. 3. HC Pseudo Code Gene a e an ini ial solu ion s0, s = s0 sa is ac ion = i ness(da e, s) While e mina ion c i e ia no me do neighbo _solu ion = Gene a e_Neighbo (s, domain) neighbo _sa is ac ion = i ness(da e, neighbo _solu ion) I neighbo _sa is ac ion > sa is ac ion hen s = neighbo _solu ion sa is ac ion = neighbo _sa is ac ion End I End While Re u n s • Simula ed Annealing (SA) Simula ed Annealing is a he modynamic analogous me hod inspi ed by he me al cooling p ocess. This algo i hm consis s in a sequence o i e a ions whe e a p og essi e dec ease o empe a u e occu s, ini ializing i in a high alue whe e each change is accep ed, being his accep ance p obabili y smalle and smalle as he empe a u e dec eases acco ding o a cooling a e. The sea ch me hod is iden ical o he HC algo i hm based on he ans o ma ion o solu ions h ough inc emen s o he p e ious solu ion, he big di e ence is ha h ough he accep ance o no o he solu ions his app oach a oids ge ing s uck wi h local min o max. 4. SA Pseudo Code Gene a e an ini ial solu ion s0, s = s0 8 sa is ac ion0 = i ness(da e, s) While empe a u e > 0.1 do s1 = Gene a e(s0, domain) sa is ac ion1 = i ness(da e, s1) I Accep (sa is ac ion0, sa is ac ion1, empe a u e) hen sa is ac ion0 = sa is ac ion1 s0 = s1 End I empe a u e = empe a u e * cooling End While Re u n s0 • Gene ic Algo i hm (GA) The Gene ic Algo i hm is based on Cha les Da win's heo y o e olu ion. I ac s on a se o possible solu ions called indi iduals o a popula ion. The algo i hm s a s wi h an ini ial popula ion and ans o ma ions a e pe o med on each o he indi iduals h ough mu a ion o c osso e , whose decision is based on a p e iously de ined p obabili y. The bes indi iduals a e chosen acco ding o an eli ism numbe o gene a e he new popula ion. The algo i hm ends when he desi ed numbe o popula ions/gene a ions is eached and he bes indi idual om he las popula ion is eached. I should be no ed ha , acco ding o se e al s udies such as he one ca ied ou a he Uni e si y o Neuchâ el in Swi ze land, i was ound ha hese algo i hms show be e esul s wi h la ge popula ions han wi h inc easing he max numbe o gene a ions [16]. 5. GA Pseudo Code Ini ialize popula ion eli e = elis ism * Popula ion-Size Fo i in ange numbe _gene a ions i ness(da e, indi idual) o each indi idual in popula ion Selec he eli e wi h he bes esul Inse eli e in o new_popula ion While new popula ion-size < Popula ion-Size IF p obabili y o mu a ion Mu a e eli e indi idual - > new indi idual ELSE C osso e eli e indi duals -> new indi idual Inse indi idual in o new popula ion End While End Fo 9 Re u n las gene a ion bes ind idual 4.6 E alua ion In o de o e alua e he pe o mance o each model, 10 uns o each one we e pe o med. Fo each we e sa ed he sco e ob ained and he compu a ion ime equi ed. Fo he expe imen all he models we e execu ed wi h da a based on he da e o May 5, 2021, aking in o accoun ha he domain co esponds o a a iable ha would change day a e day, depending on eal needs o he hospi al. No di e ence was pe cei ed in he success a e whe he conside ing 1 o 50 days. Table 2 p esen s he me ics used o e alua ing he echniques as well as a b ie desc ip ion. Table 2. Me ics Me ic Desc ip ion A e age Fi ness_Func ion Sco e Mean o all he sco es ob ained in he 10 Execu ions A e age Run Time Mean o he execu ion imes Model Sco e S anda d De ia ion (STD) STD o he sco es ob ained In a pe ec scena io, he alloca ion o beds co esponds o he daily needs o hese special ies and he numbe o unused beds ends o 0. The maximum sco e ob ained would be 2 poin s o each one o he 36 special ies, i.e. 2x36, meaning a maximum sco e o 72 poin s. I is necessa y o ake in o accoun ha o his sco e o be eached he hospi al is no in a s a e o o e /unde capaci y. All he beds would be occupied and alloca ed o he special ies co ec ly, which is no obse ed in abou 99% o he occu ences. The STD o he un ime was no eco ded since i was insigni ican di e ences among uns o he same algo i hm, wha could be he esul o he compu a ional condi ions in he de elopmen en i onmen . 5 RESULTS AND DISCUSSION 5.1 Algo i hm Se ings To un he algo i hms conside ed in his s udy i was necessa y o de ine hei ini ial inpu pa ame e s excep o HC. In he able 3 a e p esen ed he alues used o he implemen a ion o each echnique. Table 3. Algo i hms’ Pa ame e s Model Pa ame e s Random Sea ch Rounds ->10000 Hill Climbing None Simula ed Annealing Cooling Ra e -> 0.95 Tempe a u e -> 10000000000 Gene ic Algo i hm Popula ion-size -> 400 Numbe _Gene a ions -> 25 P obabili y o Mu a ion -> 0.2 Eli ism -> 0.2