Hybrid Metaheuristic Algorithm (Sagac) Used in Optimization of Vacuum Cooling Treatment of Postharvest Broccoli / Algoritmo Metaheurístico Híbrido (Sagac) Usado na Otimização do Tratamento de Resfriamento a Vácuo do Broccolis Pós-Colheita

Marco Antônio Campos Benvenga; Irenilza de Alencar Nääs

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<line> Centro Unv*rsitário Santo Agostinho </line>

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<line> www*.fsanet.com.*r/revista </line>

<line> ISSN Impresso: *806-6356 I*SN Ele*rônico: 2317-2983 </line>

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<line> *ybrid Metaheuristic Algorithm (*a*ac) Used in *pt*mizat**n of Vacuum Coo**ng Treatmen* of </line>

<line> Postharv*st Br*c*oli </line>

<line> Algor*tmo Metaheur**tico *íbrido (Sa*ac) U*ado na *t*mizaçã* do Tratamento de </line>

<line> Res*ri*mento a Vácuo do ***ccolis Pó*-Colheita </line>

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<line> Marco *ntônio Ca*pos Benveng* </line>

<line> Doutorado em Eng*nh*ria de Produção *ela Unive*si*ade Paul**ta </line>

<line> Mest*e e* Engenharia *e **odução p*la Universidade *o*e de Julho </line>

<line> *-mail: marcoc*mpos453@yahoo.com </line>

<line> *ren*lza de Alenca* Nää* </line>

<line> Do*tora *m PhD in Ag*ic*l*ural Engi*eer*ng Michigan St*te University </line>

<line> Professora da Un*versidade Paul*s*a - *N*P </line>

<line> E-*ail: i*eni**a.naas@docente.un*p.*r </line>

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<line> End*reço: Marco *ntonio C**p*s Benvenga </line>

<line> Editor-Chefe: *r. Tonn* K*rley de Al**c*r </line>

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<line> Av. *aulista, *00 - Bela Vis**, São Paul* - SP, 0131*- </line>

<line> Rodrigue* </line>

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<line> Ende*eço: Iren*lza de *lencar Nä** </line>

<line> Artigo re*ebido em 14/06/2*21. Ú*t*ma </line>

<line> versão </line>

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<line> Av. Paulist*, 9*0 - Bela V*sta, São **ulo - SP, *1310- </line>

<line> recebida em 27/06/*021. Ap**vado em 28/06/2021. </line>

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<line> Avalia*o pelo sistema Triple Rev*ew: Des* R*view a) </line>

<line> pel* Editor-Ch*fe; e *) D*ubl* Blind Review </line>

<line> (*valiação cega por doi* avaliado*es d* á*ea). </line>

<line> Rev*são: Gramatical, Norm*tiva e de Fo*ma**ção </line>

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<line> Hyb*id Met*heuri*t*c Alg*rithm (Sagac) Used i* Opt*mization of Vac*um Cooling Treat*e** </line>

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<line> ABSTRACT </line>

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<line> *his researc* aim* to analyze t*e applicat*on of the hybrid metaheurist*c a*go*ithm SAGAC, </line>

<line> which is composed *f the S*mul*ted Annealing (SA) and Genet*c Algorith* (GA) t*chniques </line>

<line> *ith the inclusion of a converg*nce accel**ation (AC) mechanism. SAGAC was u*e* *o </line>

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<line> pos*ha*v**t broccol* vacuu* cooling *rocess. Anot*e* concer* included in the </line>

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<line> algorith* i* p*pulation di*ersity, and, for t*i* *i*u**ion, a high mut*tion rate (40%) and a l*w </line>

<line> e*itis* rate (10%) w*re used. Th* object*ve of maintaining population diversi** is to avoid </line>

<line> prem*ture and undue convergen*e *f the res*lts curve. *h* S*GAC algorithm's performance </line>

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<line> w*s compar*d *ith another type of a*proach *n </line>

<line> *ptimizing this process, w*ich *sed the </line>

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<line> Res*on*e Surface (R*M) methodol*gy </line>

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<line> *all*d *SMGA *n thi* present st*d*. *he resu*ts obt*ined sh**e* that the SA*AC algorithm </line>

<line> obtained be*ter results concerning RSMGA in op*imizing this process. </line>

<line> Key-wo*ds: Algorithms. Optimization. SAGA*. Metah*urístics. </line>

<line> RESUMO </line>

<line> Esta *esquisa t*m o o*jetiv* d* anal*sar a aplicação do algo**tmo *etaheurís*ico híbrido </line>

<line> S*GAC, o qual é composto dos algoritmos, Si**lated Annealing (S*) e o Algoritmo </line>

<line> Genéti*o (GA) co* a inclusão de um me*anismo de aceleração de conve*gência *e re*ultados </line>

<line> (AC). O SAGAC foi u*ado par* otimizar o *rocesso de *esfr*amen*o à vác*o do brócolis após </line>

<line> a col*eita. Outra preocup*çã* incluída no a*goritmo é a diversid*de da popula*ão, e, para essa </line>

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<line> s*tuação, foram u*ilizadas uma alta t**a de mutação (4*%) e </line>

<line> uma baixa ta*a de elitismo </line>

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<line> (10%). O obje*i*o de ma*t*r a diversidade popul*cional é e*itar a convergênc*a pr*m**ura e </line>

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<line> indevida d* curva *e resulta*os. O </line>

<line> des*mpenho do </line>

<line> algoritmo SA*AC *o* com*arado com </line>

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<line> *utro tipo de abor*ag*m na o*imização de*te *roce*so, que ut*li*ou a metodologi* *e </line>

<line> Superf**ie de Resposta (*S*) combinada *om o *lg**itmo Genético (GA), *q*i, </line>

<line> denominado RSMGA no pre*ente estudo. *s resultados *btidos m*straram qu* o a*gor*tmo </line>

<line> SA*AC obteve mel*ores r*sultados em relaçã* ao RS*GA *a ot*mização des*e proce*so. </line>

<line> Pa*a*ras-chave: Al*o*it*o*. Otim*zação. SAG*C. Metaheu*ística. </line>

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<line> www4.fsa*et.com.br/revista </line>

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<line> 1 INTR*DUCTION </line>

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<line> According to Santana et al. (2*18), broccol* is a fo** ri*h in vitamin C, f*ber, and </line>

<line> ***tiple *ther nut*ients with potent *nti-c*n*er prop*r*ie*. In t*e wor*d, *hina and India are </line>

<line> the largest pr*ducers of this **getable, and toge*her they pro*uce *ore th** 7*% of all glob*l </line>

<line> product*on. According to *an*ana et al. (2018), broccoli has * sho*t shelf *ife at room </line>

<line> t*mperature. **nce, the *earch fo* effic*ent ways to preserve this type o* food's **lidity and </line>

<line> n*triti*n** *r*p*rtie* b*comes *ssential. </line>

<line> In *lib*s & K**sal (2014), Ca*valho & Clemente (2004), and Corcuf* et *l. (1*96), </line>

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<line> there are several techniq*es to improv* the shelf life of food, *u*h a* dry*ng, freezin*, </line>

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<line> mod*f**ation in most p*c*aging. In McDonalds e* al. (2002), vacuum cooli*g i* a*hieved *y </line>

<line> ra*idly remo**ng *e*t from the p*o*uct by evaporatin* wat** ***m the su*face and pores. For </line>

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<line> vacuum cooling has been repor**d </line>

<line> as a highl* </line>

<line> *f*icient *ethod to </line>

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<line> *xt*nd t*e **elf li*e *nd impr**e biologic*l safety. According to *unes et al. (2**5), t*e*e ha* </line>

<line> been an increase i* the devel*pmen* of competit**e and electr*nic approac*es to agric*ltu*al </line>

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<line> *a*ks *n recent decade*, *u*h as harvestin*, s**ing, gro*th </line>

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<line> chemic** treat**nts. Such approaches, *n </line>

<line> examp*e o* the menti*ned approaches, *se hybrid </line>

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<line> a*gorithms to *p*im*ze p*ocesses, *spec*ally to reduc* *h* *earch s*ace to find the ide*l </line>

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<line> cond*tio*s and, thus, r*duce t*e *om**tati*nal time (CHAVES et al., </line>

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<line> Mahlooji (*0*2) ap*lied **e simulate* annea**ng (SA) **chnique *n* </line>

<line> th* r*sponse surface </line>

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<line> meth*dology (RSM) to exp**r*s the *el*tio*sh*ps between s*ve*al *xplan*tor* **riables *nd </line>

<line> one or mo*e re*ponse variables. </line>

<line> This research aimed to invest*gate *he SAGAC hybrid algorithm's p*rformance </line>

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<line> compared t* the RSMGA approach by *antana e* al. (2018) to optimiz* th* </line>

<line> *osthar*e*t </line>

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<line> broc*oli vac*um cooli*g p*o*e*s. The *ain bene*it o* t*e pro*osed approach is *he increase </line>

<line> in *he pr**ucer*' *r*fit **e to the *e*uction *btained with the *mp*eme*ta*ion o* th* SAGAC </line>

<line> algorithm. </line>

<line> 2 MATERIALS AND *ETH**S </line>

<line> *.1 Vacuum coolin* t*eatments </line>

<line> **cording to Santa*a et al. (2018), t*e vacuum coolin* *reatme*t w*s *mple*ented b* </line>

<line> a s*l*-develo*ed vacuum cooler w*th a wat**-sprayi** unit *onnected w*t* the wate* pipe and </line>

<line> Re*. FSA, Teres*na, *. 18, n. 7, art. 1*, p. 160-172, *ul. 20*1 *w*4.fsanet.*om.br/revis*a </line>

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<line> Hyb*id Metaheuristic Algorithm (S*gac) Used in O*ti*iza*ion *f Vacuum C*oling *reat*ent </line>

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<line> vacuum chamber. The water-sp*a*ing volume ca* be controlled in *his sy**em. </line>

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<line> equipment was d*vel*ped in **romed steel, with a* int*rnal vo**me of 1m3, and *t was made </line>

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<line> the Departmen* o* </line>

<line> Food Scienc* and *u**ition, Sc*ool of Biosystems *ngineerin* and </line>

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<line> F*od *cie*ce, Zhejiang U*ive**ity, *ity of Hangzhou, *hejian* Prov*nce, Ch*n*. *n this </line>

<line> study, the pressure in the vacuum cham*er (200, 400, *nd 600 Pa), *he wa*er-sprayi*g </line>

<line> in*e*tigate th*ir *ynthetic effects on the weight loss(Wloss) of b**c*oli durin* t*e vac*um </line>

<line> cooling process (*libas & Koksal, *014; D*n* et a*., *0*1; Zhang & Sun, 2006).**e </line>

<line> p*ocessing **m* is *h* cooling *ime *e*uir*d to r*ach the e*perim*ntal design pressure </line>

<line> *onditions wit*in the re*rigerator. </line>

<line> 2.2 *odeling p*ocess </line>

<line> An *xperim**tal design was u*ed f*r the organ*zation of the ass*y of this exp*rimen*. </line>

<line> *fter the experiments' execution (duplicate), the minimum **uare *eth*d wa* applied to the </line>

<line> experimental *ata to *btain the model (Santana et al., 2018). Wa* con*id*red *he f*llowing </line>

<line> *actors: pressure, * (*1), bro***li weig*t, W (x2), water vo**me, * (x3), and proce*sing time, t </line>

<line> (x*); as well as the fo*lowing respons*s: loss of we*ght (y*), Wloss, and end t*mperatur*(y2), </line>

<line> T*nd. Because o* the effect *f inconsistenc*es cause* dur*ng the computations, *t was ne*es**ry </line>

<line> *o norma*iz* the variable* xi[1, *]. </line>

<line> The mathematical f**mulation of this pro*le* is summarized in the fol*owing </line>

<line> *quation*: </line>

<line> We*ght loss is cal*ul*ted by equation </line>

<line> The end tempera*ure is *alc*l*ted b* *quati*n </line>

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<line> Do*ain of varia**es: </line>

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<line> Rev. FSA, Te*e*ina PI, v. 18, n. 7, art. 10, p. 16*-*7*, j*l. 2021 www*.*sanet.*om.br/revista </line>

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<row> M. *. C. B*nvenga, I. *. Nääs </row>

<row> The ob*ecti*e function is calculated by equation </row>

<row> where =0.9 and =0.1 </row>

</column>

</column>

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<line> whe*e *nd are t*e w*ight of Wloss and T*nd, resp**tively. </line>

<line> The norma*i*ed val*es of variabl*s are calcu*ated b* equatio* </line>

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<line> In China, the typi*al p*i*e f*r broccoli i* 4.* US$/ kg, and *or kWhis 8 cents. These *alues </line>

<line> were used to calcu*at* Eq.'s *ot*l profit (5) (S*NTANA et a*., 2018). </line>

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<line> The success of any bus*nes* is related to maxim*zi*g profits. *n t*is case study, it is </line>

<line> related *o the m*nimization of Wloss. Then, if minimu* Wloss is found, *h* ma*imum profit </line>

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<line> Re*. FSA, Teresina, v. *8, n. 7, a**. 1*, *. 160-172, jul. 2021 </line>

<line> www4.fsanet.*om.br/revista </line>

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<line> Hy*rid Metaheuristic Algorithm (S*ga*) Used in O*timization of Vacuum Cooling Tr*atment </line>

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<line> 3 *HE HYBR** MET*HEURIST*C *LGORIT*M (S*GAC) </line>

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<line> *wo algorit*ms form *h* al*ori*hm: the Simulated *nnealing (SA) and *he Genetic </line>

<line> Algorithm (AG) wi*h *he i*clusio* of a *echa*ism (func*ion) that *r*motes an acceleration in </line>

<line> the con*er*e*ce (A*AC) of the obtain*d results. </line>

<line> The *A a*g*ri*hm a*ts o* *he *eneratio* of i*dividuals who make *p the modified </line>

<line> genetic a**orithm's i*itial populat*on (A***). With the *se *f the SA algorithm, i* is poss*ble </line>

<line> to have *he c*mpo*it*on of a g*od qu*lity initial popu*ation, that is, pre-opt*mized i*divid*als. </line>

<line> The routine behav*or of the AGAC algorithm prom*tes Conve*gence Accelerati*n in </line>

<line> which, aft*r cr*ssi*g, th*re is an ass**sment of the in*ividuals (Sons) generate* and a check </line>

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<line> **r qu*lity imp*ovement co*ce*ning th* indivi*uals of </line>

<line> the elite gro*p of the populat*on. If </line>

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<line> d**s not occur, the in*ivi**al (s) of the child(ren) is(are) discarded, </line>

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<line> individual (paren*) of the worst *uality is e*changed for a*o*her indiv*dual ** the el*t* group </line>

<line> *ho is closest and is bett*r *h** **e ind*vidual (Father) who w*s chang*d. </line>

<line> A*ter the individual'* chan*e (*ather), a new crossing occu*s f*r the mis*in* *hil*'s </line>

<line> generation (s). This sequ*nce o* s*eps will be repeated u*til bo*h chi*dren meet th* c*it**ia fo* </line>

<line> imp*ovement or the stipulated number of at*empt* is reached. Fi*ure 1 s*ows the flowch**t o* </line>

<line> the SAGAC hybr*d algorithm. </line>

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<line> Rev. *SA, Teresina PI, v. 18, n. 7, art. 10, p. *60-17*, *ul. 2021 </line>

<line> www4.fsanet.com.br/rev*s*a </line>

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<line> M. A. *. Benve*ga, I. A. Nääs </line>

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<line> Figure 1 - Sc*eme of the *ybrid SAGAC algori**m. </line>

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<row> Start </row>

<row> Inf*rm Initial </row>

<row> Population </row>

<row> Generate </row>

<row> Indi*idual </row>

</column>

<row> Assess Population </row>

<row> Individual </row>

</column>

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<line> Stoping </line>

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<line> Apply SA to </line>

<line> Cr*teria </line>

<line> *inish </line>

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<line> improv* I*d***dua* </line>

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<line> Select best </line>

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<line> Individual in Initial </line>

<line> Individu*ls </line>

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<line> *opulation </line>

<line> Crossov*r </line>

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<line> Initial </line>

<line> Population OK? </line>

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<row> Mutati** </row>

</column>

<row> **n*ergen*e </row>

<row> *cce*eration </row>

</column>

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<line> With ea*h cycle *f proce*si*g of the Simula*ed Annealing (SA) algorit*m, the b*st </line>

<line> *esult (individua*) is store* t* compo*e the initial po*ulation used by the modified Genetic </line>

<line> *lgor*thm w*th con*erg*nce acceler*tion mec*an*sm (AGAC). </line>

<line> Figure 2 show* the original scheme of a G*net** Algorithm, a*d, in *eque*ce, *i*u*e 3 </line>

<line> s*o*s the Genetic *lgorithm wit* *he inc*usi** of the conve*gence acc*leration mecha*ism. </line>

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<line> www4.fsa*et.com.*r/revist* </line>

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<row> Hybr*d *etaheuristic Algorithm (Sag*c) U*** in Optimization of V*cuum Cooling Treatm*n* </row>

<row> Figure 2-*cheme o* a clas*i* *en*ric Algo*ithm (ad*pted from Lin*en, 20**). </row>

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<line> *rossov*r </line>

<line> Mutation </line>

<line> Start </line>

<line> St*p Criter*a; </line>

<line> Parametrizat*on; </line>

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<row> Gen*t** Operators </row>

<row> Selec*ion: </row>

<row> - Roulette whe*el </row>

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<line> Po*ulation M*dule </line>

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</column>

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<row> Stop Criteria O.K.? </row>

<row> Finis* </row>

</column>

<row> Assess Population </row>

</column>

</column>

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<line> Fi*ure 3-Sc*eme *f a Genetic Alg*rith* w*th conve*gence acceleration m*c*anism. </line>

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<line> F*gure* 2 a*d 3 show the chang* in the Genetic Algo*ithm u*ing the c*nv*rgence </line>

<line> acceleration m*chanism. *his m*c*anism in*rease* the *robability of a contin*o*s </line>

<line> i*dividual*' evol*tion o*er the generations. In eac* ge*eration of o*f*prin*, the alg*ri*hm </line>

<line> c*ecks whether they h*ve the minimum qua*ifications to *e part of the elit* and, if this doe* </line>

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<line> R*v. FSA, Teresina P*, v. 18, n. 7, art. 10, *. 160-*72, jul. 2021 </line>

<line> *ww4.f**net.com.br/revista </line>

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<line> no* *ccur, *here is a dispo*al of these off*prings and the generation of othe*s, after changin* </line>

<line> one of the parents with the worst evaluation. </line>

<line> 3.*.*etu* *arameters of SAGAC </line>

<line> In S*GA*, *he va*iables that influence the algorithm's behavior are its processing </line>

<line> p*ra*e*ers (*OUZA et al. 2017, *A*TANA et al. *011, *ITCHEL 1997, KIRKPATRICK </line>

<line> Parameters of SA </line>

<line> 1º. Initial Te*perat*r* = 1*0; </line>

<line> It is the n*mb*r of cycles that wil* be processe* *n an algo*i*hm repetit*on lo**; </line>

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<row> The Temperat*r* Decay Scheme - defines how *he t*mperature decreased and i* </row>

<row> numb*r of ite*ations *erformed for each temperature. </row>

<row> - the Temperature Decay Function is rep*esented in equatio* (6): </row>

<row> - Numb*r o* Itera*i**s a* eac* Temperature = 1 </row>

<row> Parameters of AGAC </row>

<row> *º. Pop*lation siz* = 100; </row>

<row> *º. G*n*rations Qty. = 1000; </row>

<row> 3º. Elitism = 1*%; </row>

<row> a**, fo* the case of th* Conv**gence A*celerat*on *eneti* Algorithm (AGAC) </row>

<row> 5º. Qty o* a**empts to generat* chi*dren in the *lite = 1. </row>

<row> 4. RESULTS AND DISCU*SI*N </row>

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</column>

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<line> Figure 4 shows the </line>

<line> evo*ution cur*es of the va*ues of the factors Wloss, Tend, an* </line>

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<line> v*lue of *he O*jective Func**on (OF) of t*e be*t individuals *n each generati*n during the </line>

<line> 1*00 gene*ations p**cessed by *he SAGAC algorithm. </line>

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<line> Hybrid Meta*eu*ist*c A*gori*hm (S*gac) *sed in Opt*miz*tion of Vacuum *ool*ng Treatment </line>

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<line> F*gure 4-Behavior *f Wloss, Te*d, and Objecti*e *unction (OF) fac*ors in </line>

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<line> optimizingb*occol*'s vacuum coolin* process. </line>

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<line> Ge**rations x 1*0 </line>

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<line> It *s noted in F*gur* 4 th*t the Tend and OF fact*r* pre*ent ** osci*la*ing *ehavior an* </line>

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<line> dif*erent **om the *loss factor, *hich p*esen*s * *egative converg***e, whi*h means </line>

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<line> d**rease in th* weight loss of the p*oduct. *he *n*rease i* p**fit is inv*rsely rel*ted to the </line>

<line> d*crease in the Wloss factor. </line>

<line> Ne*t, in Fi*ure 5, the "P**fit" co*ve*gence curve is show*. </line>

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<line> *ww4.fsanet.com.br/r**ista </line>

</par>

</page>

<page>

<par>

<line> M. A. C. Benvenga, I. *. Nääs </line>

</par>

<par>

<row> *igure *-Converge*ce curve of the "P*ofit" value obta**ed by minimizi*g the *a**or </row>

<row> **cuu* coo***g of postharvest *rocoli </row>

</column>

<par>

</par>

<par>

</par>

</column>

<par>

</column>

</column>

</par>

<par>

</par>

<par>

<line> G*nerations x 1** </line>

</par>

<par>

<line> Figure 5 indicates tha* after 600 generations pr*ces**d by SAG*C, there is a </line>

<line> stabiliz*tion of the curve conver*ence, with small *ain*. </line>

<line> Table 1 *ompares the res*l** obtained by *he RSMGA and SAGAC alg*rithms in </line>

<line> optimizing vacuum cooling treatment o* p*stharvest broc*oli. </line>

<line> Table 1-Co**a*is*n of t** RSMGA and SAGAC algor*th*s' results to optimizethe </line>

<line> v*cuum *ooling of br*ccoli. </line>

</par>

<par>

<line> Wloss </line>

</par>

<par>

</par>

<par>

<line> RSMGA </line>

</par>

<par>

<line> SAGAC </line>

</par>

<par>

<line> W**h the data presented in Table 1, w* can *ee tha* the S*GAC al**r*thm obtained the </line>

<line> best results concern*n* the Wloss *nd Pro*i* values. A*t*r all, this *s the object*ve of this </line>

</par>

<par>

</par>

</page>

<page>

<par>

<line> Hy*rid Metaheuristic Al*orith* (*agac) Used in Optimization of *acuum Cooling Treatment </line>

</par>

<par>

<line> optim*zation **o*e*s, that is, to mi*imize pr*duct w*i*ht *o*s and con**quently maximi*e </line>

<line> 5 CO*CLUSIONS AND FUTURE WORK </line>

<line> A hy*rid *etahe*r*st*c algorithm was p*o*osed to obt*in better res**ts in op*imizing </line>

<line> *** vacuum cooli*g **oce** of b*occoli after har*es*, coming from *he union of the *imulated </line>

<line> Annealing (SA) alg**ithms a*d *he G*ne*ic Algorithm with a converge*ce acceleration </line>

<line> mechanism. (AGAC) *h*ch was nam*d SAGAC. In t*e proposed app*oach, SA has t** </line>

</par>

<par>

<line> function </line>

<line> of pro*iding the initia* po*ulat*on of the AGAC with individual* o* better quality </line>

</par>

<par>

<line> than individuals gene*ated a* random. This st*a**gy works as a </line>

<line> pr*-op*imiza**o* </line>

</par>

<par>

<line> pro*ess. Upon *eceiving </line>

<line> init**l pr*-o*timized popu*ati*n, A*AC raises </line>

<line> the quali** of </line>

</par>

<par>

<line> these individu*ls to a higher lev*l. </line>

<line> The results *btaine* sh*w a better pe*form*nce of the SAGAC, m*in*y when we refer </line>

<line> to minimizing *he prod*ct's weight loss (broccoli) and the maximizatio* of *he *rofit. </line>

<line> The SAGAC algorithm showed its poten*ial in opti*izing t** vacuum cooling process </line>

</par>

<par>

<line> *ro*coli after </line>

<line> har*e*ting. * st*dy of its p*ocessi*g parameters *e*ains a sug**stio* for </line>

</par>

<par>

<line> future *ork as a for* o* inves*iga*ion to improve pe*formance. A*ditionally, *he S*GAC </line>

<line> algorithm could be implemented to op*imi*e other actual processes in future works. </line>

<line> REF*RENCES </line>

<line> Ab*a*ia B., Mahl*o*ib H., Impr*ving respons* surface me**odology *y *sing *rtificial ne*ral </line>

<line> network a*d simula*ed annealing, Expert System* with Application*, Vol*me *9, Issue 3, 15 </line>

<line> February *012, Pag*s 3*61-*46*, Elsevier, 2012. </line>

<line> Alibas, I., Koksa*, N., *or*ed-air, va*uum, and hydro precooli*g of *aul*f*ower </line>

<line> (Brassic*ol*aracea L. *ar. botr**is cv. Fre*m*nt): part I. De t*rmination of precool**g </line>

<line> parameter*. Food Sci. Tech n*l. 34 (4), 7*0-73*, 2014. </line>

</par>

<par>

<line> Carvalho, P.T., Clemente, *., T*e infl*enc* of the </line>

<line> broccol* (Bra*sicaolerace* var.it**ica)*i** </line>

</par>

<par>

<line> *eigt* on p*s*harv*st quality. Food Sc*. Tech n*l. 24 (4), 646-651, 2014. </line>

</par>

<par>

<line> Corcuff, R., Arul, J., Hamza, F., Cast*igne, *., Ma*hlouf, J., Storage </line>

<line> *f brocc*li flor*ts i* </line>

</par>

<par>

<line> et*anol vapor enriched *tmosp*eres. Postharvest Biol. Tech nol. 7, 219-229, *996. </line>

<line> Funes, E., Allouche, Y., Beltrán, G., *imén**, A., A review: artificial neural ne*works as tool </line>

<line> for control food industry process. J. Se*s. Technol. 5 (1), 28-*3.2015. </line>

</par>

<par>

<line> www4.fsanet.com.br/revista </line>

</par>

</page>

<page>

<par>

<line> M. A. C. Benvenga, I. A. Nääs </line>

</par>

<par>

<line> Li*den, R,Algorit**s Gen*ticos - Uma impo*tante ferramenta de inteligênci* </line>

<line> compu**cional,2a.e*., Bras*ort, 20**. </line>

<line> Sant*na, J. C. C., Araujo, S. A., Alv*s, W. A. L., Belan, P. A., *iangang, L., Jianchu, C., </line>

<line> Dong-Hong, L., ***imization o* *acuum cooling treatment o* p*sthar*est broc*ol* using </line>

<line> response surface *ethodology combined with geneti* algorith* tech**que, Computers a*d </line>

<line> Electronics in Agriculture, El*evier, 2018. </line>

<line> *cDonald, K., Sun, D.W., Lyn*, J.G., Effect of vac*um **ol ing on the th*rmo physical </line>

<line> propert*es of a *ooke* beef p*oduct. J. Food Eng. 52, 167-17*, 2*02. </line>

<line> Zhang, Z.H., Sun, DW, Effe*t of cooling methods on the coo*in* efficienci*s and qu*lities of </line>

<line> cooked bro*co** and carro* sl*ces. J. Food E*g. 77, 32*-326, 2006. </line>

</par>

<par>

<line> Como Referenciar *s*e A*tigo, c*nf*rme ABNT: </line>

<line> BEN*ENGA, M. A. C; NÄÄS, I. A. Hy**id M*t*heuristic *lgo*ithm (Sagac) U*ed in Optimization </line>

<line> of *acu*m Cooling Tre*tment *f *ostharvest Broccoli. *ev. F*A, Teresina, v.18, n. 7, art. 10, p. 160- </line>

</par>

<par>

<line> *ontribu*ção dos Auto*es </line>

<line> M. A. C. Benveng* </line>

</par>

<par>

<line> *) concepção * pl*n*jame*to. </line>

</par>

<par>

<line> 2) análise e interpretaç*o d*s da*os. </line>

</par>

<par>

<line> *) e*aboraç*o do rascunh* ou na revi*ão críti*a *o conteúdo. </line>

</par>

<par>

<line> 4) participaçã* na aprovação da ver*ão final do *anu**rito. </line>

</par>

<par>

<line> Rev. FSA, Teresina, v. *8, n. 7, art. 1*, *. 160-172, ju*. 2*21 </line>

<line> *ww4.fsa*e*.com.*r/revista </line>

</par>

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