Reducing the Dimensionality of Criteria in Multi-Objective Optimisation of Biomass Energy Supply Chains

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1 A publication o CHEMICAL ENGINEERING TRANSACTIONS VOL. 29, 212 Guest Eitos: Peta Sabev Vabanov, Hon Loong Lam, Jiří Jaomí Klemeš Copyight 212, AIDIC Sevizi S..l., ISBN ; ISSN The Italian Association o Chemical Engineeing Online at: DOI: 1.333/CET Reucing the Dimensionality o Citeia in Multi-Objective Optimisation o Biomass Enegy Supply Chains Liija Čuček* a, Jiří J. Klemeš b, Peta S. Vabanov b, Zavko Kavanja a a Faculty o Chemisty an Chemical Engineeing, Univesity o Maibo, Smetanova ulica 17, 2 Maibo, Slovenia liija.cucek@uni-mb.si b Cente o Pocess Integation an Intensiication CPI 2, Reseach Institute o Chemical an Pocess Engineeing - MÜKKI, Faculty o Inomation Technology, Univesity o Pannonia, Egyetem utca 1, 82 Veszpém, Hungay This contibution pesents a novel appoach, by which the numbe o iect envionmental ootpints is euce to a minimum numbe o inepenent ones (INDFs) though coelations among the ootpints that show simila behaviou. The coelations ae investigate between iect cabon, enegy, wate, wate pollution, an lan ootpints. Those ootpints that show simila behaviou ae goupe in subsets o coelate ootpints. In each subset only one ootpint, an INDF is taken into the multiobjective optimisation, whilst the est o the epenent ootpints (DFs) ae evaluate ate the optimisation om the INDFs. In this way, the imensionality o the citeia within the multi-objective optimisation is signiicantly euce, so that a multi-paametic optimisation is peome with INDFs as paametes. The subjective weighting o envionmental an social inicatos o ootpints is thus avoie. This novel appoach is illustate using a emonstation case stuy o ieent biomass enegy supply chains. 1. Intouction The wol is cuently acing envionmental, inancial an social challenges, pimaily ue to human population gowth, globalisation, the unsustainable use o esouces, an the unsustainable gowth o wol economy ove the last ecaes (Lio, 212). Sustainable evelopment equies an integation o economic, envionmental an social components at all levels, an thus leaing to a multi-objective optimisation poblem, as illustate by De Beneetto an Klemes (29). Usually ε-constaint metho is applie (Pieagostini et al., 212) an ieent sets o Paeto optimal solutions ae obtaine. In many stuies just one objective (e.g., cabon ootpint) is consiee an evaluate besies an economic citeion, which most likely leas to simpliie conclusions. Howeve, moe ealistic solutions ae obtaine i moe impacts ae consiee (e.g., cabon, nitogen, wate ootpints). Impotant limitation in this case is that computational buen gows apily in size with the numbe o objectives (Guillén-Gosálbez, 211). Othe limitations ae that multi-objective optimisation can be time consuming, an thee is iiculty in visualisation an intepetation o the objective space (Pozo et al., 212). It also pevents the caying-out o an exact optimization, esulting in only two- o at most theeimensional Paeto pojections, thus poviing only a naow view with uneestimate envionmental metic estimates (Kavanja, 212). Usually, the numbe o objectives is euce into aggegate single sustainability inicato (e.g., Kavanja an Čuček, 212). Howeve, this appoach has the awbacks o subjective weighting an iiculty o selecting the best solution. Reuction o the imensionality is thus equie, an shoul be base on a systematic mathematical appoach. Reuction o the imensionality is an aea o statistical Please cite this aticle as: Čuček L., Klemeš J. J., Vabanov P. S. an Kavanja Z., (212), Reucing the imensionality o citeia in multi-objective optimisation o biomass enegy supply chains, Chemical Engineeing Tansactions, 29,

2 multivaiate analysis. The methos inclue pincipal component analysis, acto analysis, multiimensional scaling, clusteing systems, etc. Seveal papes ae ealing with the euction o the imensionality o multi-objective optimisation poblems. Deb an Saxena (25) popose an evolutionay multi-objective optimizationpcoceue, while Pozo et al. (212) evelope a metho base on pincipal component analysis. Bockho an Zitzle (29) calculate an appoximation eo to quantiy to which extent the ominance stuctue o the poblem changes when omitting objectives. Guillén-Gosálbez (211) evelope a MILP-base metho, whee the eo o omitting objectives is minimise, an emonstate that some o objectives behave in a non-conlicting manne, an thus imension o the poblem can be euce. Vaskan et al. (212) applie the MILP metho o the optimal esign o heat exchange netwoks consieing envionmental impacts. Gutiéez et al. (21) use pincipal component analysis an multiimensional scaling methoology in oe to euce imension o the poblem. This pape pesents the novel appoach, by which the ootpints that show simila behaviou ae goupe in subsets o coelate ootpints. Dieent citeia ae popose o etemining the coelations among ootpints an selecting the INDFs: i) atio between pai o ootpints, ii) ovelap o ootpints in pocess vaiables, an iii) aveage absolute nomalise eviation. INDFs ae then taken into multi-objective multi-paametic optimisation. The DFs ae thus evaluate om the INDFs using linea o nonlinea coelations. Methoology o the evelopment o linea an nonlinea coelations among ieent ootpints within a multi-objective optimisation appoach pesente in Čuček et al. (212a) is applie. 2. Desciption o the popose appoach The imensionality euction in multi-objective optimisation consists o thee steps. Fist, the coelations among ootpints ae ientiie, an INDFs ae selecte. Then, multi-paametic optimisation is peome o the INDFs using the ε-constaint metho. Finally, non-linea quaaticbase coelations ae peome o DFs, which ae evaluate ate the optimisation om the INDFs. 2.1 Ientiication o coelations among ootpints Ientiication o coelations among ootpints is peome iectly om the matix o the pocess vaiables an ootpints. The iect envionmental ootpints (buening o the envionment) ae thus obtaine using the ollowing equation: av, xv (1) whee a v, ae the matix coeicients, an x v ae the coesponing pocess vaiables at thei optimal values, whee poit is maximise. Thee measuements wee popose: i) Ratio between pais o ootpints ( an ): a a x v, v, v ( ) a, v, v, R F F a Fo peect coelation the atio between ootpints is 1. Because R, can ie om R,, geometic mean is calculate using the ollowing equation: GR R R F F (3),,, ii) Ovelap o pai o ootpints ( an ) in pocess vaiables: a x O F F a a (4) v, v, v, v, (2) 1232

3 This measuement epesents a similaity between pais o ootpints. I ootpint is eine by the same pocess vaiables as ootpint, then the ovelap coeicient is 1. Because O, om O,, geometic mean is calculate:,,, can be ieent GO O O F F (5) iii) Aveage absolute nomalise eviation between pai o ootpints ( an ): av, 1 a a v, v, v ( ), v, D F F a (6) ( 1) 1 x Small values inicate goo ageement between pai o ootpints. Again, geometic mean is calculate because D, can be ieent om D,, : GD D D F F (7),,, Fom above citeia two o thee INDFs ae selecte. 2.2 Multi-objective optimisation In the secon step a multi-objective optimisation is peome o selecte N i INDFs, i FI. ε- constaint metho is applie to this multi-paametic optimisation whee sequences, one o each ootpint, o constaine single-objective mixe-intege non-linea pogamming (MINLP) i 1,..., poblems ae thus solve o INDFs as the maximisation o the poit subjecte to elative INDFs. Relative INDFs ae being eine as the INDFs ivie by thei eeence values. A multi-imensional gaph o Paeto optimal solutions is thus obtaine. 2.3 Coelations among epenent an inepenent ootpints in goup A ew INDFs can be selecte applying citeia i)-iii). In this way, two o thee goups with simila behaviou ae ientiie. DFs ae evaluate om INDFs in each goup using linea o nonlinea coelations (Čuček et al., 212a). Fo bette cuve itting quaatic-base non-linea coelations is use. 3. Demonstation case stuy The concept escibe above is applie within a case stuy o egional biomass an bioenegy supply chains (Čuček et al., 21) extene o simultaneous assessment o ootpints (Čuček et al., 212b). It ollows a ou laye stuctue, which consists o havesting, collection an pe-pocessing, coe pocessing, an usage o poucts incluing the tanspotation lows within an between the layes. Dieent biomass souces ae consiee, con gains an stove, woo chips, municipal soli waste, manue an timbe. Dy-gin pocess, anaeobic igestion, incineation an sawing convet biomass into valuable poucts, heat, electicity, bioethanol, an istilles ie gains with solubles, igestate, an boas. Besies pocesse poucts, also oo can be pouce. Supply chains incopoate ieent envionmental pessues, an consie ieent iect ootpints, cabon, enegy, wate, wate pollution an lan ootpints. 3.1 Results an iscussion Applying citeia i) iii), similaity among ootpints was estimate. With geate accuacy thee INDFs shoul be selecte, cabon, wate, an lan ootpints. When less exact, only two INDFs can be selecte. In this way, two goups with simila behaviou ae ientiie. Thee-imensional poblem is obtaine with selecte two INDFs, whee the poit is the main citeion, an cabon an wate ootpints ae ientiie as INDFs. Figue 1 shows the esults, obtaine by multi-paametic optimisation. in i 1233

4 Enegy ootpint (GJ/(km 2 y)) Poit (M /y) Poit (M /y) Wate ootpint (kt/(km 2 y)) Cabon ootpint (t/(km 2 y)) Figue 1: Poit vesus INDFs DFs ae evaluate om INDFs using nonlinea quaatic-base coelations (Čuček et al., 212a). Cabon ootpint (CF) is goupe with enegy ootpint (EF). Wate ootpint (WF) is goupe with wate pollution (WPF) an lan ootpints (LF). Nonlinea coelations base on quaatic unction o cabon ootpint ae taken om Table 2 in Čuček et al. (212a). The coelations among the ist goup cabon an enegy ootpints ae pesente on Figue 2 an the coesponing poit epenent ootpint 2D pojection on Figue Cabon ootpint (t/(km 2 y)) Relative enegy ootpint Figue 2: EF vesus CF Figue 3: Poit vesus elative EF at changing WF In the secon goup wate ootpint is selecte as INDF. DFs in the secon goup ae expesse though wate ootpint. Linea an non-linea coelations among ootpints, whee wate ootpint is selecte as INDF ae pesente in Table 1. The coelation among the secon goup wate an wate pollution, an wate an lan ootpints ae pesente on Figues 4 an 5, espectively. These coesponing poit epenent ootpint pojections ae given on Figues 6 an

5 Poit (M /y) Poit (M /y) Wate pollution ootpint (t/(km 2 y)) Lan ootpint (km 2 /(km 2 y)) Table 1: Obtaine linea an non-linea coelations among ootpints, whee wate ootpint is selecte as INDF Footpint Linea coelation Non-linea coelation base on quaatic unction ENF ( ) j,enf j,enf CF ( ) j,cf j,cf WPF ( ) j,wpf j,wpf LF ( ) j,lf j,lf Wate ootpint (t/(km 2 y)) Wate ootpint (t/(km 2 y)) Figue 4: WPF vesus WF Figue 5: LF vesus WF Relative wate pollution ootpint Relative lan ootpint Figue 6: Poit vesus elative WPF at changing CF Figue 7: Poit vesus elative LF at changing CF 4. Conclusions an utue wok In the pesente contibution, a methoology (pinciple an poceue) o ientiication o coelations among ieent objectives (ootpints) has been intouce. Following this poceue, the imensionality o the citeia set can be euce signiicantly to a minimum o INDFs. The methoology was successully applie to a emonstation case stuy o biomass enegy supply chains whee the imensionality o ootpints has been euce om ive to two. Fo utue wok, the coelations om othe ootpints shoul also be investigate, such as nitogen an phosphous ootpints, an the issue o bioivesity, measue by bioivesity ootpints. In oe to achieve moe ealistic solutions, also iniect (unbuening) eects shoul be inclue, theeoe obtaining total eects (buening an unbuening) (Čuček et al., 212b). 1235

6 The application to heat an powe geneation an istibution shoul also be pusue, as one o the poblem aeas o geat impact on the envionment an the economy. Acknowlegement The authos ae gateul o the inancial suppot om the EC FP7 poject Design Technologies o Multi-scale Innovation an Integation in Post-Combustion CO2 Captue: Fom Molecules to Unit Opeations an Integate Plants" CAPSOL, Gant No , the Slovenian Reseach Agency (Pogam No. P2-32 an PhD eseach ellowship contact No ) an om the Hungaian poject Tásaalmi Megújulás Opeatív Pogam (TÁMOP) Tuományos képzés műhelyeinek támogatása TÁMOP-4.2.2/B-1/ Reeences Bockho D., Zitzle E., 29, Objective Reuction in Evolutionay Multiobjective Optimization: Theoy an Applications. Evolutionay Computation, 17, Copao-Ménez P.J., Guillén-Gosálbez G., Jiménez L., 212, Rigoous computational methos o imensionality euction in multi-objective optimization, Compute Aie Chemical Engineeing, Elsevie, 3, Čuček L., Lam H.L., Klemeš J.J., Vabanov P.S., Kavanja Z., 21, Synthesis o egional netwoks o the supply o enegy an biopoucts, Clean Technologies an Envionmental Policy, 12, Čuček L., Klemeš J.J., Vabanov P.S., Kavanja Z., 212a, Coelations among Footpints within Biomass Enegy Supply-Chains, Compute Aie Chemical Engineeing, Elsevie, 31, Čuček L., Vabanov P.S., Klemeš J.J., Kavanja Z., 212b, Total ootpints-base multi-citeia optimisation o egional biomass enegy supply chains, Enegy, 44, De Beneetto L., Klemes J., 29. The Envionmental Peomance Stategy Map:LCA Base Stategic Decision Making. Chemical Engineeing Tansactions, 18, 1= Deb K., Saxena D.K., 25, On ining Paeto-optimal solutions though imensionality euction o cetain lage-imensional multi-objective optimization poblems, KanGAL Repot No. 2511, Kanpu Genetic Algoithms Laboatoy (KanGAL), Inian Institute o Technology Kanpu, Inia. Guillén-Gosálbez G., 211, A novel MILP-base objective euction metho o multi-objective optimization: Application to envionmental poblems, Computes & Chemical Engineeing, 35, Gutiéez E., Lozano S., Moeia M.T., Feijoo G., 21, Assessing elationships among lie-cycle envionmental impacts with imension euction techniques. Jounal o Envionmental Management, 91, Kavanja Z., 212, Pocess systems engineeing as an integal pat o global systems engineeing by vitue o its enegy envionmental nexus, Cuent Opinion in Chemical Engineeing, 1, Kavanja Z., Čuček L., 212, Multi-objective optimisation o geneating sustainable solutions consieing total eects on the envionment. Applie Enegy, oi: 1.116/j.apenegy Lio N., 212, Sustainable enegy evelopment (May 211) with some game-changes, Enegy, 4, Pieagostini C., Mussati M.C., Aguie P., 212, On pocess optimization consieing LCA methoology, Jounal o Envionmental Management, 96, Pozo C., Ruíz-Femenia R., Caballeo J., Guillén-Gosálbez G., Jiménez L., 212, On the use o Pincipal Component Analysis o eucing the numbe o envionmental objectives in multiobjective optimization: Application to the esign o chemical supply chains, Chemical Engineeing Science, 69, Vaskan P., Guillén-Gosálbez G., Jiménez L., 212, Multi-objective esign o heat-exchange netwoks consieing seveal lie cycle impacts using a igoous MILP-base imensionality euction technique, Applie Enegy, 98,