P ocedia Enginee ing 186 ( 2017 ) 491 – 498
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Pee - e iew unde esponsibili y o he o ganizing commi ee o he XVIII In e na ional Con e ence on Wa e Dis ibu ion Sys ems
doi: 10.1016/j.p oeng.2017.03.261
ScienceDi ec
XVIII In e na ional Con e ence on Wa e Dis ibu ion Sys ems Analysis, WDSA2016
Hyb id op imiza ion me hod o s a egic con ol o wa e
wi hd awal om wa e ese oi wi h using suppo ec o machines
Pa el Mensika
*
and Daniel Ma ona
aB no Uni e si y o Technology, Facul y o Ci il Enginee ing, Ins i u e o Landscape and Wa e Managemen , Ve e i 95 ,B no 602 00, Czech
Republic
Abs ac
The aim o s a egic con ol is he e o o achie e op imal wa e esou ce managemen (wa e ese oi ). Classic s a egic
con ol o wa e wi hd awal om wa e ese oi a e based mainly on he ules and ules cu es, which a e c ea ed by
gene aliza ion o his o ical da a o wa e in lows o he ese oi s and wa e demand. Discha ge se ies a e changing in he ime
due o expec ed clima e change. I is necessa y o looking o in elligen wa e wi hd awal con ol, which will allow o eac on
hese hyd ological changes and con ibu e o he e icien use o accumula ed wa e o ensu e wa e demand. The pape will
desc ibe he algo i hm based on adap i e con ol. The no mal adap i e con ol equi ed knowledge o he wa e low medium-
e m p edic ion in o he ese oi . The c ea ed algo i hm o in elligen wa e wi hd awal con ol does no equi e knowledge o
hyd ological p edic ions. This con ol me hod is based on a sui able combina ion op imiza ion me hod wi h he Suppo ec o
machines me hod. The con ol algo i hm is one o he possible measu es o mi iga e he nega i e impac s o d ough s and wa e
sca ci y. The algo i hm o adap i e con ol is applied o he con ol o wa e wi hd awal om selec ed single- ese oi . The
esul s a e compa ed wi h usual ules o wa e wi hd awal con ol.
© 2016 The Au ho s. Published by Else ie L d.
Pee - e iew unde esponsibili y o he o ganizing commi ee o he XVIII In e na ional Con e ence on Wa e Dis ibu ion
Sys ems.
Keywo ds: Adap i e; E olu ion Algo i hms; Ope a i e Con ol; Rese oi ; S a egic Con ol; Op imiza ion; Suppo Vec o Machines; Wa e
Demand; Wa e Resou ce; Wa e Wi hd awal
* Pa el Mensik. Tel.: +420-541-147-773; ax: +420-541-147-771.
E-mail add ess: mensik.p@ ce. u b .cz
© 2016 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
Pee - e iew unde esponsibili y o he o ganizing commi ee o he XVIII In e na ional Con e ence on Wa e Dis ibu ion Sys ems
492 Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
1. In oduc ion
O e he las ew yea s we ha e been able o obse e mo e equen occu ence o hyd ological ex emes. Floods
ha e become mo e equen and d ough s ha e become mo e se e e. Expe s udies in he ield o clima e science
ha e been poin ing ou he occu ence o hese ex eme e en s o a long ime now. As an example, he yea s 2011
and 2012 a e wo h men ioning, which in e ms o hyd ology we e e alua ed as ex emely d y [1], as was also he
las yea 2015 [2]. I may be an icipa ed in he nea u u e ha such e en s will occu mo e o en, and hei nega i e
e ec will show a p og essi e end.
In eali y i is possible in he case o a sequence o occu ences o se e al d ough s o longe du a ion ha he
s o age unc ion o some wa e sou ces may become jeopa dized. Supposing ha his h ea will become eali y and
he wa e s o age in wa e ese oi s will no be su icien o ope a ing hem, a possible solu ion will lie in a change
o he ope a ing hyd aulic s uc u es. Such changes will be mainly based on al e a ions o he me hod o
manipula ion wi h con olled ou low. In an ex eme case, i all o he op ions o adap a ion measu es o ensu e wa e
managemen se ices a e exhaus ed and when clima e changes can no longe be sol ed by o he means o hei
un easibili y o disp opo iona e cos s, i will be possible o ex end he exis ing ese oi s by new ones.
The exis ing s a e o he ac i e s o age capaci y con ol is su icien bu conside ing he clima ic de elopmen s, i
may soon become insu icien . Classical con ol o he s o age capaci y o wa e ese oi s is p edominan ly based
on con ol ules [3] o ules cu es [4]. The es ablishmen o he abo e men ioned guidelines was in luenced by he
pe o mance o he compu e echnology o ha ime, esul ing in hei conside able simpli ica ion. The guidelines
a e based on his o ical discha ge se ies. The use o his o ical discha ge se ies does no allow o he guidelines o
espond adap i ely o ac ual hyd ological condi ions. Fo his eason, he exis ing con ol guidelines may collide
wi h limi a ions due o he changing hyd ological condi ions which canno be included in he his o ical discha ge
se ies. Mode n compu e echnology pe o mance allows o he con ol me hods used o be enhanced by he so
called in elligen con ol me hods. In elligen con ol allows app op ia e manipula ion on hyd aulic s uc u es.
App op ia e manipula ion allows o p e en sys em ailu es such as lack o wa e supply, and also allows e ec i e
wa e managemen o hyd opowe pu poses.
The commonly used con ol me hods can be enhanced by in elligen con ol me hods. The in elligen con ol
me hod is based on he p inciple o adap i i y. An adap i e app oach can espond o he con inuously changing
hyd ological condi ions. Such con ol usually equi es he knowledge o p edic ion o he wa e low in o he
ese oi s. In p ac ice, i is possible o pa ly elimina e p edic ion inaccu acies using he adap i i y p inciple.
Al hough he esul s o such con ol show a high po en ial [5], [6], [7] he success ulness o ese oi con ol is
signi ican ly dependen on he p edic ion accu acy. One o he possibili ies o how o achie e g ea e success in
ese oi con ol is o imp o e he p edic ion model. Ano he possibili y is c ea ing such in elligen con ol ha
would be able o espond dynamically o he changing hyd ological condi ions, and he con ol p ocess i sel would
no be dependen on wa e low p edic ions. Such algo i hm o in elligen ese oi con ol no equi ing he
knowledge o wa e low p edic ions is p esen ed in his pape . This con ol me hod is based on an app op ia e
combina ion o he op imiza ion model and he Suppo Vec o Machines me hod [8]. Suppo Vec o Machines
(SVM) is a ela i ely new me hod belonging among he me hods o machine lea ning. The p oposed con ol
algo i hm may be used as a suppo ool o he wa e managemen con ol depa men , p o iding i wi h sui able
suppo in he decision making p ocess when con olling mo e complex sys ems wi h a numbe o ese oi s and
conside ing a numbe o wa e managemen pu poses. The p esen ed con ol algo i hm p o ides one o he possible
measu es o mi iga ing he nega i e impac s o d ough s and wa e sca ci y.
2. Me hods
The hyb id op imiza ion me hod o con olling he s o age unc ion o wa e ese oi s is based on he p oposed
algo i hm combining he op imiza ion model and he SVM me hod. De ailed desc ip ions o he op imiza ion model
and he SVM me hod a e p o ided in he ollowing ex .
493
Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
2.1. Op imiza ion model
Pu simply, he op imiza ion model may be iewed as an op imiza ion me hod wi h he aim o ind an op imum
solu ion. An op imum solu ion co esponds o he ound op imum alues which a e unknown a he beginning o he
solu ion, and which desc ibe ese oi ope a ions (wa e wi hd awal om he ese oi ) o se e al ime s eps
(mon hs) N ahead. I means ha , based on he limi ing condi ions o he ypes o equa ions and inequali ies, and
based on he en e ed bounda y and ini ial condi ions, he chosen op imiza ion me hod inds he desi ed alues o he
unknown, o which he chosen c i e ial unc ion eaches he desi ed ex eme. A de ailed desc ip ion o he
ma hema ical model and he op imiza ion model i sel a e desc ibed e.g. in [9]. The solu ion uses he op imiza ion
me hod o Di e en ial E olu ion.
The op imiza ion model in a hyb id con ol me hod is used o inding op imum wa e wi hd awal om ese oi
WT,
W
. Op imum mon hly wi hd awals WT,
W
a e sough o each yea
,,...,2,1 MT
whe e M is he o al numbe o
yea s and o indi idual ime s eps
,N1,2,..., L
W
whe e N+L is he numbe o ime s eps (mon hs) o he
discha ge se ies o he mean mon hly wa e lows in o he ese oi IT,
W
. Fo N,
LN  12
applies, and o L,
11,1L
applies. The numbe o yea s o he chosen ime pe iod M consis s o he numbe o yea s o he his o ical
mon hly lows HMF and he numbe o yea s o he es ima ed discha ge se ies. The es ima ed cou se o he
discha ge se ies exp esses he changing hyd ological condi ions co esponding o he chosen clima e change scena io
FMF ( u u e mon hly lows). Indi idual yea s T a e di ided in o wo pa s. The i s pa
N1,2,...,
W
ep esen s he
pas and he second pa
LN1,...,N
W
ep esen s he u u e. The ime pe iod
LN1,...,N
W
is in he
u u e only om he iewpoin o he op imiza ion model, and may be designa ed as, e.g. a quasi- u u e pe iod. Fo
he quasi- u u e pe iod we know he eal alues o mean mon hly wa e lows in o he ese oi . The i s s ep o he
quasi- u u e pe iod in e ms o eal con ol will co espond o he eal u u e pe iod o which we will es ima e he
mean mon hly wa e wi hd awal om he ese oi WT,
W
and o which
1M  T
and
1N 
W
apply. The
wi hd awal alue om he ese oi WT=M+1,
W 1
is es ima ed (p edic ed) using he SVM me hod. The op imiza ion
model algo i hm is shown in Fig. 1.
2.2. Suppo Vec o Machines
The SVM me hod uses he ad an ages p o ided by e ec i e ke nel machine algo i hms o inding he linea
bounda y while main aining a highly complex non-linea unc ion. One o he basic p inciples is he ans e o he
gi en o iginal en ance space in o ano he , mul idimensional one, whe e classes can be sepa a ed om each o he
linea ly. By his app oach he SVM me hod di e s om o he me hods o machine lea ning, e.g. om he mos
di use me hod o a i icial neu al ne wo ks. O iginally, SVM was ocused on he classi ica ion o da a poin s, la e i
was enhanced by he possibili y o sol ing non-linea eg ession p oblems. A p esen , he SVM me hod can be used
o p edic ion. The SVM me hod o sol ing eg ession p oblems is called Suppo Vec o Reg ession (SVR) [10].
The SVR me hod in he hyb id con ol me hod is used o p edic ion (es ima ion) o he alues o mean mon hly
wa e wi hd awals om he ese oi WT,
W
in he u u e pe iod
1M  T
and
1N 
W
. Fo lea ning he SVR
model, mean mon hly wa e lows in o he ese oi IT,
W
a e used, o
,,...,2,1 MT
N1,2,...,
W
and co esponding
op imum alues o mean mon hly wa e ou lows om he ese oi WT,
W
o each yea
MT ,...,2,1
o he quasi-
u u e pe iod
1N 
W
. The lea ned SVR model es ima es he amoun o he mon hly wa e wi hd awal om he
ese oi WT=M+1,
W 1
. The ou low is es ima ed based on he mean mon hly wa e lows in o he ese oi IT,
W
which
in e ms o ime, ake place in he nea pas om he u u e ime pe iod, o which he SVR model es ima es he
wi hd awal amoun (
1,M T
N1,2,...,
W
). The algo i hm o he SVR model is shown in Fig. 2.
494 Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
Fig. 1. Op imiza ion model.
495
Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
Fig. 2. Suppo ec o eg ession me hod.
3. Applica ion and Resul s
A p og am has been de eloped based on he desc ibed hyb id con ol algo i hm. The p og am is c ea ed in he
p og amming language R using he ex ension package DEop im (Di e en ial E olu ion) and e1071 (SVR). The
conside ed hyb id me hod o ese oi con ol has been applied in he s o age unc ion con ol o he Vi I ese oi
( u he e e ed o as Vi ). The Vi ese oi is loca ed in he Czech Republic and has a s o age olume o 44.056
million m3. Ve i ica ion o he hyb id con ol me hod du ing eal ope a ion on he Vi ese oi would be p ac ically
impossible; he e o e, a simula ion model has been used o e i ica ion. I is a classical simula ion model whe e
con ol guidelines a e subs i u ed wi h he epea ed algo i hm o he hyb id con ol me hod. Simula ion o he Vi
ese oi con ol was conduc ed in he his o ical pe iod o 1987 o 1995. The pe iod o he yea s 1990 and 1992 was
chosen o e alua ion o he success ulness o con ol ex eme d y yea s. In e ms o ex eme d y yea , he yea 1987
was abo e a e age, and so i is possible o conside a he beginning o simula ion a ull ac i e s o age olume o
he ese oi .

496 Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
En y da a o he hyb id con ol me hod:
x his o ical discha ge se ies o mean mon hly wa e lows in o he ese oi ; pe iod om 1950 o 1987) –
,37 HMF
x es ima ed discha ge se ies o mean mon hly in lows in o he ese oi o he chosen clima e change scena io
(ENSEMBLES [11]); pe iod om 2000 o 2100 –
,101 HMF
x alue o he equi ed wa e wi hd awal
,.0.2
13 
smW
R
x
,138 M
x
,6 L
x
.6 N
Fo he pu pose o compa ing he success ulness o hyb id con ol (HC), he con ol is compa ed wi h he mon h
o mon h con ol. The mon h o mon h con ol co esponds wi h he con ol guidelines ha a e cu en ly used o
ope a ion on he Vi ese oi (RC). This con ol me hod does no use wa e low p edic ions ei he , and co esponds
wi h common con ol me hods.
Fo e alua ion o he success ulness o indi idual ese oi con ol me hods in he pe iod om 1990 o 1992, he
amoun o unsupplied wa e is es ablished. Ideally, 89.6 million m3 wa e should be supplied while main aining he
equi ed WR o a pe iod o 17 mon hs. Unde RC con ol, only 64.1 million m3 wa e a e supplied o he whole
pe iod. Unde hyb id con ol, 66.5 million m3 wa e a e supplied o he whole pe iod.
Fig. 3 shows he cou se o mean mon hly wa e lows in o he ese oi (I). The equi ed wa e wi hd awal om
he ese oi is shown (WR). Fu he mo e, he igu e shows he cou se o mon h o mon h RC con ol, and he cou se
o HC con ol. Fig. 4 shows he cou ses o s o age olumes o indi idual con ol a ian s, simila ly as Fig. 3.
Fig. 3. The esul ing cou ses o he con ol in he ex eme d y pe iod – mean mon hly wa e lows.
497
Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
Fig. 4. The esul ing cou ses o he con ol in he ex eme d y pe iod – mean mon hly s o age olumes.
4. Conclusion
The aim o he pape was o ou line an al e na i e me hod o s a egic con ol o wa e wi hd awal om a wa e
ese oi . S a egic con ol o wa e wi hd awal om ese oi s (con ol pe iod wi hin he ime s ep o a mon h) is
e y impo an in he con ex o occu ence o a d ough ; i allows conduc ing app op ia e manipula ions on wa e
ese oi s.
I is ob ious om he case s udy ha he o al amoun o unsupplied wa e is la ge in he case o con ol using
ules cu es compa ed o he hyb id con ol me hod. I may be an icipa ed ha wi h a di e en ese oi we will also
ob ain e y in e es ing esul s using he hyb id con ol me hod. In e ms o wa e managemen on he ese oi , i
may be obse ed ha hyb id con ol ends o wi hhold a la ge amoun o wa e in he ese oi , sa ing wa e o a
u u e pe iod.
In he u u e, i is ad isable o y hyb id con ol wi h a di e en choice o L (N), combined wi h a choice o a
di e en clima e scena io o he es ima ed discha ge se ies o mean mon hly in lows. The hyb id con ol me hod
should also be used in he con ol o a di e en wa e ese oi , o he con ol be applied on a sys em o ese oi s. I
is expec ed ha e en mo e in e es ing esul s migh be ob ained his way. In he u u e, he ob ained esul s could be
compa ed wi h he con ol using p edic ions o mean mon hly in lows.
The esul s ob ained in his pape poin ou he possibili y o a p ac ical use o he hyb id con ol me hod. The
p esen ed con ol me hod could se e as a means o make wa e managemen on ese oi s mo e e icien . In
gene al, in elligen con ol me hods may be a suppo p o iding ool o he wa e managemen con ol depa men in
he p ocess o decision making.
Acknowledgemen s
The a icle is he esul o speci ic esea ch p ojec FAST-S-16-3444 “P oposal o hyb id me hod o con olling
ac i e s o age capaci y o wa e ese oi ”.
498 Pa el Mensik and Daniel Ma on / P ocedia Enginee ing 186 ( 2017 ) 491 – 498
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