Non-Linea Ma ine Spa ial Zoning
Th ough Pa icle Fil e ing
1s Leonidas Ioannou
Ma i ime Digi alisa ion Cen e
Cyp us Ma ine and Ma i ime Ins i u e
La naca, Cyp us
[email p o ec ed]
2nd Neo y os Dimi iou
Ma i ime Digi alisa ion Cen e
Cyp us Ma ine and Ma i ime Ins i u e
La naca, Cyp us
[email p o ec ed]
3 d Ioannis Ky iakides
Ma ine Technology Di ision
Cyp us Ma ine and Ma i ime Ins i u e
La naca, Cyp us
[email p o ec ed]
Abs ac —Ma ine Spa ial Planning (MSP) is a c i ical ap-
p oach o alloca ing ma ine a eas o a ious ac i i ies and com-
pe ing sec o s – such as ishe ies, enewable ene gy, conse a ion,
and ou ism – while managing hei ope a ions o balance ecolog-
ical, economic, and egula o y conside a ions. This wo k explo es
he applica ion o Sequen ial Mon e Ca lo (SMC) and Pa icle
Fil e ing me hods o MSP, and in pa icula ma ine zoning. We
e alua e he me hod using syn he ic da a se s ha we e gene a ed
o zones wi h g ound u h o a ying spa ial compac ness and
connec i i y. Fu he , we conduc a sensi i i y analysis on he
pa ame e s o he me hod and iden i y ha dec easing pa icle
noise injec ion du ing op imiza ion imp o es ime o con e gence
and he F1-sco e. The esul s highligh he po en ial o SMC-
based op imiza ion o e icien and adap i e ma ine zoning
decisions, p o iding a scalable app oach o suppo sus ainable
ocean managemen .
Index Te ms—Ma ine Spa ial Planning, Zoning Op imiza ion,
Sequen ial Mon e Ca lo, Non-Linea Op imiza ion
I. INTRODUCTION
MSP aims o minimize con lic s among ma ine use s,
p omo e syne gies, and ensu e en i onmen al sus ainabili y
h ough spa ial alloca ion and empo al scheduling o ocean
ac i i ies [1]. His o ically, ma ine and ma i ime ac i i ies we e
la gely un egula ed, in pa due o he common misbelie
ha he ocean was an inexhaus ible esou ce [2]. How-
e e , ising p essu es om o e ishing, pollu ion, and habi a
deg ada ion ha e unde sco ed he u gen need o s uc u ed
spa ial planning amewo ks and sophis ica ed algo i hmic
solu ions, he ein e med In elligen Ma ine Spa ial Planning
(iMSP) [3] [4].
A key applica ion o iMSP is ma ine zoning, i.e. des-
igna ing a eas o economic ac i i ies, such as ones ela ed
o aquacul u e o he ma i ime sec o , conse a ion e o s,
e.g. designa ing new Ma ine P o ec ed A eas (MPAs), and
sus ainabili y, e.g. o sho e wind a ms. E ec i e zoning e-
qui es a coo dina ed decision-making app oach ha in eg a es
mul iple ac o s, including ecological cons ain s, p oximi y
o exis ing in as uc u e, and spa ial dependencies be ween
This wo k was co- inanced by he Eu opean Union – Nex Gene a-
ionEU, h ough he Resea ch and Inno a ion Founda ion unde he p ojec
MSP4GROWTH (G an Numbe : ENTERPRISES/0223/Sub-Call1/0131), he
SeaTecHub p ojec , unded by he Eu opean Union unde G an Ag eemen
No. 101087162, and he EU H2020 Resea ch and Inno a ion P og amme
unde G an Ag eemen No. 857586 (CMMI-MaRITeC-X).
ma i ime ac i i ies. The p ima y challenges in ma ine zoning
a e wo old: da a- ela ed challenges, encompassing issues such
as da a a ailabili y, quali y, dimensionali y, and asynch onici y
ac oss di e se sou ces; and me hodology- ela ed challenges,
including limi ed cu en esea ch and inadequacies o exis ing
me hods in add essing he complexi y o ma ine spa ial op i-
miza ion p oblems bo h e ec i ely and e icien ly a -scale [5].
Mul i-C i e ia Decision Analysis (MCDA) echniques ha e
been p e iously used o e alua e si e sui abili y based on
mul iple ac o s [3]. Unde he umb ella o MCDA ech-
niques, Mul i-Objec i e In ege P og amming (MOIP) p o-
ides a s uc u ed amewo k o maximizing spa ial e iciency
by op imizing mul iple con lic ing objec i es such as p oximi y
o po s, he coas line, wind a ms, Ma ine P o ec ed A eas
(MPAs), and shipping lanes, ensu ing sus ainable and con lic -
ee zoning. [5]. Howe e , MOIP canno be adop ed o la ge
a eas unde conside a ion as i s compu a ional complexi y
g ows polynomially wi h he numbe o cells, posing chal-
lenges o la ge-scale eal-wo ld applica ions.
Al e na i ely, non-linea me hods, such as Sequen ial Mon e
Ca lo (SMC) me hods, p o ide an e icien app oach o MSP
by i e a i ely e ining solu ions ia esampling and spa ial ex-
plo a ion [3]. The compu a ional complexi y o hese me hods
ypically scales linea ly wi h he numbe o pa icles and can
he e o e enable la ge-scale MSP.
This wo k explo es he applica ion o Sequen ial Mon e
Ca lo (SMC) and Pa icle Fil e ing me hods o MSP and, in
pa icula , ma ine zoning. We e alua e SMC me hods using
a newly in oduced e alua ion amewo k [5] o assess hei
e ec i eness in op imizing ma ine spa ial planning syn he ic
scena ios. In pa icula , we de elop p obabilis ic models ha
u ilize pa icle il e ing-based spa ial explo a ion o iden i y
op imal ma ine zones. We conduc expe imen s on syn he ic
da ase s, as in oduced by Basi a i e al. [5], o assess he
me hod’s pe o mance ac oss di e en spa ial scena ios, ca e-
go ized as “Ve y Compac ”, “Compac ”, and “No Compac ”.
Ou expe imen al esul s co obo a e o he e ec i eness o
he pa icle il e ing-based spa ial explo a ion me hod.
II. PROBLEM DEFINITION
Ma ine zoning in MSP in ol es iden i ying an op imal a ea
o a new ac i i y wi hin a busy ma ine en i onmen . Exis ing
applica ions equi ing ma ine zoning, such as shipping lanes,
po s, and ma ine p o ec ed a eas, impose cons ain s ha mus
be espec ed. To ensu e compa ibili y wi h exis ing ac i i ies,
he zoning p oblem mus sa is y se e al key c i e ia, including
dis ance cons ain s, spa ial compac ness, and en i onmen al
sui abili y.
Dis ance cons ain s a e c ucial o main aining spa ial sep-
a a ion be ween ma ine ac i i ies, p e en ing con lic s, and
ensu ing ope a ional easibili y. The placemen o new zones
mus accoun o e.g. hei p oximi y o shipping lanes and
po s o a oid in e e ence wi h essel a ic and ensu e sa e
na iga ion. Simila ly, ma ine p o ec ed a eas (MPAs) equi e
s ic sepa a ion o p e en dis up ion o sensi i e ecosys ems
and ensu e compliance wi h en i onmen al egula ions. Addi-
ionally, con lic zones such as pipelines, ene gy in as uc u e,
and es ic ed a eas mus be a oided o minimize isks and
ope a ional challenges.
Beyond spa ial sepa a ion, spa ial compac ness is essen ial
o e ec i e ma ine zoning. The designa ed zone should be as
con iguous as possible o minimize agmen a ion, ensu ing
ha he new ac i i y is e icien ly con ained wi hin a well-
de ined a ea. A compac zoning layou also suppo s long-
e m spa ial planning by educing spa ial con lic s and making
u u e expansions o modi ica ions mo e manageable. A he
same ime, en i onmen al sui abili y cons ain s ensu e ha
si e selec ion aligns wi h ecological and egula o y guidelines.
Fo example, he ba hyme y and subs a e ype in luence he
easibili y o speci ic ac i i ies, such as aquacul u e, whe e
s able seabed condi ions a e necessa y o in as uc u e place-
men . Wind speed is ano he c i ical ac o , as high wind ex-
posu e can impac o sho e s uc u es and ope a ional s abili y.
By inco po a ing spa ial cons ain s in o he op imiza ion
p ocess, he p oposed amewo k ensu es ha ma ine zoning
p o ides an e icien app oach o spa ial planning in complex
ma ine en i onmen s.
III. METHODOLOGY
A. Da a Gene a ion
To e alua e he op imiza ion model, syn he ic ma ine spa ial
da ase s a e gene a ed, ollowing an app oach o ensu e eal-
is ic zoning scena ios [5]. The ma ine space is modeled as a
as e g id, whe e each cell is assigned a andomly gene a ed
in e es alue. While andom in he da a gene a ion p ocess,
hese in e es alues concep ually ep esen he usion o
mul iple eal-wo ld ac o s, such as en i onmen al sui abili y,
economic iabili y, and egula o y cons ain s.
Key spa ial elemen s, including shipping lanes, po s, and
es ic ed zones, a e andomly placed wi hin he g id o c ea e
di e se ma ine zoning scena ios. This app oach ensu es a
comp ehensi e e alua ion o he p oposed op imiza ion model
unde di e en spa ial con igu a ions.
B. Bu e ing Technique
To educe he compu a ional bu den o he op imiza ion
p ocess, a a bu e ing echnique, as in oduced by Basi a i e
al. (2021) [5] is applied. This p ep ocessing s ep iden i ies he
easible zoning a ea by sys ema ically elimina ing egions ha
ail o mee ce ain condi ions (e.g. less han 30 me e s) o
speci ic c i e ia (e.g. ma ine p o ec ed a ea).
Minimum dis ance cons ain s ensu e ha a eas oo close
o exis ing ac i i ies a e excluded om he easible egion.
Maximum dis ance cons ain s main ain accessibili y by p e-
en ing he selec ion o zones ha a e oo a om essen ial
in as uc u e. By elimina ing in easible a eas, he sea ch space
is signi ican ly educed, allowing he op imiza ion algo i hm o
ocus on high-po en ial loca ions and imp o ing compu a ional
e iciency.
C. Sequen ial Mon e Ca lo
The op imiza ion model employs a Sequen ial Mon e Ca lo
(SMC) app oach o i e a i ely e ine ma ine zoning decisions.
This non-linea op imiza ion me hod is capable o na iga ing
h ough he possibly mul imodal su ace o a cos unc ion ha
conside s a ious spa ial and en i onmen al ac o s. [3] The
p ocess begins wi h an ini ializa ion s ep, in which hypo heses
ep esen ing candida e zones a e uni o mly dis ibu ed wi hin
he easible sea ch space.
Each hypo hesis unde goes an i e a i e s a e upda e p ocess
du ing which i s posi ion is adjus ed using a s ochas ic mo e-
men model. The mo emen o each hypo hesis is go e ned by
a con olled s ep size and a Gaussian noise e m. The posi ion
upda e equa ion o each pa icle a i e a ion jis gi en by:
xl,j =xl,j−1+V ηl,j (1)
whe e: xl,j is he posi ion o he l- h pa icle a i e a ion j,Vis
a diagonal ma ix con olling he s ep size and ηl,j ∼ N(0, σ2)
is a ze o-mean Gaussian noise ec o , allowing pa icles o
explo e he sea ch space.
Each pa icle is assigned a sui abili y sco e based on i s
loca ion wi hin he spa ial in e es map. The sui abili y alue
o each cell, wi, is o iginally de ined on a disc e e domain:
wi∈ {1,2,3,4,5,6}(2)
To enhance he selec ion p essu e owa ds op imal loca ions,
he sui abili y alues o each cell a e p o ided by he ol-
lowing, whe e γcon ols he con as be ween high and low-
in e es a eas:
w′
i=wγ
i, γ > 1(3)
whe e: wiis he o iginal sui abili y alue o cell iand γ
is a scaling exponen ha ampli ies he di e ences be ween
op imal and subop imal loca ions.
Pa icles a e weigh ed based on hei ans o med sui abili y
sco es, ensu ing ha highe -weigh ed pa icles— hose in mo e
sui able a eas—ha e a g ea e p obabili y o su i al. Lowe -
weigh ed pa icles, ep esen ing subop imal zones, a e e-
placed wi h new candida es in mo e p omising a eas, ollowing
he esampling p ocess:
P(xl,j) = w′
l,j
Plw′
l,j
(4)
whe e P(xl,j) ep esen s he p obabili y ha a gi en poin
in ma ine space is sui able o his ac i i y. This ensu es
ha pa icles in highly sui able zones a e mo e likely o be
p opaga ed while main aining di e si y in he sea ch p ocess.
To e ine he sea ch, a esampling p ocess is applied a
each i e a ion. This i e a i e p ocess allows he pa icle se
o con e ge owa d high-sui abili y zones, ensu ing ha he
inal zoning solu ion maximizes spa ial e iciency.
IV. RESULTS
We conduc ed a sensi i i y analysis o assess how a ia ions
in key pa ame e s in luence he e ec i eness o ou me hodol-
ogy. Speci ically, we es ed di e en alues o he numbe o
gene a ed pa icles, he ini ial noise le el, and he a e a which
noise changes h oughou he op imiza ion p ocess. The noise
a ia ion was examined unde h ee scena ios: inc easing,
dec easing, and ixed. Addi ionally, we analyzed he impac o
he s ep a which noise adjus men s begin, as well as he a e
o hese changes. By sys ema ically al e ing hese pa ame e s,
we aimed o iden i y hei e ec s on he s abili y and e iciency
o he op imiza ion model.
A. E alua ion
Following he me hodology applied by Basi a i e al. [5],
we e alua e ou model’s pe o mance using h ee di e en
ypes o con ol a eas ha ep esen op imal loca ions in ou
gene a ed maps:
•Ve y Compac : A highly con iguous zone wi h minimal
gaps.
•Compac : A somewha con iguous zone wi h a ew small
gaps.
•No Compac : A agmen ed zone wi h mul iple dis-
join ed sec ions.
Fu he mo e, o assess he pe o mance o ou model, we
compu e he F1sco e a each i e a ion. The F1sco e is a
widely used me ic ha balances p ecision and ecall, p o-
iding a comp ehensi e measu e o accu acy. In ou con ex ,
p ecision e lec s he p opo ion o gene a ed pa icles ha all
wi hin he con ol a ea, while ecall measu es he ex en o
which he con ol a ea’s op imal loca ion is co e ed by hese
pa icles.
By acking he F1sco e ac oss i e a ions, we no only
e alua e he model’s accu acy bu also de e mine he numbe
o i e a ions equi ed o each a sa is ac o y pe o mance
le el. This app oach helps us unde s and how e icien ly he
op imiza ion p ocess con e ges o an op imal solu ion and
p o ides insigh s in o pa ame e uning o imp o ed esul s.
B. Sensi i i y Analysis Resul s
Fi s , we analyzed how di e en noise a ia ion scena -
ios—inc easing, dec easing, o ixed—a ec he F1sco e o
he h ee ypes o con ol a eas (Ve y Compac , Compac , and
No Compac ). The esul s a e summa ized in Table I, showing
he maximum F1sco e achie ed unde each scena io.
F om hese esul s, we obse e ha he dec easing noise
scena io consis en ly leads o he highes F1sco e (1.00)
ac oss all ypes o con ol a eas. This sugges s ha linea ly
educing noise a each i e a ion allows he model o be e
TABLE I
MAXIMUM F1SCORE ACHIEVED FOR EACH NOISE CONFIGURATION AND
ACROSS THE DIFFERENT CONTROL AREA SCENARIOS.
Noise Scena ios
Types o con ol a eas Inc easing Dec easing Fixed
Ve y Compac 0.82 1.00 0.94
Compac 0.80 1.00 0.9
No Compac 0.79 1.00 0.97
con e ge owa ds he con ol a ea, imp o ing accu acy. In
con as , he ixed noise scena io pe o ms sligh ly wo se, and
he inc easing noise scena io esul s in he lowes F1sco es,
indica ing ha excessi e noise can dis up con e gence.
Since dec easing noise was he mos e ec i e s a egy, we
conduc ed a sensi i i y analysis o e alua e how di e en ini-
ial noise alues and decay imings in luence he con e gence
a e, measu ed as he numbe o i e a ions equi ed o achie e
F1sco e = 1.
The ini ial noise alues we e de ined as he s anda d de i-
a ion o a ze o-mean Gaussian dis ibu ion, which in luences
he deg ee o andomness in he sea ch p ocess. We es ed
h ee le els o ini ial noise. The i s , N1(0.1), in oduces
low noise, leading o minimal explo a ion and mo e localized
mo emen s. The second, N2(0.5), p o ides a mode a e le el
o noise ha balances explo a ion and con e gence. The hi d,
N3(1.0), in oduces high noise, enabling la ge explo a o y
mo emen s ac oss he map in he ea ly i e a ions.
In addi ion o a ying noise le els, we examined di e en
decay imings, which de e mine when he noise begins o
linea ly dec ease. The i s se ing, D1(1s i e a ion), ini ia es
noise educ ion immedia ely. The second, D2(5 h i e a ion),
ep esen s an ea ly decay s a egy, while D3(10 h i e a ion)
in oduces a mode a e decay iming. Las ly, D4(20 h i e a ion)
delays he educ ion o noise o a longe pe iod be o e
dec easing.
Fo each combina ion o ini ial noise le el and decay iming,
we measu ed he numbe o i e a ions equi ed o each an
F1sco e o 1 ac oss h ee di e en con ol a ea ypes: Ve y
Compac , Compac , and No Compac . This analysis helps
de e mine he op imal noise con igu a ion ha minimizes
con e gence ime while ensu ing e ec i e explo a ion and
accu acy.
The esul s e eal a ia ions in con e gence beha io ac oss
di e en con ol a ea ypes, ini ial noise alues, and decay
schedules. Ins ances whe e he model ailed o achie e F1=
1wi hin he 50 obse ed i e a ions a e ma ked wi h ”–” o
indica e non-con e gence.
A key obse a ion is ha ea lie noise decay (D1-D2)
accele a es con e gence, pa icula ly o lowe noise le els
(N1= 0.1). In con as , delayed decay (D3-D4) inc eases
he numbe o equi ed i e a ions, wi h a p onounced e ec in
Ve y Compac and No Compac con ol a eas. Fo N3= 1.0
a D3and D4, he model o en ails o each F1= 1,
sugges ing ha high noise le els combined wi h la e decay
impede con e gence.
TABLE II
NUMBER OF ITERATIONS REQUIRED TO REACH F1= 1 FOR DIFFERENT
INITIAL NOISE VALUES AND DECAY TIMINGS
Decay Timing Con ol A ea
Type
N1(0.1) N2(0.5) N3(1.0)
D1(1s I e a ion)
Ve y Compac 24 26 26
Compac 24 27 22
No Compac 22 23 23
D2(5 h I e a ion)
Ve y Compac 24 27 26
Compac 20 27 33
No Compac 23 30 35
D3(10 h I e a ion)
Ve y Compac 21 26 –
Compac 24 37 –
No Compac 26 40 –
D4(20 h I e a ion)
Ve y Compac 30 – –
Compac 30 48 –
No Compac 32 – –
Fo Ve y Compac a eas, mode a e noise le els (N2= 0.5)
wi h in e media e decay iming (D2-D3) p o ide a balanced
ade-o be ween explo a ion and con e gence speed. How-
e e , Compac and No Compac a eas exhibi highe sensi i -
i y o noise and decay iming, whe e delayed decay equen ly
esul s in ex ended con e gence imes o ailu e o con e ge.
O e all, ea lie decay (D1, D2) and lowe noise alues
(N1= 0.1) p omo e as e con e gence, whe eas highe noise
(N3= 1.0) and la e decay (D3, D4) o en lead o ins abili y,
pa icula ly in Compac and No Compac a eas.
Building on hese indings, we analyze he sensi i i y
o he dec easing noise a e o an ini ial noise alue o
N1= 0.1, which demons a ed he mos consis en and apid
con e gence. This analysis examines whe he adjus ing he
noise educ ion a e can u he op imize con e gence ime
o in oduce s abili y a ia ions ac oss con ol a ea ypes.
By sys ema ically a ying he decay a e, we assess whe he
he p e iously obse ed end—whe e ea lie decay (D1, D2)
led o as e con e gence— emains alid unde di e en noise
educ ion a es. The goal is o iden i y he op imal s a egy o
N1= 0.1, ensu ing an e ec i e balance be ween explo a ion
and con e gence e iciency.
TABLE III
SENSITIVITY ANALYSIS OF DECREASING NOISE RATE FOR INITIAL NOISE
VALUE N1= 0.1
Dec easing
Noise Ra e
Con ol A ea
Type
D1
(1s I e .)
D2
(5 h I e .)
D3
(10 h I e .)
Slow Decay
Ve y Compac 24 29 25
Compac 33 28 40
No Compac 22 40 26
Mode a e Decay
Ve y Compac 25 24 30
Compac 35 26 33
No Compac 35 25 25
Fas Decay
Ve y Compac 27 24 21
Compac 24 20 24
No Compac 25 23 28
The esul s indica e ha as e noise decay gene ally im-
p o es con e gence, pa icula ly a D2(5 h i e a ion), whe e
he lowes i e a ion coun s a e obse ed o Compac and No
Compac a eas. Ve y Compac a eas bene i mos om as
decay a D3, whe e he lowes i e a ion coun (21) is eco ded.
Con e sely, slow decay equi es mo e i e a ions, especially
in Compac and No Compac a eas, whe e g adual noise
educ ion o en delays con e gence o leads o ins abili y in
eaching F1= 1.
These indings ein o ce he impo ance o an app op ia ely
uned decay a e, pa icula ly in non-compac a eas whe e
delayed noise educ ion can signi ican ly hinde con e gence
e iciency.
C. Implemen a ion
This wo k was implemen ed in Py hon 3.10 on a
Linux/Ubun u sys em. NumPy, Pandas, Ma plo lib, and
Seabo n we e used o da a p ocessing and isualiza ion.
Expe imen s we e conduc ed on an AMD Ryzen 9 5900X
12-co e p ocesso wi h 64 GB o RAM, ensu ing e icien
compu a ion.
V. DISCUSSION
He ein, we ha e explo ed a pa icle- il e ing based op i-
miza ion me hod o ma ine spa ial planning, conduc ing a
sensi i i y analysis o e alua e how di e en noise se ings
impac con e gence e iciency and solu ion accu acy. Unlike
p io applica ions o op imiza ion models in spa ial zoning,
his wo k sys ema ically examines he ole o noise a ia ion,
decay iming, and ini ial noise le els, p o iding empi ical
insigh s in o hei in luence on zoning e ec i eness and e -
iciency. The esul s emphasize ha dec easing noise o e
ime leads o he highes F1sco es, s iking he igh balance
be ween space explo a ion and exploi a ion.
In con as , ixed and inc easing noise se ings esul ed in
lowe F1sco e, sugges ing ha excessi e andomness dis up s
con e gence. I is impo an o highligh ha p e ious wo ks
in MSP [3] [4] assumed a cons an noise scena io, which
con as s wi h he signi ican ly imp o ed con e gence and
pe o mance obse ed when noise is g adually educed.
One o he mos signi ican indings is he e ec o noise
decay iming on con e gence speed. The analysis shows ha
ea ly decay (D1, D2) consis en ly accele a es con e gence,
pa icula ly when pai ed wi h low ini ial noise (N1). On he
o he hand, delayed decay (D3, D4) ex ended con e gence
imes o led o non-con e gence, highligh ing he impo ance
o adap ing noise le els dynamically. Addi ionally, he s udy
ound ha spa ial compac ness in luences op imiza ion pe -
o mance, as Ve y Compac con ol a eas achie ed as e
con e gence han No Compac a eas, whe e agmen a ion
in oduced addi ional complexi y. These insigh s can guide
esea che s in making in o med me hodological decisions ai-
lo ed o hei speci ic use cases.
ACKNOWLEDGMENT
The au ho s would like o exp ess hei g a i ude o And eas
Hadjipie is o his aluable assis ance in op imizing he code.
REFERENCES
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