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Stochastic Radial Basis Function Algorithm for Global Optimization

Stochastic Radial Basis Function Algorithm for Global Optimization

by

 

Solves computationally expensive black-box global optimization problems with box constraints

Data=datainput_Schoen_10_4_3
function Data=datainput_Schoen_10_4_3
%Schoen test function

%--------------------------------------------------------------------------
%Copyright (c) 2012 by Juliane Mueller
%
% This file is part of the surrogate model module toolbox.
%
%--------------------------------------------------------------------------
%Author information
%Juliane Mueller
%Tampere University of Technology, Finland
%juliane.mueller2901@gmail.com
%--------------------------------------------------------------------------
%

Data.xlow=zeros(1,10); %variable lower bounds
Data.xup=ones(1,10); %variable upper bounds
Data.dim = 10; %problem dimension
Data.objfunction=@(x)myfun(x); %objective function handle
end %function

function y = myfun(x)
x=x(:)';

StatPoint = [...
0.51616122720246271000  0.06405242002069214100  0.51561886261625600000  0.15603303374601987000  0.32478638540069149000  0.36715067959168513000  0.75257620265320202000  0.07897335436601030100  0.61477726445244441000  0.56239948959788255000  
0.22524593356835063000  0.26785666352930254000  0.59165528492945840000  0.42599069837530606000  0.46549207765751360000  0.79054588290834460000  0.94891619099566815000  0.23811957618208010000  0.37939433401669936000  0.49558847084911600000  
0.18366340207258622000  0.82585047860357264000  0.70050739474255264000  0.82298687734591702000  0.48962817222103605000  0.32319026230233222000  0.92006050642576576000  0.61212696534777089000  0.57375983199373359000  0.82982688242915092000  
0.21630124360794264000  0.33526178039234611000  0.02034817598035622600  0.05117691640827966300  0.53517237989973354000  0.52431084060121691000  0.24540208887094433000  0.49582246444614109000  0.84137267221898215000  0.76023809041573653000  
0.42718217294268229000  0.96502454427067108000  0.11180995901473459000  0.00025708496755501097  0.08675439291204610500  0.52874053814147715000  0.11448102364299538000  0.76835887098032774000  0.97957490871636188000  0.71876949856150552000  
0.97057539859810160000  0.29565066410292035000  0.79437843706197320000  0.61819737628835314000  0.62855051937148354000  0.95550385479500166000  0.17990157073410382000  0.37120727133908077000  0.38927829277848702000  0.71846221902327789000  
0.82154452901631081000  0.38127938236431458000  0.12230030573744609000  0.84637986129916298000  0.35962619014642488000  0.14428050957285760000  0.76682984008230193000  0.31912549999007245000  0.83603124434417264000  0.08457233231450812800  
0.36934789892902603000  0.62369212239478977000  0.35000203236819571000  0.74690525383794260000  0.97970407437834928000  0.45055690586122793000  0.66261094123329423000  0.18430543719337397000  0.63663891120155824000  0.71119767057630301000  
0.02953686801016654200  0.38525596651878691000  0.86517388175593124000  0.56112407311861845000  0.33259961919805409000  0.50069046191340572000  0.88981252025824042000  0.11385230422008578000  0.13220950616096819000  0.31706591285125008000  
0.19186462955785397000  0.18634703029167535000  0.25772233971861280000  0.88222103910010896000  0.28000433189631674000  0.73749698753046400000  0.12325930227830950000  0.91691529341780498000  0.21542582912334921000  0.76724649666110067000  
0.24708839087460119000  0.22479452620999746000  0.27987248957816663000  0.16854978212229416000  0.29018018810629859000  0.11422293102063247000  0.33717240880031402000  0.58330864988556619000  0.43662319463695104000  0.54286602138406026000  
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0.61106100556434784000  0.04401599600624128700  0.35406199974893826000  0.94367317622150271000  0.12513467839882239000  0.78149137044381478000  0.98104231429720468000  0.72576235577478221000  0.14594723171569157000  0.03572135701163077500  
0.04848371768459032400  0.31832671671246132000  0.88853103249051246000  0.85771806538780893000  0.04838593827484805000  0.06682573170495212400  0.09439006023040071000  0.02167355265558013100  0.06949524868489075100  0.23743422047412482000  
0.80770419186250164000  0.51992908800800763000  0.02239267729272165200  0.43557822521383532000  0.53152403610603449000  0.09959802609525149300  0.56683504099556048000  0.71589290097457292000  0.33934832494886430000  0.63483033584055770000  
0.50865649331485008000  0.33386208621522590000  0.22669641757920533000  0.83141223606879766000  0.62273350273406858000  0.49576032399674780000  0.43429016871267301000  0.94285716508894735000  0.38253260839065134000  0.13097581327241214000  
0.31527313846828836000  0.72359224181228243000  0.11610005941216647000  0.93635090377154850000  0.05599339072821966200  0.02872011486859927000  0.17607545881126038000  0.10315453372562364000  0.22105193217842928000  0.88657288330701611000  
0.91300055918526957000  0.12744886034533212000  0.71728757940320997000  0.74480810552668719000  0.70606956455371173000  0.57109202232385026000  0.26552064945583775000  0.59970799193246083000  0.76926195280129972000  0.04031023521665432600  
0.59072651112543872000  0.91578404577493999000  0.36839262704966641000  0.58452098024891475000  0.52825718068418070000  0.38022672783421824000  0.95078377450868590000  0.14656680430169813000  0.82092170936316744000  0.69783085835633862000  
0.57513131364947312000  0.27577919582181121000  0.76272115886578218000  0.43179435394573040000  0.97014802622934215000  0.11395933577018548000  0.16822334317639961000  0.13759894015683147000  0.17691369478967256000  0.34509092983672124000  
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0.15920938523054676000  0.68197479288946139000  0.71532725208267622000  0.73038638832910374000  0.26581081610866181000  0.74746733602896676000  0.41124055088549222000  0.26243066520503983000  0.92778584844455247000  0.84858941507116614000  
0.27492996230350947000  0.17342136659620910000  0.17400994552943297000  0.79587560446132954000  0.95486062555556184000  0.11685978223939070000  0.34045305777059209000  0.52534539689024395000  0.15526913719093441000  0.96322430137338710000  
0.73791729671080908000  0.12800239299473817000  0.33432066712222719000  0.66449175773662694000  0.62012331489932282000  0.78411511463441241000  0.86586234725572442000  0.00425827418660169440  0.94070997228066011000  0.73091204772909157000  
0.51148322373625021000  0.42674509187184351000  0.69214869901097631000  0.47793497104136301000  0.55857058664775028000  0.02659477575327292100  0.18398677402782954000  0.37165434091924598000  0.91475804238271974000  0.36442356269287962000  
0.19489097130924940000  0.08442272498202418900  0.91751562716829194000  0.13898399605117898000  0.01099479488016837300  0.50218275199995766000  0.56527588969719111000  0.16185427092847221000  0.26654747924312222000  0.06617696576856249600  
0.86756918921696835000  0.79793459485381157000  0.03141913434826271200  0.29018151256444036000  0.22219779375894358000  0.97134618400809503000  0.81201874043526301000  0.35365146426245564000  0.95123894257536956000  0.52659739189180366000  
0.63407279998600041000  0.00729543039289006980  0.96883988399352716000  0.44762932293278301000  0.68810951458414549000  0.56176966881114565000  0.59328311150199742000  0.35000562445481948000  0.50751854079282355000  0.69060692874190077000  
0.39523088619683783000  0.66482268406911627000  0.34424759799190335000  0.11287159937627635000  0.61795565018481180000  0.54777911359505294000  0.37904247153163251000  0.33402527302050133000  0.66160875552727449000  0.68926755678419904000  
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0.02156650164323271500  0.58541770092783441000  0.08110227698420464900  0.77229649966207636000  0.04053054621516733600  0.11303228753300568000  0.07649956852451556000  0.73318118607959115000  0.79973107970851265000  0.93598635853043677000  
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0.52165625786161074000  0.99346852731038027000  0.42283504580571152000  0.11071615745728723000  0.79560350534858182000  0.27341095612895783000  0.41513050670018020000  0.10219460131211119000  0.77286278497154726000  0.97240243552606243000  
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0.43406067829988071000  0.87061949351150081000  0.13485886683290998000  0.95350265472281304000  0.25703087611531578000  0.01042287865927410100  0.81104411196298920000  0.29151633950779532000  0.56102522233546948000  0.04393178982371986900  
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0.65367394710277882000  0.76507394309867838000  0.46995071794928583000  0.38346302982158392000  0.58073568044403923000  0.37045347530629152000  0.15335401471319823000  0.45146032223857646000  0.69232307514142322000  0.88151688010685081000  
0.19061798883768430000  0.42287343685513101000  0.37064310327893152000  0.03550403323937390000  0.13016181194356768000  0.37840764652615971000  0.68504303904645969000  0.95120083883816975000  0.06645548716470779700  0.78473974804664903000];  

StatValue = [...
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
35.10835455561429800000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
43.85109260435986300000
100.00000000000000000000
100.00000000000000000000
3.87481784334364530000
5.01383575540721260000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000
100.00000000000000000000];

k = length(StatValue);
Xtemp = ones(k,1)*x;
TempNorm = sum((Xtemp-StatPoint).^2,2);
TempProd = ones(1,k);
for i = 1:k
    TempProd(i) = prod(TempNorm(1:(i-1)))*prod(TempNorm((i+1):k));
end
y = (TempProd*StatValue)/sum(TempProd);

end %myfun

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