1. Soft Computing (Immune Networks)
In Artificial Intelligence
Yasuhiko Dote
Muroran Institute of Technology
Mizumoto 27-1, Muroran 050 8585,Japan
dote@,csse.muroran-it.ac.jp
ABSTRACT
iliis paper proposes a novel reactive distnbuted artificial usualh achieve theu tasks i n groups. llcactive a y i t s are sittiatcd
~ntcIiigeiice (dvnaniic)using immune networks and other soft they do not take past e~eiits account. a i d can iiot Ibrcsee rlic
into
Loiiiptitiiig inethods Fusth. extended sot? computing is defined ftiture. Their action is based on hat happens no. ho the ~ C I I ~ ~
In .idding iiiuiiuiie networks and chaos theory including fractal distmzuish situations ui Ilie aorld. on the ~ a vthev resognve
and ivavelet to conventional sott computing which is the fusion or world indexes and react accordingly llius. reacuve agents can not
coinbinatioii of tiizzv systenis.neural networks and genetic plan ahead what they will do But, what can be considered as a
.~lgoritlinis and is suitable to cognitive distnbuted artificial weakness is one of theu strengths because the! do not ha^ to
~ i i ~ c l l i ~ e n(static) Next, a novel fuuv neural net(genera1
ce revise their world model when perturbations chaiige the orld in
parameter radial based function neural network) is developed in an tmepected u a ) Robustness and tatilt toleraiict arc t n o 01 the
order to use it for communication among agents in immune main properties of reactive agent swttiiis. j2 group of r e ; ~ c t ~ w
iictnorhs The geiieral paraineter method is &ended to an agents can coinplete tasks even when one o l them b r d s doun.
adaptive structured genetic algorithm to obtain much faster The loss of one agent does iiot prohibit the coinpietion o l the
convergence rate An unbiasedness criterion using distorter( a whole task, because allocation of roles is achieved locall bv
radial based ftiiiction network i order to optimize parameters
n perception of the enviroiunental needs. 'Thus, reactive ageiit
resultiiy in die reactive distributed artificial intelligence hnd of svstems are considered as v:
e flexible and adaptive because[ I 1
(;MD!i) is applied to better generalization propertes. Then, t h s In this p a p e r ;I nozcaI re;ictive distributrtl ;irtif'i(,i:il
developed I'tvrv neural net is extended to a h g h performance int r llige nrr is proposvd us1 ti g Ish igrii ro's i n i i i i i i ne
1. INTRODUCTION n r t w o r k ;11~[~r(~~1t~Iil'l;in'li:(il ot1ic.r +oft rwmputin?
:inc
I<eactivit is a hehavior-bewd model of activitv,as opposed to approaches In section 11. soft coinpiit ing propoawl I)?
x
the svmbol inanipulation model u.wd in planning.This leads to the L1r.L .i.Zadrh[-i] is r x t r n t l t d by :Ititling rhaos coinpiti ing
iiotioii of cognitive c0st.i e.. the complexity of the over and iinmunr net,work theory. i novel fuzzy neural
,Irchitecture needed to achieve a task Cognitive agents support a n r h v o r k with grneral p;lr;imrt.c-r statistics calculus taking
coinplz architecture which inems that their cognitive cost is advantages of both fiii.z ins arid neural iictnorhs i n section
IiigIi.Copnitive agents have intenml representation of the world 111 In section IV this IS eaciided to a high perfonnoiice radial
l i i ~ l iiiiiist he in adequation with the morld itself T h e process of hasis tiiiiction iieural iitturh using oii adaptive structure genetic
rslating the tiitenial representation and the world is considered as algorithinl5 I close to the seneral parciiiieter iiicthod arid o kind 01'
'I task On the other hand. reactive agents are simple.
~oinple- (iMnH[61. In section V these developed nctorks are applied to
cash to uiiderstwd and do not support intemal representation of optiiiiize Ishiguro's uimiune network reactive distributed artiticial
the world. Ilius. their cognitive cost is low, and tend to what is intelligence.
cognitive economy. the property of being able to perfom
~alled
cvcn complsr actions with simple architectures Because of their 11. EXTENDED SOFT COMPUTING
complexit. cognitive agents are otteii considered as self- Soft coiiiputing is proposed bv I)r I* A./.adch/-ll to coiistrtict
~iitlicicrit the can nork alone or nith a ten other agents.0n die ne generation Ai [ macliiiie .intelligeiicc quatient) and to solve
coiitrm. reackive agcnts need companionshp 'I'hey can iiot work noiiliiiear and inatliematicallv iiimioJelld systems prohlenis
isolated and they usually achieve their tasks in groups. Reactive (tractability) especiallv for cognitive artilicial intelligence In this
agents me companionship. They can not work isolated and thev section by adding chaos coiiiptituig arid iiiuiitiiie network thron.
198 $10.00 0 1998 IEEE
0-7803-4778-1 ,
1382

2. ilii extended soft computing is detined for explaining, what thev s t a r t i n g from t h e same initi;il conrhtions. In t h e first
call. complex svstems(7). hunune networks are promising case. :I coiivcsiit ioniil I2HF" wiis uswl w i t h in~livi~Iu;il
approachos to construct reactive artiticial intelligence[21 and [ 3 ]as adjusting of i t s vciights. I n t h e s;c.c:ontlc:ise. ( ~ l ' - l i l $ l ~ N
Illustnltcd 111 Fig I was simuliitrtl with leiirning iilgorit hili (2) 'l'h~,
Hiinian I~eirig i k e .AI
l vfficirnc? of both mrthorls w e r r ~ o n i i ~ ~ r byd using
r
~~-
Cogniriw t h e following m r a s u r e of convergrncr sprrd
Fuzzy 1)istribur~d
Systern ;I (Stnticl
Fig.1 Soft computing in AI
111. NOVEL FUZZY NEURAL NET
I 'J
I irst. id consider the (iP approach to KHFN weights adjust~ng. Figure2. The simplest G P - R R F N
;s soon iis IIRI,'N IS linear on its eights. the (iP method may
bo impIementc.d in a straightfonxard manner The equation
dcscribiiig (if'-RBFN for a single output network is
U IirrI, 1:
. fisrcl initial v a l u e s of' network we1ght.s: p: 0'
400 800 1
si:;il;ir grnrr;il p a r a m e t e r t,o be adjusted with t h e
fol I ow 1ng algori t hin Figure 3 Im;trning algorithm c:onvt!rgc!nc:o:
ti) conventional IZUCN: 11) [;I'-ltt3FN
1383

3. ~linic.nsioniilit> IeiirninC sprrtl of (;P-RBFS hits
iiicreasril reliitivelj- convent.iona1 RBFN.
IitlFN to be used in adaptive fuzzy system ( A F S ) . in
comnion case. is a s s u m e d to be t.ririned by m e a n s of t h e D(P:
Q=-
iiiiniiiiuiii necessary nunibrr of rules (hidden unit
n u m b e r ) ilc.trrniin:ition a n d adjusting of t h e mean a n d
vwtorh of' iiithvidu:il hidd[,n nodes a s well as
v;iri:incc~ Thereforr. the C: KHFNAFS Jetc,rniines Ih c , " t r u r "
P
thrJir eight5 In t h i s p:iper. t h e simplest CP RBFN fuzz! rulrj n u m b e r b; incrt~iiir~nt;lli!
rwruii iny: I1 1 ~
li;isc~tl :idapt ive fuzzy system for aut.oinatic fuzz!- rule r a k i i l basis fuiiction units ant1 cant inuous est i n i i i t ion
niiinbrr tletemiination is proposed (Fig4). Only t h e of t.he approxlmtition quality through critrriii (4)
nrtworli weights have been a s s u m e d t.o be adjust.ed by evwluat.ion for each fixed GP R B F S structure. T h e
the' (:P algorithm while t h e c r n t r e s a n d widt.hs of unit network t o be determined is the network with 1r:ist
+nsit I V P zon6.s yere ooiiipletel>- tleteriiiined w i t h the v:ilue oi' i, anr! its unit n u m l ~ r rC :issiinic,~l h.
I to
n(,tworli input Gign;il r:iiigr :inil u n i t r,qu;il t o t h e f'uzzy r d c ~
nuiiilwr C I ~c l i t * "s:lnililt~"
i'uzz> .ystc"
Let consider t h e proposed procrdure in c1et.d for r h r
siiiiplest case of t h e (P RBFN AFS Lvith
: sciil;rr input
1 signal
i n p u t slgniil II ( E ' : u := 0 ) iintl linovn nuni1ii.r of
(:aussian units r] (for t h e first stage. y = I ) thr
sensitive zone center coor&n;ites :ire calculiitcd by
, relationship (5).
CP KBFN BASED AFS
- - ___
Figure4. G P RBFN adaptive furLy system
nuiiihrr during riich training rpoch
whrrr. I is ii current unit n u m b e r For y = I ;incl I =I
. "s:iniplr" fuzz!- systrm h a s been present.ed by RBFN
Ui t h I he "unknown" n u m b e r of hidden units (i.e.. fuzzy for rsiiiiiplr. o n r ['tin recrivr (': = 0
rules) Starting t'rom the single-unit-(;P-RBFN. the
nr.twork learning h a s been performed by t h e scii1:ir 3 ) The initial (basic) sensitive zone w i d t h rqu;il i'or all
grneriil piiriiiiieter iirljusting in the Learning netu.orli units I:, c;ilcul;itt.tl as ((5)
blorli ~
l ' r ~ ~ c c ~ ~ l u r ~ T h e stratly st iitr general p a r a m e t e r
( ~ ~ ~it T I
: I ion f<[fl ;ind viiriiince D { P ) have been
c,:ilcul:ittd hy GP Statist,ics Estimnt.or. The
;~pproxiniationquality cnterion (1B) w a s evalutit.etl for
( h p current (:P KRFN st.ructurr. rind decision on
rh;inging o ' nrtwork structure p:ir:iiiirter iicljusting
f
iii t IIP 1,riiriiing Prow[iurr, L~lock. T h e stezicly s t a l e
gr~iii~riil p:ir:iniet<Jr ~ ~ s p e c t ; i t i o n E[P}antl
viiriiince U ( P : have been c;ilculatrd by GP Stat.istics
l%timwt.or. The approx"t.ion quality crit.enon (1:3)
viis n ~ : i I i i ; i t c dfort he current (:P RBFN st.ructure. and
1384

4. IC; p r t o r n i e d biised on input-out,put s a m p l e d;itii In this section. the 1JnbiasediiessCriterion tisiiig Distorter I I K I ) )
;icwrtlingly to the ;iIgorithm ( 2 ) . Simiiltmeousl>- t h r approach( 8 I is used. which has been shon provldlng iiiiproved
features in coiiipare to conveiitioiial methods. such as ~ k a i k e
gc'nrr;il p;ir:iiii~ter iJspwt;it ion E { P ) and viiriiince
Infomiation Cntenon ( A I C ) [ 9 ] and its modification for neural
networks Network Infonnation Criterion (MC) [IO], f i n l n i u m
D[,& :ire estimated with some conventional method.
Descnption Length (MDL)[ I I].
for rs-ample. by t h e movlng average calculation. Let consider the IJCD method application to the GP RBFN A F S
The overall svstein block diagram IS shown ui Fig. 6.5
Both of them are (iP RBFN with a lemiing procedurs llie
same signals are ted uito the network inputs The diiYerelici: I 111
the u a y of the teaclung signal usage While the reaching signill is
fed mto uppa loop without any changes, the lower iietuork is
trained by "distorted", i.e. nonliiirarly traiisfonned, sample d ~ t a
The output of the lower network is also changed hv the
transfoniier of the same transfer function as fir teachins sgiitl
The critenon ol' the iietuork structure optimality is derivedI61.
nhich IS otthe tonnc 7)
%ax (*,; (:2
:1 0
- 60-. C: umax
I .( 'D = 5
/=I
(U ) - I.-? (7 ) ]
(7)
IJiguref,. Definition of GP RBFN basic parameters
where ' ' j-th set (vector) ofthe network input data. 17 overall
c.v;iIii,ii NI :iii(I iiiemorizrtl. variables of the both networks. Tlie structure of the netnork n i t h
the least value of the cntenon 7 1 is assumed to be a soliition ot
the problem
-
:'I ,-
-
'5 ... -
:,
,
,_
-
:!
,
- ...
: '
8 ) The strucciirr of GP RHFN is modified by one inore '.- . . .
[:iiussiaii u n i t recruiting: y = q + l . T h e st.eps 1) - 6)
:I r i a rvl)i.at 6.i I .Y , .VI
The, r r s i i l t of t h e algorif hni 1 ) - 8 ) imp1ement;ition is :I
Fig.6 Determinution of number of units by dibtorter
111 I'uiivtion u n i t s i n c:P IiBFS
The proposed general paaiiieter method in scctioii Ill I
,
$1h i ( . h provic1c.s I he best :ipproxiniating accur:icy In the
again illustrated in Fig.7.. This idear is extended to aii adaptive
car ti is of' fuzxy system theory i t iiieiiiis t h e fuzzy rule
structure genetic algonthm[j]. Geiiotvpe has an adaptive
ii ii m1)c.r clrtc~rminiitionproblriii solution. [8]
structure . The string representation is constructed by two l a y s
1V 1 IJ(il.1 PERFOIWANCE RI3k.N
One is nanied locus l a y . the other .operon l+er as slio!!ii iii
l'he prohiein of the reliahiliiy n1' the denved model is one of thc
IFig 8 For this reprcseiitatioii .live ne genetic o~)er~i~i~iiis
iirs
iiiost iiiipottaiit ones. ansing duruig the identitication task solving
detined in order to scll~orgaiii/t:the siring itriicture and dsvclo1)
Hic model over-titting prevention IS a crucial point tor inam
adaptive genctic change 111 the evolutioiial pro
y l c t i c a l iinplrmeiitations 11s i t WJS discussed ui the preceding
approach bnngs attractive optiiiiiimoii results fbr probizins
sections, there are several approaches to cope with this ditficultv
including (iA-dilticultv.Suice genetic algorithm and chaos
1385

5. Loinputnips are heuristic approaches, they have capabilities of a fashion.Namelv.onlv one antibodv is allowved lo activate and act
creative thinking ivav or evolution its corresponding its action to the ivorld 11' its coiiceiitratioii
H i these techniques the Iuzzv neural net in section III turns Into surpasses the prespecitied the threshhold As shovii in Fig10 . ilic
<I high pcrlbnnancr radial basis fuiictlon neural network concentration of the aiitibodv is influenced b the stimulatioii iuid
!
Fig.7 General parameter method suppression from other antibodies . the stiiiiulation froin antigeii.
String and the dissipation Factor t i c. natural death ). The concentration 01
I-th antibody .which is denoted by a, . is calculated b ( X )
! (I and
0 are the rate of interaction ainong antigens and antibodird.
+. ..... ....
~ a l u elist t i x e d lenzth
+ .~
........ _ - ~ _
Locur libel V V ............
~
.~ ......
V
General Parameter
. . _ ~ ~ -
...
..
..
.. .......
.......
......
N!:eight layer (fixed nominal value)
-. __ ..-
/I;, ... -- .........
Ili,,
-
li:,
.......
II, ... It,;,"
_- r
.---.; * -.:
*.
1 ......
......
? --
i ~ _ _ _
~
:
- ~-~
-~ .
.
.
._. .
~
~
Inputs : blutually Inputs : Mutually
Correlated ' Correlated_ _ -
I
.
. - .... - ...
I .. --
Fig.8 Adaptive string structure o f genetic algorithm N N N
V. SOFT COMPUTLNG I REACTIVE
N tlA,(tvdt=( (L ( XI11 il (1) XI11 ) n i Llll .<I. ( 1 )
DISTRIBUTED ARTIFICIAL J-I 1 1 k 1
INTELLIGENCE I
Is1l l G [ J R O 3 REACTIVE IIISTRIBIJTED ARTIFICIAL X IN:, - 0 111: k. ~ ii: (t) (8)
IN'TEI.Ll(;ENCE WITH M J E NETWORKS[Z] and [i]
MN k=I
i'he detected current situation and competence modules as il. ( t - I ) -1.. (l.rxp(O. 5 - A . ( t ) ) )
.iitigciis and Antibod~es,respzctiveI~ liere N IS die number of antibodies. a i d nil denotc~inatclinis
lo inake a iinonoido(antihody) select a suitable antibodv against ratio hrtneen antibod! I and antigen .m), denotes dcgrce 01
that
ilw wrreiit antigen, it IS highlv important I i o ~ the antibodies disalloance of antibod I for antibod! I 'The first and sccond
arc described .Moreover.it is noticed that the unmunogical tenns of nght hand side denote the stiiiiulatioii and supprzssioti
dntration inecliamsm select an antibody in bottom up manner by from other antibodies, respectively The thrd tenii represents lhr
~ommuiiicating aiiioiig the antibodies. To rwlize the above stimulation from antigen, and the forth tenn thtl natural death
-~ . . ~ _ _ _ ~ - .
rcquireineiits. the descnptioii the description of antibodies are -7zEED
Idiotour
defined as follons The identitv of a specific antibody is generally
. . . ~ ~~
ilcleniiinzd h? the stncture of its paratope and idiotope F i g 5
dcplcts thc represetitation of antibodies As shown iii this tigure.a
pair of precondition action t o paratope .the nuinher of
ll~wllord antibodies and thc degrce ot' disallowance to idiotope
,irc respectively assigned In addition, the structure of paratope is Food Bark Middle Hwkwud
Obsmclr I vtl FW KlEhi
J I ided into four portions: objects, direction,distance, and action. EnrrgY
_ i.cn and c , r .
. - ~
ni>d et,'
For adequate selection of antibodies . one state variable called Fig.9 Represent;rtion of antibodies
concentration is assigned to each antibody. The selection of
;Ilitibodics IS simply carried out i
n a wiimer-take a l b
1386

6. hi order to optimize this reactive distributed artificial intelligence. Heunstic Model Selection Cnterion I king Distorter and
h e deve1opr:d ftiziv neural net is applied to communication Its Application to Detenmiumatioii of the Nuinher oI
aiiioiig agents( antigens and antibodies ) The developed radial Hidden IJIUIS in RBFN', .louiial o t rhr: .lap Soc 01'
hasis function neural net is used to optimize parameters in (8) and Syt.Contr. and Inf.,Vol Il,N0.2,l99X.pp6 1-70
lbr a inetadyaniics whch produces and removes antigens and Y.Dote,"Sott Coniputmg( Immune Networks) 111
ailtibodies to make reactive tables.[f] Artificial Intelligence". Web.site:http-//bik.csse
Muroraim.Japan. I997
VL. CONCLUSION D FhE;hntetov.Y.Dote and M S ShaiMi."Sstriii
1111s paper proposes extaidtxl sott computing to construct 10% Identilicetion bv the (iciieral l'urumeier Netd
cos^ reactive distrihuted artificial intelligence resutmg in excellent Netuorks nith Fuzzy self-or~anizaiion"f'rep. o t the I I"'
decision iiiahng. Table IFAC SVmP on Svsrelll
I shows the comparison of the proposed system vvith fuzzy I 997.~~829-8.34
IdentiIication,Kitak~shu,Japaii,Vol.2,
svstems on decision making. H.Al;aike."A New Look at the Statistical Model
Ideiiti!ication".IEEE Tran. On AC.Vol 19.I974.pp71b
Tirblel Comparison of immune network- 72 3
based with fuzzy reiisoning approach M.Murata.S Yoslukava uid S.Aiiian."Nt.r~orL
Infonnation Cntenoii-l)eieniuiuimg die Nuinher ol'
Iiiiiiiuiic iietnork-bawd T'wn reasoning
Hidden IJiUts for Anilicial Neural Nelnork
t3ottoiii-up decentralized Top-dow~ centralized Model".IEEE Tran. on Neural
IIsplicit uiteraction Implicit interaction
1)viiamir: static Net,Vol.j,No.j, I994,pp865-872.
J kssanen,"A IJniversal Prior tor Integers and
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