Searching Optimal Buyer Coalition Structure by Ant Colony Optimization


 Edwina Mason
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1 Seachig Optial Buye Coalitio Stuctue by At Coloy Optiizatio Ao Sustiewog Abstact I ecet yeas, seveal buye coalitio schees have bee poposed by eseaches i ode to fo effective coalitios ad achieve the axiu beefit fo cosues i a electoic aet. Howeve, thee ae few algoiths applyig the at coloy optiizatio fo foig buye coalitio. I this pape, we peset the appoach based o the At Coloy Optiizatio (ACO). The appoach called the At Coloy Optiizatio fo Foig of Buye Coalitio (ACO_FBC) algoith fo the foatio of buye coalitio with budles of ites. The algoith ivolves seachig fo the optial buye coalitio stuctue by patitioig the whole goup of buyes ito salle coalitios so that the aggegate of discout of the whole buyes is axiized. A ube of atificial ats seach to fid the best disjoit subgoups of all buyes based o the total utility fuctios. The esults of the ACO_FBC siulatio ae copaed with the geetic algoith (GAs) i the tes of the global optial buyes' beefits. It idicates that i ost situatios ou poposed algoith sigificatly ipoves the utility of the buye coalitio. Keywods At coloy optiizatio, buye coalitio, coalitio stuctue, electoic coece, siulatio. T I. INTRODUCTION O date, thee exist seveal olie shops available o the Iteet such as, ad Soe of these olie shops adopt ay stategies to expedite thei sellig. Budle of ites ca be a ipotat issue fo selles. Budle of ites ae paced with a vaiety of ites ad piced a few lowe tha what they would be if bought idividually. Soe budles give bous ites that ca be obtaied by buyig a budle o the Iteet. I additio, soe olie shops lie offe wholesale pice to custoes. These pices ae usually about half the pice of soethig that could be puchased at etail stoe. But, the wholesale selles offe a pice at a 00% to the etail custoe. O the othe side, buyes pefe to obtai a deductio fo the pice list offeed by selles i etu fo payet. The accessibility of the Iteet ad lowe costs of doig tasactios have give ise i custoes bagaiig powe ad itese global copetitio [28]. Of couse, bagaiig is oe of the taditioal stategies fo buyes ad selle to each beeficial ageeets. Oe coo shoppig tactic which ost buyes ae liely to ae is a goup buyig because a lage goup of Ao Sustiewog is with School of Sciece ad Techology, Ifoatio ad Techology Depatet, Bago Uivesity, Bago, 00, Thailad. (eail: buyes gais oe egotiatig powe. A buye coalitio is set of buyes who agee to joi togethe to bagai with selles, so buyes ca gai volue discout pices. The othe stategy is the buye coalitio schee. Seveal buye coalitio schees exist with the ai of havig the best goup utility [], [3], [4]. Howeve, few schees coside foig goup of buye with budles of ites which ca be ofte occuig i the eal wold. Thee ae seveal oppotuities that it ca be happeed, such as a case that buyes caot puchase the budles of ites by thei ow because the pacages of poducts sold by selles ae coposed of hudeds of ites o ultiple type of ites. The algoith i [5] called GoupPacageStig schee applies geetic algoiths (GAs) to fo buye coalitios with budle of ites. Howeve, this algoith does ot coside the situatio of patitioig the whole goup of buyes ito salle goups. The patitioed goup is called a coalitio stuctue (CS). Soe eseaches have developed ad evaluated the pefoace of aytie CSG algoiths to seach fo optial coalitio stuctues i chaacteistic fuctio gaes (CFGs) [6]. It is also applied i ay coplex autooous applicatios as electoic aetplace, [7] []. The CS ais to axiize the utility of the coalitios, but ofte the ube of coalitio stuctues is too lage to allow fo the exhaustive seach fo the optial oe [2]. The optial solutio of the pobles ca esult at ay of the levels of the coalitio stuctue. Futheoe, fidig optial coalitio stuctue is NPcoplete. The size of the seach space is expoetial i the ube of agets. Give a set of ebes, A = {a, a 2,, a ad a subset o coalitio C A, thee ae two challegig stages ivolvig i this pape: Seach fo the best coalitio stuctue of all i which the uio of subsets equals A by usig the at coloy algoith (ACO). Copute the total utility of the whole goup. Give a coalitio stuctue CS, we deote the value of CS by V ( CS ) = v( C, CS ), () c CS whee v ( C, CS ) is the value of coalitio stuctue of C CS. Ad, the optial coalitio stuctue is oted as Issue 4, Volue 5,
2 CS * Hece, = ag ax V ( CS ). (2) i= CS L L is ow as a laye, ad the set of all CSs is i L = L. I CFG the value of each coalitio is give by a i chaacteistic fuctio which is siply defied as the su of the values of the coalitios that it cotais. Refeece [2] shows the calculatio of the total ube of coalitio stuctues as follow, a i= Z ( a, i), (3) whee a is the ube of agets. Ad Z ( a, i) is the ube of coalitio stuctues with i coalitios, Z ( a, i) = i * Z ( a, i) + Z ( a, i ), (4) whee Z ( a, a) = Z ( a,) =. If a is sall, a = 4, the ube of coalitio stuctues is 5, see Fig.. Howeve, whe ube of agets iceases liealy, the size of the poble, 2, iceases expoetially [27]. This is such a difficult tas to seach fo optial solutio whe the ube of aget is bigge. So, the algoith called ACO_FBC is poposed to seach fo the optial solutio. The poposed algoith is based o at coloy algoiths (ACO) which ae ispied fo the behavio of eal ats. The ajo shotcoig of the ACO_FBC is that it povides o guaatee to fid the optial solutio because ACO is oe of the heuistic fuctios. Howeve, it sees to wo well i ou pactice. The pupose of this pape is to seach fo the optial buye coalitio stuctue by applyig ACO techique. The pape is divided ito five sectios icludig this itoductio. The est of the pape is ogaized as follows. Sectio 2 descibes basic at coloy optiizatio. I sectio 3, we show the otivated exaple icludig the atheatical details of the poposed algoith. I sectio 4, we show the expeiets. To esue the quality of the algoith, the siulatio esults ae copaed with the GoupPacageStig schee. Fially, the coclusios ad futue wo ae i the last sectio. II. ANT COLONY OPTIMIZATION BACKGROUND At coloy optiizatio (ACO) is a pobabilistic techique fo fidig optial paths i fully coected gaphs though a guided seach, by aig use of the pheooe ifoatio [29]. It is a paadig fo desigig etaheuistic algoith fo cobiatoial optiizatio pobles [5]. The ai idea i at coloy algoiths is to use atificial ats that iteatively costuct solutios to cobiatoial optiizatio pobles. The fist ACO algoith was iitially poposed by Coloi, Doigo ad Maiezzo [2] [23] i 997 which ow as At Syste (AS). Now, thee ae seveal adaptatios of such algoiths to coplex optiizatio pobles [9], [7] [9], [24]. The global ats pefo a siple evaluatio of soe egios defied i the seach space, i ode to update the egios fitess. The ACO was applied to seveal pobles such as the tavelig salesa poble [7] ad the shop schedulig poble ad ixed shop schedulig [8]. I atue, eal ats ae capable of fidig the shotest path fo a food souce to thei est without usig visual cues [20]. The geeal stuctue of ACO algoiths ca be descibed as follows. Step : Iitialize the pheooe tails ad paaetes. Step 2: While (teiatio coditio is ot et) do the followig:  Costuct a solutio;  Ipove the solutio by local seach;  Update the pheooe tail o tail itesities. Step 3: Retu the best solutio foud. I the ACO, the pocess begis by iitiatig copletely ado ats. Theses atificial ats build solutios to a optiizatio poble while updatig pheooe ifoatio o its visited tail. Atificial ats build a feasible solutio by ecuetly applyig a stochastic geedy ule. While ceatig its tou, a at deposits a substace called pheooe o the goud ad follows the path by peviously pheooe deposited by othe ats. Oce all ats have copleted thei tous, the at which foud the best solutio deposits the aout of pheooe o the tou accodig to the pheooe tail update ule. The best solutio foud so fa i the cuet iteatio is used to update the pheooe ifoatio. The pheooe τ, associated with the lie joiig i ad j, is updated as follow: τ ( ρ) τ + τ, (5) = whee ρ is the evapoatio ate which ρ (0, ]. The easo fo this is that old pheooe should ot have too stog a ifluece o the futue. Ad is the aout of pheooe laid o lie (i, j) by at : / Q L τ = 0 τ whee Q is a costat, ad L is the legth of the tou pefoed by at. By costuctig a solutio, it stats fo the statig city to visit a uvisited city. Whe beig at the city i, the at selects the city j to visit though a stochastic echais with a pobability If lie (i, j) is used by at. (6) othewise, p give by: Issue 4, Volue 5,
3 whee N i is a set of feasible eighbohood of at, epesetig the set of cities what at has ot bee visited. α ad β ae two paaetes which deteie the elative ifluece of pheooe tail ad heuistic ifoatio, ad η, which is give by: p α β τ η α = τil ηil c il N i 0 η =, (8) d whee d is the legth of the tou pefoed by at betwee cities i ad j. III. SEARCHING OPTIMAL BUYER COALITION BY ANTS This sectio gives the foal defiitio of the buye coalitio addessed i this pape. The otivated exaple of ou poble is show to deostate the difficulty of the poble. A. The otivated exaple β if j N i othewise, Olie shoppig ifoatio such as ew poduct elease, pootio, ad othe ews ae ostly etieved aually by pospective buyes fo idividual website o webpage [25]. Suppose soe selles sell thee ids of poduct, x, x 2 ad x 3. Pice is oe of the ost ifluetial factos that ca easily icease o decease poduct dead [26]. Taditioally, these selles pepae a lage stoc of goods with ay attactive pices show i Table. We assue that these selles ca supply uliited ites of ay poducts. Ad, selle policy is based o o the ube of ites. The oe ites is with a sigle pacage, the oe discout. The pacage ube 3 ae sigleite pacages. The pacage ube 4 of selle coposed of oe ite of X, X 2 ad X 3 is set to be sold at the pice of 54.0 dollas, which is 0% of the oigial pice. The pacage ube 4 of the sae selle copised of oe ites (0 ites of X 2 ad ite of X 3 ) is set to be sold at the pice (7) of 80 which is 20% discout of the oigial pice. The axiu discout of the selle ube is 30%. The discout policy fo the selle ube 2 is diffeet fo the selle ube. The selle ube 2 has ade 5 diffeet pacages. The pacage ube 3 ae also a sigleite pacage. The pacage ube 4 of the selle ube 2 is copised of 50 ites of X. It is set to be sold at the pice of which is about 25% discout of the oigial pice. Selle TABLE I. Poduct (=3) THE EXAMPLE OF PRICE LIST Pacage X X 2 X 3 Pice ($) Discout of oigial pice (%) % % % % % % 0 eas that the selles do ot put the ite i the pacage. Buye TABLE II. THE EXAMPLE OF BUYER REQUESTS Buye equests (=3) Locatios X X 2 X 3 L =0 L 2=5 L 3=30 a a a a eas that the buyes do ot wat to buy that ite. Fig. Coalitio stuctue of 4 buyes show i [4] Issue 4, Volue 5,
4 Moeove, if the buye puchases oe ites fo oe selle, this buye ay get fee shippig. I electoic aetplaces, ay buyes coe fo diffeet places because the buyes ode poducts fo aywhee fo the iteet. Suppose thee ae thee buyes called a, a 2, a 3, ad a 4. Afte they have see the pice list of both selles, they have ade thei decisio to buy soe poducts. Of couse, buyes pefe to puchase poducts as lowe as they ca. Howeve, they do ot wat to buy the whole pacage to get the special pice. They have coe to joi thei equests i the goup buyig. Thei equests ae show i the Table 2. As we ca see, the a ad a 2 ae esided i the sae aea, locatio L. If they joi thei equest, the selle set the whole pacage to oe of the without shippig cost. Ad, the best pacage fo both a ad a 2 is pacage ube 5 fo the selle ube. They would pay at ost 70.0 dollas. Suppose a 3 ad a 4 asseble thei equest to buy the pacage ube 5 fo the selle ube 2. They eed to pay at least 525 dollas icludig the shippig cost. It is because they ae esided i the diffeet aeas. I geeal case, the selle would sed the whole pacage to oe peso which has the lagest dead without the shippig cost. So, the selle ube 2 seds the pacage ube 5 to a 3. The, a 3 seds 0 ites of X 2 to a 4 with the cost of 5. The total spedig fo both a 3 ad a 4 ae = 785 dollas. As the buye coalitio is foed, a) Gaph of solid lie epesetig the ebeship of the sae sub goup b) Gaph of dotted lie epesetig the elatio betwee sub goups Fig.3 The exaple of gaph epesetig fo {{b,b 3,b 8,b 2,{b 2,b 4,b 5, {b 6,b 7,b 9,b 0,b a) Gaph of solid lie epesetig the ebeship of the sae sub goup the total sped is = 955 dollas. If all buyes uite ito oly oe goup, they eed to buy a set of pacage ube 5 fo the selle ube ad a set of the pacage ube 4 fo the selle ube 2. The total cost is = 940 dollas. Howeve, buyes ae located i diffeet places. The selle set all poducts to a 3 because a 3 has the biggest ode. Whe a 3 gets the poducts, a 3 passes 5 ites of X to a with the shippig cost of 0. Ad, a 2 seds 5 ites of X ad 2 ites of X 3 to a 2 with the shippig cost of 0 dollas. Fially, a 2 seds 0 ites of X 2 to a 4 with the shippig cost of 30 dollas. The total shippig cost is = 35. So, the total spedig fo foig the goup buyig is = 975 dollas. As we ca see that i this case foig the goup buyig by patitioed the whole goup ito salle goups, {a, a 2 ad {a 3, a 4, uses lowe cost tha foig the whole buyes ito oe big goup {a, a 2, a 3, a 4, which is about = 20 dollas. The poble is that how ca we fid the optial solutio. Specially, whe the ube of buyes is big, the possible ube of patitioed goups is also big. b) Gaph of dotted lie epesetig the elatio betwee sub goups Fig.2 Repesetig the possible elatioship betwee buyes (ube of buyes = 2) B. The ceatio of paths though the disjoit subsets of all buyes I the fist step, the poble is epeseted as gaph whee the optiu subgoup of buyes ca be defied i a cetai way though this gaph. To follow the ats to wal though the gaph of CS, the ew epesetatio of gaph is defied as show i Fig. 2. Give a set of 2 buyes, B = {b, b 2,, b 2, thee ae two possible lies coectig betwee each buyes. Howeve, due to the seveal lies betwee buyes, the gaph is split ito two gaphs; oe is the solid lie epesetig the Issue 4, Volue 5,
5 ebeship of the sae sub goup, ad the othe is dotted lie epesetig the elatio betwee sub goups. Fo of buyes, the total lies coected betwee two buyes is equals 2(). Ad, the total lies of the poble is equal to 2((+)/2) = (+). So, fo = 2, thee ae 2(2) = 22 lies betwee two buyes ad the total lie of the whole gaph is 2(2+) = 56. If oe of the coalitio stuctue is {{b,b 3,b 8,b 2,{b 2,b 4,b 5,{b 6,b 7,b 9,b 0,b, the possible gaphs of this paticula coalitio stuctue poble is show i Fig. 3. Thee ae 3 sub coalitios; {b,b 3,b 8,b 2, {b 2,b 4,b 5 ad {b 6,b 7,b 9,b 0,b. Fo the fist sub coalitio, the solid lie coects two ebes i {b,b 3,b 8,b 2. Rule applied to the foatio of buye coalitio with of buyes. a. Thee ae two types of lies; solid lie ad dotted lie; coected betwee two buyes. b. Fo geeatio the solutio via ACO_FBC algoith, the algoith allows each buye holds exactly two lies. C. Poble foulizatio The poposed algoith ivolves patitioig a set of eleets ito subsets based o the utility fuctio that ae associated to each subset. The foulizatio of the ACO_FBC algoith ca be descibed as below. Give a set of buyes A = {a, a 2,, a, thee ae two ids of elatioships betwee two buyes which ae epeseted by edges. If buye a i ad a j, i j, ae i the sae subgoup, thee is a path usig solid lies to wal fo a i ad a j. But, it is ot ecessay to have a solid lie diectly coectig betwee a i ad a j. Let A is divided ito diffeet = = goups ( C, C,..., C ) ad 2 C = φ, C A, whee. = Thee exits a dotted lie coectig betwee C ad C l whee l. Fo exaple, let a set of A = {, 2, 3, 4, 5, 6, the coalitio stuctue of A ae show i Fig. 4. But, fo ou ethod the gaph ca be epeseted i Fig. 5 (a). Buyes ae epeseted as vetices. So, thee ae exactly 2*(6) = 0 lies fo each buye to coect to othes. If A is divided ito two subgoups, C = {, 2, 4 ad C 2 = {3, 5, 6, the gaph epeseted the elatio aog buyes ca be show i Fig. 5(b). Also, it ca be epeseted as Fig 5(c). These gaphs ae ceated duig the seach by atificial ats so they ae called the ACO_FBC gaph. If A is divided ito thee subgoups, C = {, 2, 4, C 2 = {3, 6, ad C 3 = {5, the the gaph epeseted the elatio aog buyes ca be show i Fig. 5(d). The exaple of the ACO_FBC gaph of {,2,3{4{5{6 is show i Fig. 5(e). The ats built the path fo each buye to uvisited buyes util all the buyes have bee visited. This eas that each buye ca be visited oly oe tie duig the costuctig of the path except fo the fist buye. The, the ACO_FBC gaph becoes the closed gaph. I additio, the total ube of edges fo costuctig the ACO_FBC gaph is , whee is the ube of buyes. I this pape, the poposed algoith elies o the assuptio that the value of a coalitio is idepedet of othe coalitios i the coalitio stuctue. All buyes i the goup paticipate i the pocess of the algoith, ad each buye is epeseted exactly oce i the ACO_FBC gaph. At the begiig all of the pheooe values of each pacage ae iitialized to the vey sall value c, 0 < c. The atificial at, called at, chooses all ebes fo fidig the best goup s utility o etu. Afte iitializig the poble gaph with a sall aout of pheooes ad defiig each at s statig poit, seveal ats u fo a cetai ube of iteatios. The pobability of the at to choose oe ebe called i to joi with the othe called j with the elatio (whee T = {dotted lie, solid lie) is below: p defied foally as Fig. 4 Coalitio stuctue of six buyes Issue 4, Volue 5,
6 whee D is the costat value, ad both U ad { a U ae, a {{ a i j {{ a i j deived by (8) ad (9). The pheooe τ, associated with the lie joiig a i ad a j, is updated as follow: (a) All of the possible paths coectio aog six buyes τ ( ρ) τ + τ, (2) = D. ACO_FBC algoith The ACO_FBC algoith fo foig buye goup with budles of ites ca be descibed by the followig pocedue: (b) {, 2, 4{3, 5, 6 (c) {, 2, 4{3, 5, 6 (d) {, 2, 4{3, 6{5 (e) {, 2, 3{4{5{6 p α β ( τ ) ( η ) α = ( τil ) ( ηil ) d d i l A d T 0 β whee α ad β ae two paaetes which deteie the elative ifluece of pheooe tail ad heuistic ifoatio ad is the aout of pheooe laid o the lie betwee τ a i ad a j o eithe solid lie o dotted lie by the at defied as follow: /( Uc ) τ 0 If = dotted lie, the C = {{ ai { aj. If = solid lie, C = {{ a i a j. Ad, η is give by: ( D Uc = η = ( D Uc = Fig.5 The ACO_CS gaph of {,2,6{3,4{5 ) {{ ai { aj ) {{ ai, aj if = 0 if l A ad a l has ot bee selected (9) othewise, if a i ad a j wee selected by at with the elatio, (0) othewise. othewise, () Pocedue ACO_FBC(){ Iitializatio all pheooe values to a sall ueical costat c > 0  Iitializatio of the ACO_FBC  T = {0 = dotted lie, = solid lie; while ot (isfiish(iteatio )){ fo At = to MaxAt { MaageAtsActivity(); EvapoatePheooe(); Calculate the Utility based o (8) ad (9) ad save the best solutio foud so fa. UpdatePheooe(); MaageAtsActivity(){ While ot (isatfiish(tou)){ Choose a buye a i to be visited with pobability p i (9), (0), ad (). If selected path is a dotted lie (T=0), the {a i sepaate with {a j. If selected path is a solid lie (T=), the {a i uio with {a j. EvapoatePheooe(){ Old pheooe should ot have too stog a ifluece o the futue. The evapoatio ate value is ρ which is iitialized to be sall, ρ (0, ]. UpdatePheooe(){ Update the all the path accodig to (2). E. Algoith evisited ad its Exaple Give a set of six agets as show i Table, the syste as a whole ust see a axiizatio of its beefits. The poble we solve i this pape depeds o two factos, buye equest ad buye locatio. Each aget ca have seveal equests of X i. Agets joi with othes whe they get the best utility that is defied i the utility fuctio (see (3)). Issue 4, Volue 5,
7 Suppose the cuet at, called at, chooses the aget fo the statig poit. The, the at seaches fo the ext agets based o the pobability p show i (9). If thee agets,, 2 ad 6, have bee chose espectively to be i the sae sub goup deoted as {, 2, 6. I the ACO_CS algoith, the cuet at geeates the path coectig aog selected agets. Theefoe, solid lies ae used to joi thee of these agets, See Fig. 6(a). The utility of the subgoup {, 2, 6 is 575, see the calculatio of Util {,2,6. Agai, the cuet at fids the ext aget with the pobability show i (8). Suppose that the at chooses the path fo vetex 6 via a dotted lie to aget 3, see Fig. 6(b). If the aget ube 3 ad 4 have high possibility to be chose ito the sae sub coalitio, deoted as {3, 4, the the at chooses a solid lie betwee 3 ad 4, see Fig. 6(c). The utility of {3, 4 is 450, see the calculatio of Util {3,4. The last aget, aget ube 5, is joied with o oe. It is a isolated aget, theefoe this aget is coected with the othe by two dotted lies, see Fig. 6(d) ad Fig. 6(e)). Its utility is 330, see the calculatio of Util {5. The, the coalitio ca be witte as {,2,6{3,4{5 with the gad total utility of 355. Fially, the at deposits the aout of pheooe o the tail accodig to the pheooe value i (0). U C = a C a a ( L * ), X i = a = C a a ( L * ), 2 X z a ( * ) 2 * i = a a K X + K Max a = ( ( * )) 3, C Li X K = a C i = =... a a ( * ), L X i = z a C = (3) whee K, K 2 ad K 3 ae the costat, ad X a is the equest X of a aget a. So, = v ( CS). (4) U C C Let s the costat K =00, K 2 = 2, ad K 3 =50. So, utility of each sub coalitio, {, 2, 6, {3, 4, ad {5 ca be calculated as follows. Util {,2,6 =K (2++2+2)+K 2 (4*5)(4*5+2*0+*5)K 3 = 00*7+2* = 575 Util {3,4 =K (2++3)+K 2 (2*30)(2*30+4*5) K 3 = 00*6+2* = 450 Util {5 =K *4+K 2 (4*0)K 3 = 00*4+2*4050 = 330 v ( CS) = U C C = Util {,2,6 + Util {3,4 + Util {5 = = 355 (a) Costuctig {,2,6 (b) Costuctig {,2,6{3 (c) Costuctig (d) Costuctig {,2,6{3,4 {,2,6{3,4{5 (e) The fial gaph of {,2,6{3,4{5 Fig. 6 The ACO_CS gaph of {,2,6{3,4{5 IV. SIMULATION AND EXPERIMENTS This sectio explais the idea of how the ACO_CS algoith by usig a epiical exaple. The, it shows the expeiet esults i detail. I the expeiet, we use the paaeteized fuctio as stated i (3) ad (4), so that we ca egulate soe data ad alte the seach space to obseve ou poposed fuctio i pactice. I ou algoith, we assue that all buyes ae equested to paticipate i costuctig the coalitio stuctue. To test the ACO_FBC algoith, a siulatio was developed usig Java pogaig laguage. The siulatio us o a Petiu(R) D CPU 2.80 GHz, 2 GB of RAM, IBM PC. ACO_FBC paaetes iclude α = 0.5, β =, ad the ube of atificial ats = 000. Seveal expeiets have bee coducted usig a diffeet set of buyes by ado with 5, 0, 20, ad 30 buyes espectively while the pice list is show i Table. The suay esults of ou expeiets ae peseted i Issue 4, Volue 5,
8 Table 3. I ost cases, the aveage esult (te us) of all tests deived by the ACO_FBC algoith is bette tha the esult of GoupPacageStig schee. Fo test we ca see that whe the ube of buyes is sall, =5, both ACO_FBC algoith ad GoupPacageStig schee give siila esults. This is because fo this specific test the whole goup of buyes caot be patitioed. All of these five buyes should be joiig i a sigle goup, so both ACO_FBC algoith ad GoupPacageStig schee have vey siila esults. Howeve, whe the ube of buyes is bigge ( > 5), ACO_FBC algoith sees to wo bette, see test ube 24. It seaches the bette coalitio stuctue yieldig the optial scoe. I aveage, ACO_FBC algoith yields about ( )/3 =.84% bette tha the GoupPacageStig schee. This is because the GoupPacageStig schee seaches fo the optial esult fo the whole goup of buyes, while ACO_FBC algoith patitios the whole buyes ito salle subgoups i ode to fid the best utility. Test No. Nube of buyes () TABLE III. SIMULATION RESULTS Expeietal Results Aveage of Utility (0 us) ACO_FBC algoith Nube of sub coalitios Aveage Utility (% ove GoupPaca gestig) (0%) (8.37% ) 88.0 (6.52%) (0.64%) GoupPacageStig Nube of sub coalitio s V. CONCLUSIONS AND FUTURE WORK Aveage Utility I this pape, we peseted a ethod seachig fo the optial buye coalitio stuctue whee the buye coalitio is foed though the use of at coloy optiizatio techique. The poposed algoith called ACO_FBC algoith is based o a iitatio of the foagig behavio of eal ats. The efficiecy of the ACO_FBC algoith was evaluated though the pefoace of seveal expeiets, fou diffeet sets of buyes by coplete ado. The siulatio esults show that the aveage utility of ay coalitios foed by ACO_FBC is bette tha the GoupPacageStig schee. It has bee cocluded that the ACO_FBC algoith ca be efficietly used fo seachig the optial buye coalitio stuctue pobles. Howeve, thee ae soe estictive assuptios fo ou poposed algoith as follow: ) The buye coalitio is foed coceig oly the pice attibute. 2) Buyes ca ae ode equests with seveal choices of ites. 3) Budle of ites is paced with a vaiety of ites i a pacage at oe pice which is below the su of the idepedet pices. The aveage pice of each ite will be cheape tha the pice of a sigleite pacage. 4) Selles ca supply uliited ites of ay poducts 5) the discout policy of selles based o the ube of ites budled i the pacage. These estictios ca be exteded to ivestigate i futue eseach. We also pla to adapt the poposed algoith to othe ealcoplex wold pobles to see how well to apply. Futue wo will iclude ivestigatio of the ACO_FBC algoith pefoace i othe algoiths ad eal life pobles. REFERENCES [] K. Laso ad T. W. Sadhol, Aytie coalitio stuctue geeatio: A aveage case study, I Poceedigs of the Thid Iteatioal Cofeece o Autooous Agets, New Yo: NY, ACM Pess, pp , 999. [2] T.W. Sadhol, K. Laso, M. Adesso, O. Shehoy, ad F. 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9 [8] T. Yaada, ad C.R. Reeves, Solvig the Csu peutatio flowshop schedulig poble by geetic local seach. i: Poc. of 998 IEEE Iteatioal Cofeece o Evolutioay Coputatio, pp , 998. [9] D. V. Dag ad N. R. Jeigs, Geeatig coalitio stuctues with fiite boud fo the optial guaatees, I AAMAS, 2004, pp [20] M. Doigo, L.M. Gabadella, At coloies fo the tavelig salesa poble, BioSystes 43, pp. 73 8, 997. [2] A. Coloi, M. Doigo, ad V. Maiezzo, Distibuted optiizatio by at coloies, i: Poc. of ECAL'9, Euopea Cofeece o Atificial Life, Elsevie Publishig,Asteda, 99. [22] M. Doigo, V. Maiezzo, ad A. Coloi, The at syste: a autocatalytic optiizig pocess, Techical Repot TR906, Politecico di Milao, 99. [23] M. Doigo, Optiizatio, leaig ad atual algoiths, Ph.D. Thesis, Politecico di Milao, Milao, 992. [24] J. Raa, T. Mila, ad S. Daa, At Coloy Optiizatio Applied to Miiu Weight Doiatig Set Poble, i Poc. of the 2th WSEAS Iteatioal Cofeece o Autoatic Cotol (ACMOS '0), Modelig & Siulatio, Cataia, Italy, May 293, 200, pp [25] Lee Yea Hooi, Mohd Aza Osa, Rosah Idus, Ta ShiagYe, Acceptace Level of Push Techologybased Olie Shoppig Widget aog Malaysias: Applicatio of Techology Acceptace Theoy, WSEAS Tasactios o Busiess ad Ecooics, Volue 7, pp , 200. [26] H.J. Yu, X.Y. Li, ad Y.X Wag, Picig Stategy of Ecological Idusty Chai Based o Gae Theoy, WSEAS tasactios o systes, vol. 7, pp. 780, [27] S. Chattaul, Advaces i Pactical Optial Coalitio Stuctue Algoith, Docto of Philosophy Thesis, School of Sciece ad Softwae Egieeig, Faculty of Ifoatics, Uivesity of Wollogog Thesis Collectio s, 200. [28] Ab Haid, NR., Cosues' Behaviou Towads Iteet Techology ad Iteet Maetig Tools, Iteatioal Joual of Couicatios, Volue.2, No.3, pp , [29] Aa Veoica Bateia ad Calos Oppus, Iage Edge Detectio Usig At Coloy Optiizatio, Iteatioal Joual of Cicuits, Systes ad Sigal Pocessig, Issue 2, Volue 4, pp , 200. Ao Sustiewog eceived the B.Sc. i applied atheatics fo Kig Mogut s Istitute of Techology Ladabag, Thailad i 992. He eceived his aste s degee i egieeig fo the Uivesity of Coloado, Deve, U.S.A. i 994. He is cuetly a assistat pofesso i the depatet of copute ad techology at Bago Uivesity i Bago, Thailad. His cuet eseach iteests iclude: evolutioay ultiobjective optiizatio, evolutioay algoiths i geeal. Issue 4, Volue 5,