AN EFFICIENT AND ROBUST GENETIC ALGORITHM APPROACH FOR AUTOMATED MAP LABELING

Transcription

1 AN EFFICIENT AND ROBUST GENETIC ALGORITHM APPROACH FOR AUTOMATED MAP LABELING Fan Hong * Lu Kaun 2 Zhang Zuxun Natonal Laboratory of Informaton Engneerng n Surveyng Mappng and Remote Sensng of Wuhan Unversty No.29 Luoyu Road Wuhan Chna Zp code:4379) 2 Management college of Huazhong Unversty of Scence and Technology Luoyu Road Zp code: 437) Keywords: genetc algorthm label placement optmal combnaton problem mutate on conflct gene comparson experment ABSTRACT: Ths paper put forward an new soluton whch adopted the genetc algorthm to obtan the global optmal soluton approxmate) of automated label placement of pont feature. In the paper the basc thought and desgn framework of usng genetc algorthm to solve pont feature labellng was frstly ntroduced then some practcal technque and new mproved method durng the experment procedure of genetc algorthm adopted by the author were presented n detal. Fnally n order to prove the advantage of genetc algorthm some experment were conducted whch compare the effcency of genetc algorthm wth hll clmbng algorthm smulated annealng neural network etc. The result of comparson experment was gven out whch has proved the superorty of genetc algorthm especally proved the genetc algorthm s a knd of hgh-effcent robust all-purpose algorthm wth wellexpansblty and s the most promsng soluton for automated map labellng. I. INTRODUCTION Label s an mportant component of a map wth the ad of map label user can recognze the mportant obects and obtan ts relevant nformaton of obects. However for a long tme map label has been a tme-consumng manual work. So the automated map label has been always one of the mportant study contents of computer-aded cartography all the tme. On the other hand the automated map label s one artfcal ntellgence puzzle. It has been already proved that fndng the optmal soluton of automated map label s a NP-hard problem [Marks 99]. Ths paper put forward one new approach to fnd the global optmal soluton of automated map labelng wth genetc algorthm. Genetc algorthm s a knd of method wth global searchng characterstc. It orgnates from smulatng the bologcal evoluton course of nature and possesses many merts ncludng hgh-parallel self-organzaton self-adaptaton selflearnng and hgh effcency etc. Besdes genetc algorthm s smple easy to operate and expand. Through plenty of experments we thnk genetc algorthm s a potental soluton for automated map labelng. II. TRADITIONAL METHOD S DISADVANTAGES It has gone nearly thrty years snce Yoel began to study pont feature labelng and many scholars have put forward varous method to solve pont feature labelng problem [Yoel 972; Imhof 975; Ahn Freeman 984; Langran and Polker 986; Zoraster 99; Chrstensen ef.al ]. In the eghtes of 2 th century a lot of automated labelng expert system were developed [Zoraster 99] that ncludes NAMAX AutoNapetc. The dsadvantages of expert systems s low-effcency and great developng cost. Another routne algorthm s exhausted searchng algorthm [Jones 989; Cook and Jones 99; Ebnge and Goulette 99; Doerschler and Freeman 992]. These algorthm can be expressed as searchng n dgraph or drecton tree whch mght cause concatenate backtrackng and even deadlock So ts severest problem s low effcent therefore t s only ft to small-scale problem. Another knd of mportant algorthm s a knd of searchng strategy based on the problem soluton space. Representatve examples nclude the energy mnmzaton algorthm put forward by Hersch [Hesh 982] and the dscrete gradent descent algorthm [Chrstensen ef.al ] etc. There possbly appear two knds of problems n these local search algorthms. Frst they do not accept degenerated soluton therefore unable to ump out the local mnmum trap; second t may fall nto dead loop. III. POINT LABELING RULES Consder pont labelng accordng to the common labelng prncples combnng Chnese topographc map plottng pattern and regulatons n the labelng experment of the resdence topographc map wth the scale :25 our research wll focus on the followng three mportant prncples especally:. The canddate postons and ther prorty: generally the canddate poston of pont feature labelng has four knds of stuatons ncludng four-canddate-poston fve-canddateposton eght-canddate-poston and n-canddate-poston. Four-canddate-poston as ndcated n fgure a) regard the rght as frst top left and bottom followed respectvely n successon these labelng postons can be marked wth prortes from to 3. Fve-canddate-poston as ndcated n fgure b) smlarly regard the rght as frst the next are top left bottom rght-vertcal respectvely n successon these labelng postons are expressed wth prortes from to 4. Eght-canddateposton as ndcated n fgure c) regard the rght as frst the next are top left bottom rght-top left-top left-bottom rghtbottom respectvely n successon these labelng postons are expressed wth prortes from to 7. The n-canddate-poston s llustrated n fgure d). 2. Forbd conflct: the labels of pont features can t overlap conflct ) wth one another. * fh@mal.lesmars.wtusm.edu.cn

2 3. Forbd and avod overlap: Pont label should not overlap the mportant lnear feature of the same color such as ralways and maor roads etc Whle overlap s unavodable efforts should be made to decrease t. ) Determne the encodng framework; 2) Generate ntal populaton; 3) Determne the ftness functon; 4) Desgn genetc operator ncludng selecton crossover and mutate operators; 5) Determne the mportant parameters of genetc algorthm. Fgure the canddate labelng poston of pont feature Ths paper studes the labelng problem of the followng two knds of pont features manly. The algorthm of solvng fourcanddate-poston s easy to expand to apply n the stuatons of 5 8 and n canddate-poston. Problem I: consder the pont feature n map f adoptng fourcanddate-poston labelng mode namely choosng the rght top left and bottom four canddate postons of pont feature respectvely as ndcated n fgure a) the dstance between label and pont resdence s mm) try desgnng and mplementng labelng algorthm to make globally conflct least. In the actual labelng problem besdes consderng elmnatng label conflct also need to consder dodgng mportant map features and choosng the canddate pont wth hgher-prorty thus the above problem becomes more complcated problem as follow. Problem II: consder the pont feature n map f adoptng fourcanddate-poston labelng mode namely choose the rght top left and bottom four canddate postons of pont feature respectvely as ndcated n fgure a) the dstance between label and pont resdence s mm) try desgnng and mplementng labelng algorthm make globally conflct least the overlap to other features mnmum and the labelng poston optmal. IV. GENETIC ALGORITHM OF SOLVING POINT FEATURE LABELING Because genetc algorthm s an all-purpose algorthm wth extensve applcablty n desgn often need combne tself wth the specal rule of problem doman. In applcaton course we have put forward some optmzaton strateges accordng to the characterstcs of labelng problem and has mproved the performance of the algorthm greatly. The remans of ths paper wll n detal ntroduce our genetc algorthm and some crucal desgn theores and optmzaton strateges adopted by our genetc algorthm. 4. Determne encodng framework The map label s the optmzaton target of genetc algorthm. One of the map placements can be expressed wth a nteger vector. Each component represents the localzaton of one label. Assumed there are m canddate postons whch can be expressed wth codes of ~m- for nstance when consderng four-poston label the four canddate postons can be expressed wth the codes of ~3. Encode the map label placement wth nteger vector and a pece of chromosome s a nteger vector representng an nstance of a map label placement. The length of chromosome s n the number of pont features label) and every component gene) represents one pont feature label the doman of gene s [ m-] where m s the number of canddate postons the gene code set of four-canddate-pont labelng problem s { 2 3}. Now fgure 2 gve an example t shows a map wth twenty pont features one placements of ths map and the correspondng chromosome encodng. Genetc Algorthm was developed by Professor J.H.Holland hs fellows and hs students n Mchcan Unversty of U.S.A. n the sxtes of the twenteth century. At present t has been appled to solve varous optmal problems such as layout scheme selfadaptve control game rules pattern cognton transportaton problem travellng salesman problem optmal control and database query optmal etc most of them are famous NPcomplete problems[zhou Mng 999 ]. The bology has been always evolvng accordng to the rule of survval of the fttest and natural genetcs course genetc algorthm s exactly the randomzed calculatng model orgnated from smulatng the bologcal evoluton course. In the solvng course genetc algorthm always keeps a populaton of potental soluton. Begn from one ntal populaton through selecton crossover and mutatng to produce the next generaton populaton n ths way seek the optmal soluton generaton after generaton untl meetng the termnatng condton. In order to solve one gven problem genetc algorthm must go through the followng fve steps generally [Zbgnew Mchalewcz 2]: Fgure 2 Pont feature labelng placement and ts encodng 4.2 Generate ntal populaton Accordng to the characterstc of labelng problem the followng strateges to generate ntal populaton was adopted. ) Randomly generate an ntal populaton wth certan sze and randomly select every gene for the chromosome. 2) Accordng to the characterstc of labelng problem for all free labels when selectng optmal poston for them overlap and conflct never appear) n ntal populaton select the optmal postons for the correspondng genes of all chromosomes.

3 The above ntal populaton strategy has selected the optmal postons for free labels. That means free label s poston can be solved wthout through optmal process. It also means the reducton of the scale of problem and the acceleraton of the evolvement of genetc algorthm. 4.3 Determne the ftness functon The target of labelng problem s to fnd the label placement wth the hghest qualty. Therefore the ftness functon s defned as the labelng qualty evaluaton functon. Here adopt such a way: frst defne a labelng qualty evaluaton functon whch consders these factors ncludng conflct overlap poston prorty and so on now adopt the way of markng namely mark the conflct overlap and poston prorty of each label and then calculate the total score of each label through weghted average of summaton fnally calculate the summaton of all the labels thus obtan the score of the whole labelng placement. The hgher the score s the hgher the labelng qualty s ths s exactly consstent wth the meanng of the ftness functon the larger the ftness value s the better the ndvdual s). Accordng to ths thought by referrng to the demands of optmzaton target of dfferent labelng problems defne the correspondng ftness functon. Now ntroduce t wth two examples of optmzaton targets.. The least conflct target Frst consder the pont labelng problem I; t only consders the optmzaton target of least conflct. Under ths knd of stuaton defne of the ftness functon see equaton ). ft L) = N E conflct L ) = If < < n d L L ) > ) E ) = ll conflct L 2) otherwse Where E ) conflct L s - conflct evaluaton functon whose defnton s shown n expresson 2) n whch L represents the label of -th pont feature when there s no conflct between and the other labels the functon equals otherwse t equals. Ths knd of ftness functon s defned as the sum of the labels whch don t overlap wth other labels. By usng ths knd of ftness functon genetc algorthm can solve the global conflct better. 2. The target of the least conflct overlap and optmal poston Now consder the pont labelng problem II t has three optmzaton targets and the ftness functon needs to consder conflct overlap and poston prorty therefore defne the ftness functon as equaton 3): E L ) = E L ) W overlap E overlap L BF) = + W poston E poston L ) N ft L) = E L ) = 3) Where we let W over l ay = ; W = The meanng of every symbol s as follows: ) f L.. don'.. t Conflct) otherwse pos t on. L E L BF represents the overlap evaluaton value when overlay L s on the canddate poston f adoptng smple overlap evaluaton functon t s defned as the hghest mportance weght of the features overlapped wth the label when there s no overlap E L BF =99 the hgher the mportance of overlay overlad feature s the severer the overlap s accordngly the lower the overlap score s. BF represents the -th background feature overlad by the label; the predcate overlap O O2 ) ndcates the two obects O O2 overlap wth each other. Now defne E L BF as overlay E overlap L BF) = 99 no... overlap 99 max{ W BF ) overlap L BF ) BF BF} wth.. overlap 4) In equaton 4) W BF ) represents the mportance evaluaton functon defned by background feature t value called mportance grade or weght). Smlarly adoptng the mark system ~99 the score of the feature whch can t be overlad s 99 the lower the mportance the lower the score s the score of the feature wth the lowest mportance s. Now defne W BF ) as equaton 5): W BF ) = ~ E L pos t on represents the poston evaluaton value when s on the canddate poston adopt sorted poston evaluaton functon and s calculated accordng to equaton 6). When the canddate postons are fnte and can be enumerated such as four-poston labelng or eght-poston labelng). We sort them n the descendng order of ther prorty let Pos L ) L represents the -th labelng poston of L Order Pos L )) represents the order number of canddate the the the mn mal medan max mal mpor tan ce mpor tan ce mpor tan ce poston after sortng we can defne the poston evaluaton functon as the dfference of 99 and Order Pos L )). Namely the score of the poston wth the hghest prorty s 99 the scores of the other postons decrease n order. The defnton of E L pos t on see equaton 6): Eposton L ) = 99 Order Pos L )) By adoptng ths knd of ftness functon genetc algorthm not only solves conflct but also solve the optmzaton of the overlap and poston prorty. In addton f only consder the target of least conflct and most optmal poston let W over l ay = n equaton 3) then We can have equaton 7): 6) 5)

4 E L ) = E L ) W ) = poston E poston L N ft L) = E L) = Where W pos t on =. Now consder the example n fgure 2 the fgure gves out ts chromosome. Consder the targets of least conflct and most optmal poston adopt the ftness functon 7) and calculate ts ftness value: 4.4 desgn genetc operators 4.4. Selecton operators The labelng algorthm adopts roulette-wheel selecton as selecton method. When the populaton sze s very large can use elte strategy namely retan the optmal ndvduals of the prevous generaton nto the next generaton s populaton. The mplementaton algorthm of roulette-wheel selecton s as follow: ) Calculate the ftness value of ndvdual 2 n) ft V ) =... ; 2) Calculate the accumulatve ftness value of ndvdual Accft V ) 2... n) value laccft V ) 2... n) = and relatve accumulatve ftness Re =. 3) Generate a random r n [ ] here suppose Re V ) = laccft If RelAccft V ) < r RelAccft V ) 2... n) then select the ndvdual. If L wthout conflct otherwse 2 ft L) = E L ) = = 96. = 7) = The pont-crossover operator s dvded nto sngle-pontcrossover and multpont-crossover. The sngle-pont-crossover randomly selects a cross pont on two father strngs and then exchanges the correspondng sub-strngs of the two strngs. The multpont-crossover randomly generates several cross pont every tme and then exchanges the correspondng sub-strngs of father strngs respectvely [Pan Zhengun 998]. Fgure 3 gves a chromosome pont-crossover example of two labelng placements wth the strng length 8 and the gene code set { 2 3} Conflct gene mutate namely mutate on conflct gene) For nteger vector encodng the common mutaton ncludes pont-mutaton and even-mutaton. The former selects sngle pont the latter selects pont accordng to some template and then randomly relocate the selected pont. As for map labelng we put forward a new mutaton operator whch s called conflct gene mutaton to replace the routne pont-mutaton and even-mutaton. The basc theory of conflct gene mutaton s that: select the gene of conflct label randomly generate a labelng code to replace the orgnal gene. Experments have proved the conflct gene mutaton s very effectve. Fgure 4 shows the comparson result of the conflct gene mutaton and even-mutaton wth the same genetc parameters the number of teratons s 3 populaton sze s 5 crossover probablty s.75 mutaton probablty s.2). From fgure 4 we can fnd that the conflct gene mutaton s obvously superor to the even-mutaton. The possble reasons are as follows: ) The pont-mutaton and even-mutaton are blnd and the conflct gene mutaton utlzes the heurstc nformaton of label conflct to mprove the bad sub-soluton so the probablty of obtanng good sub-soluton s bgger. 2) In actual maps there s lttle conflct n the area wth sparse labelng pont the mutaton probablty should be smaller however n the area wth dense labelng pont there s more conflct and the mutaton probablty should be relatvely larger. The conflct gene mutaton meets ths demand Crossover operator Fgure 3 the example of pont-crossover The nteger vector generally adopts two knds of crossover operators: pont-crossover and even-crossover. The experments have proved there s no too much dfference between the nfluences of two knds of crossover operators on the performance of labelng algorthm. Therefore the labelng algorthm adopts the pont-crossover strategy. Fgure 4 compare conflct gene mutaton wth even mutate 4.5 determne the mportant parameters of genetc algorthm Accordng to references and experment concluson there are the followng prncples n determnng the genetc parameters of automated labelng:

5 ) The populaton sze N: t affects the valdty of genetc algorthm recommended t no more than 3. In ths paper the doman of N s [3 3]. 2) Crossover probablty P c: t controls the frequency of crossover operaton. Generally t s between.25 and.85. In ths paper t s between.6 and.8. 3) Mutaton probablty P m: t s the second factor n ncreasng the dversty of populaton. Generally P m s between. and.2. Ths paper doesn t have to use ths parameter. 4) Termnatng number of generaton: when populaton evolves over the specfed largest evoluton number of generaton termnate the evolvement course so ths parameter should guarantee the populaton has matured. There are two condtons to udge whether the populaton has matured: ) through several operatons the approxmate optmal ndvdual can be gotten stably; 2) contnue evolvng the optmal ndvdual s not mproved obvously agan. V. GENETIC ALGORITHM EXPERIMENTS AND CONCLUSION The experment of genetc algorthm scheme s composed wth two parts of data. The frst part s some random maps generated by the algorthm developed by ourselves; the second part s the actual topographc maps that ncludes three complete feature topographc maps from Natonal Topographc Map Database of :25 among them every map s composed wth nneteen layers ncludng hydrogen road vegetaton boundary and so on. The three topographc maps contan pont resdences and 2734 respectvely. From the evolvement experment on the map contanng 5~3 pont features we can fnd that n the teraton course wth the gradual ncrement of the ftness value of optmal ndvdual genetc algorthm becomes steady ths ndcates the populaton has matured. The algorthm should be termnated after the populaton has matured. Usually the map wth no more than 3 pont features becomes matured wthn 3 generatons. when the populaton s matured the soluton wll not be made better. If the evolvement generatons are very few the smple ncrement of populaton sze s not very useful to mprove the soluton. The experments nclude the experment on three actual topographc maps whch belong to the problems of moderate dffculty. Genetc algorthm can elmnate nearly all the conflcts only or 2 are not elmnated) n 2~3 seconds. Fgure 5 s a part of the labelng result of H48 25 pont features). VI COMPARISON EXPERIMENT AND CONCLUSION In order to verfy the performance of genetc algorthm ntroduced n ths paper we compare genetc algorthm wth smple random algorthm hll clmbng algorthm smulated annealng and neural network algorthm. The smple random algorthm s one of the smplest algorthms. It specfes randomly a labelng poston for every pont feature but not mplement any optmzaton t s algorthm qualty s the lowest lmt of labelng qualty. Hll clmbng algorthm s a knd of smple local optmzaton algorthms. It begns from an ntal soluton of randomly gven labelng placement or be calculated by other methods or be specfed drectly) search the n adacent new solutons generated randomly from the current soluton and select the optmal soluton and contnue searchng n new solutons untl the soluton can t be mproved agan. In order to guarantee the comparablty we set up the numbers of teratons as 2~3 generatons n experments namely let the program start to search n 2~3 dfferent ntal solutons and search thrty adacent strngs every teraton. Chrstensen and hs fellows have put forward a knd of pont feature labelng algorthm based on smulated annealng. Smulated annealng algorthm s a knd of smple global searchng algorthm and t s the mproved hll clmbng algorthm whch adopts randomly relocatng n labelng but allows the degenerated soluton wth certan probablty n order to ump out the local mnmum. About the kernel algorthm please refer to [Chrstensen 995]. Chrstensen has proved smulated annealng algorthm possesss a lot of performance superor to tradtonal algorthms. The smulated annealng n ths paper adopts the processng flow and parameters n Chrstensen s work. In order to guarantee the comparablty we set up the number of teratons as 2~3. Neural network algorthm adopts the model put forward by Fan Hong and Zhang Zuxun [Fan Hong Zhang Zuxun 997] after settng up the neural network of solvng pont labelng problem let the network run teratvely the runnng result s regarded as the labelng placement. In order to guarantee the comparablty we also set up the number of teratons as 2~3. Fgure 5 the labelng result of H48 usng genetc algorthm The experments also nclude the comparson of usng genetc algorthm on maps wth dfferent complextes and the comparson of usng genetc algorthm wth dfferent parameters on the same map. The experments ndcate that when processng the problems of dfferent complextes wth the same genetc parameters the results are dfferent. When keepng certan populaton sze the ncrement of evolvement generatons wll ncrease the ftness of soluton. But once reach certan degree The expermented data s a group of pont maps generated randomly. The experment methods are carred on based on the same data background and subsdary data condtons. Before usng algorthms we have set up the same conflct detecton table and overlap detecton table. The experment compares the labelng qualtes of dfferent algorthms manly. In order to compare convenently all consder the four-poston labelng problem of pont feature and consder the followng two optmzaton targets: ) only

6 consder conflct optmzaton; 2) consder conflct and poston optmzaton but not consder overlap. Under the stuaton of only consderng conflct we expressed the labelng qualty wth the rato of non-conflct labels to the total of labels. We randomly generate 8*5 map sheets of pont feature wth pont features respectvely fgure 6 shows the comparson result of these algorthms. The result n fgure 6 s the average of the labelng results on fve maps. calculaton the press of tsnghua Unv. Zhou Mng Sun Shudong the prncple and applcaton of Genetc Algorthm the press of Natonal defense ndustry. Herbert Freeman and John Ahn. On the problem of placng names n a geographc map. Int. J. of Pattern Recog. and Art. Intell. ): HerschS.A. An Algorthm for Automatc Name Placement Around Pont Data. 982 The Amercan Cartographer vol 9) Imhof E. 975 Postonng Names on Maps The Amercan Cartographer vol 22) pp James E. Mower 993 Automated Feature and Name Placement On Parallel Computers Cartography and Geographc Informaton Systems Vol.22) pp Jefrey S. Doerschler and H. Freeman. A rule-based system for dense-map name placement. Comm.of the ACM 35: Anthony C. Cook and Chrstopher B. Jones. A Prolog rule-based system for cartographc name placement. Computer Graphcs Forum 92): Jon Chrstensen Joe Marks and Stuart Sheber. An emprcal study of algorthms for pont-feature label placement. ACM Transactons on Graphcs 43): Lee R.Ebnger and M. Goulette99 Nonnteractve Automated Names Placement for the 99 Decennal Census. Cartography and Geographc Informaton Systems Vol. 7) pp Fgure 6 performance comparson among 5 knds of algorthms From the above comparson experment we can draw two conclusons. ) From fgure 6 we fnd that the soluton of genetc algorthm has the hghest qualty to the map wth the same complexty the next s neural network algorthm the next agan s smulated annealng algorthm and hll clmbng algorthm and the qualty of random algorthm s the lowest whose labelng qualty s the lowest lmt of avalable soluton qualty. From the angle of labelng qualty genetc algorthm> neural network algorthm > smulated annealng > hll clmbng algorthm. Genetc algorthm has the hghest comprehensve performance. 2) Genetc algorthm ntroduced n ths paper s a knd of robust and expansble automated labelng algorthm wth wellperformance. It possesses the followng merts: easy to add the consderaton of other optmzaton factors well expansblty. The encodng form can be determned by problem and easy to expand accordng to problem. In addton genetc algorthm s very robust t wll not generate nvald soluton. The parameters of genetc algorthm are easy to modulate. Its prmary parameters have been determned by system the workload of parameter modulatng s very lttle. ACKNOWLEDGEMENTS Thanks for the supportng from Natural Scence Fund of P.R.Chna No. 49). References: Zbgnew Mchalewcz 2 evolutonary programmng the press of scence. PanZhengun KangLshang ChenYupng998evolutonary YoelP.972 The logc of Automated Map Letterng The cartographcal Journal vol. 92)pp.99-8 Chrstopher B. Jones and Anthony C. Cook. Rule-based name placement wth Prolog. In Proc. Auto-Carto 9 pp Davd S. Johnson Umt Basoglu.989 The Use of Artfcal Intellgence n The Automated Placementof Cartogrphc Names Proceedngs of Auto-Carto 9 DoerschlerJ.and H. Freeman989 An Expert System for Dense-Map Name Placement. Proceedngs of Auto-Carto 9pp FreemanH.J.Ahn.984 AUTOMAP:An Expert System for Automatc Map Name Placement Proceedngs of the Frst Internatonal Symposum on Spatal data Handlng pp Davd S. Johnson Umt Basoglu.989 The Use of Artfcal Intellgence n The Automated Placementof Cartogrphc Names Proceedngs of Auto-Carto 9 DoerschlerJ.and H. Freeman989 An Expert System for Dense-Map Name Placement. Proceedngs of Auto-Carto 9pp John Ahn and Herbert Freeman. AUTONAP - an expert system for automatc map name placement. In Proceedngs Internatonal Symposum on Spatal Data Handlng. pages