AN EFFICIENT GENETIC ALGORITHM AND ITS COMPARISON EXPERIMENT FOR AUTOMATIC MAP LABELING
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1 AN FFICINT GNTIC ALGORITHM AND ITS COMPARISON XPRIMNT FOR AUTOMATIC MAP LABLING Fan Hong 1 Lu Kaun 2 Zhang Zuxun 1 (1 Natonal Laboratory of Informaton ngneerng n Surveyng, Mappng and Remote Sensng of Wuhan Unversty, No.129 Luoyu Road, Wuhan, Chna, Zp code:430079) (2 Management college of Huazhong Unversty of Scence and Technology, Luoyu Road, Zp code: ) 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 detaled 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 well-expansblty, and s the most promsng soluton for automated map labellng. I. TRADITIONAL MTHOD S DISADVANTAGS 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, 1972; Imhof, 1975; Ahn Freeman, 1984; Langran and Polker, 1986; Zoraster, 1991; Chrstensen ef.al, 1995, 1997 ]. In the eghtes of 20 th century, a lot of automated labelng expert system were developed [Zoraster, 1991] that ncludes NAMAX, AutoNap,etc. Thr dsadvantages s loweffcency and great developng cost. Another commonly used algorthm s exhausted searchng algorthm [Jones, 1989; Cook and Jones, 1990; bnge and Goulette, 1990; Doerschler and Freeman, 1992]. These algorthm can be expressed as searchng n dgraph or drecton tree, whch mght cause concatenate backtrackng and even deadlock, therefore they only ft to small-scale problems. Another knd of mportant algorthm s searchng based on the problem soluton space. Representatve examples nclude the energy mnmzaton algorthm put forward by Hersch [Hesh, 1982] and the dscrete gradent descent algorthm [Chrstensen ef.al, 1995, 1997], 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. II. POINT LABLING RULS AND TH STUDID PROBLM 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 1:250000, our research wll focus on the followng three mportant prncples especally and two representatve problems. 1
2 stuatons ncludng four-canddate-poston, fve-canddate-poston, eght-canddate-poston and n-canddate-poston. 1. The canddate postons and ther prorty: generally the canddate poston of pont feature labelng has four knds of In ths paper, we adopt four-canddate-poston rules, as ndcated n fgure 1(a), regard the rght as frst, top, left and bottom followed respectvely n successon, these labelng postons can be marked wth prortes from 0 to 3. Fvecanddate-poston, as ndcated n fgure 1(b), eght-canddate-poston, as ndcated n fgure 1(c), n-canddate-poston s llustrated n fgure 1(d). 2. To forbd conflct: the labels of pont features can t overlap (conflct ) wth one another. 3. To 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. Fgure 1. The canddate labelng poston of pont feature So, our paper focus on the labelng problem of the followng two knds of pont features manly. Problem I: consder the pont feature n map, f adoptng four-canddate-poston labelng mode, namely choosng the rght, top, left and bottom four canddate postons of pont feature respectvely (as ndcated n fgure 1(a), the dstance between label and pont resdence s 1mm), try desgnng and mplementng labelng algorthm to make globally conflct least. In the actual labelng problem, stuaton may be more complex, besdes consderng elmnatng label conflct, also need ng 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 four-canddate-poston labelng mode, namely choose the rght, top, left and bottom four canddate postons of pont feature respectvely (as ndcated n fgure 1(a), the dstance between label and pont resdence s 1mm), try desgnng and mplementng labelng algorthm, make globally conflct least, the overlap to other features mnmum and the labelng poston most optmal. III. GNTIC ALGORITHM OF SOLVING POINT FATUR LABLING 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, self-adaptve control, game rules, pattern cognton, transportaton problem, travellng salesman problem, optmal control and database query optmal, etc, most of them are famous NP-complete hard problems[zhou Mng, 1999 ]. 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 problem-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, 2000]: (1) 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. 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 2
3 strateges adopted by our genetc algorthm. In the end of ths paper, we wll ntroduce some experments and comparson experments detaled, and also present our experment results. 3.1 Determne encodng framework The good map label placement s the optmzaton target of genetc algorthm. One of the map placements can be expressed wth a nteger vector. ach component represents the localzaton of one label. Assumed there are m canddate postons, whch can be expressed wth codes of 0~m-1, for nstance when consderng four-poston label, the four canddate postons can be expressed wth the codes of 0~3. ncode 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 [0, m-1], where m s the number of canddate postons, the gene code set of four-canddate-pont labelng problem s {0, 1, 2, 3}.Use a map wth 20 pont features as an example, Fgure 2 show one placements of ths map and ts correspondng chromosome encodng. 3.2 Generate ntal populaton Fgure 2. Pont feature labelng placement and ts encodng Accordng to the characterstc of labelng problem, the followng strateges to generate ntal populaton was adopted. (1) 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. 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. Ths ntal procedure also help reduce the scale of problem and accelerate the evolvement of genetc algorthm. 3.3 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. In ths paper, we adopted a labelng qualty evaluaton functon whch consders these factors ncludng conflct, overlap, poston prorty and so on. It s basc thought s: frst of all gve a score for the conflct, overlap and poston prorty of each label, and then sum them by multplyng a set of weghts for each label, fnally, aggregate the total scores of all the labels, that s 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, n terms of the demands of optmzaton target of dfferent labelng problems, the correspondng ftness functon could be desgned. Because the lmt of space of paper, we use two optmzaton targets as examples and dscuss how to derve ther ftness functon. 1. 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, the ftness functon s easly gven as equaton (1). ft( L) N 1 conflct ( L ) 3
4 (1) Where ( ) conflct L s 0-1 conflct evaluaton functon whose defnton s shown n expresson (2), n whch L 1 If (,0 n,, d ll ( L, L ) 0) conflct ( L ) 0 otherwse (2) represents the label of -th pont feature, when there s no conflct between L and the other labels the functon equals 1, otherwse t equals 0. In ths case, the value 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 conflcts globally much 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): ( L ) W W overlap ft ( L ) ( L poston N 1, ) overlap 0 ( L poston ( L ), ( L, BF ), f ( L, Where we let Wover l ay 100 ; W 1 The meanng of every symbol s as follows: ) pos t on... don ' t.. Conflct otherwse ) (3) L s on the canddate poston, f adoptng smple overlay ( L,, BF)represents the overlap evaluaton value when overlap evaluaton functon, t s defned as the hghest mportance weght of the features, whch overlapped wth the label. When there s no overlap, overlay ( L,, BF)=99, the hgher the mportance of overlad feature s(that mean the severer the overlap s), accordngly the lower the overlap score s. quaton (4) defne overlay ( L,, BF). BF represents the -th background feature overlad by the label; the predcate overlap( O,O 1 2 ) ndcates the two obects O,O 1 2 overlap wth each other. 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 of background feature (ts value also called mportance weght). Smlarly adoptng the score system of 0~99, the features wth the most mportance ( no overlap permtted ) s gven a score 99, those wth the lowest mportance(overlap permtted ) s desgned a score of 0. So, we have equaton (5) to defne W BF ) : ( 0 W ( BF ) 1 ~ the the the mn mal medan max mal mpor tan ce mpor tan ce mpor tan ce In equaton (3), pos t on( L, )represents the poston evaluaton value when L s on the canddate poston, t s defned as equaton (6), whch we call sorted poston evaluaton functon. 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 ) represents the -th labelng canddate poston of L, Order ( Pos ( L )) represents the order number of ths poston after sorted, we can defne the poston evaluaton functon as the dfference of 99 and (5) 4
5 Order Pos ( L )) ( n ther order.. Namely the score of the poston wth the hghest prorty s 99, the scores of the other postons decrease poston ( L ) 99 Order( Pos ( L )) (6) By adoptng the above ftnes functon, genetc algorthm not only solve 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 Wover l ay 0 n equaton (3), then we can have equaton (7): ( L ) ( L ) W poston ft( L) N 1, poston 0 ( L ) ( L ), If( L, wthout conflct ) otherwse Let W 1.Now consder the example n fgure 2, the fgure gves out ts chromosome of an nstance of map pos t on placement. Consder the targets of least conflct and most optmal poston, adopt the ftness functon (7), and be able to calculate ts ftness value as follow: (7) 3.4 desgn genetc operators Selecton operators The labelng algorthm adopts roulette-wheel selecton as selecton method. When the populaton sze s very large, elte strategy are also used, namely retan the optmal ndvduals of the prevous generaton nto the next one. The procedure of roulette-wheel selecton s as follow: (1) Calculate the ftness value of ndvdual ft V ) 1,2,..., n ( ; (2) Calculate the accumulatve ftness value of ndvdual Accft( V ) 1,2,..., n and relatve accumulatve ftness value RelAccft( V ) 1,2,..., n. (3) Generate a random r n [0, 1], here suppose Re laccft ( V0 ) 0 If, Re laccft( V 1 ) r Re laccft( V ) ( 1,2,... n), then select the ndvdual Crossover operator 20 ft( L) ( L )
6 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 no too much dfference between these two operators on the performance of labelng algorthm. Therefore the labelng algorthm adopts the pont-crossover strategy. The pont-crossover operator s dvded nto sngle-pont and multpont crossover. The former randomly selects a cross pont and then exchanges the correspondng sub-strngs of the two strngs. The latter randomly generates several cross pont each tme, and then exchanges the correspondng sub-strngs. [Pan Zhengun, 1998]. Fgure 3 gves a chromosome pont-crossover example of two labelng placements wth the strng length 8 and the gene code set {0, 1, 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 mutaton. The basc thought of conflct gene mutaton s: select the gene of conflct label, randomly generate a labelng code to replace the orgnal gene. xperments 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 300, populaton sze s 50, crossover probablty s 0.75, mutaton probablty s 0.2). From fgure 4 we can fnd that the conflct gene mutaton s obvously superor to the even-mutaton. The possble reasons are as follows: (1) 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, n those areas wth sparse pont and lttle conflct, the mutaton probablty should be smaller, however n those area wth dense labelng pont and more conflct, and the mutaton probablty should be relatvely larger. The conflct gene mutaton meets ths demand. Fgure 4. Compare conflct gene mutaton wth even mutate 6
7 3.5 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: (1) The populaton sze N: t affects the valdty of genetc algorthm, suggest: no more than 300. In ths paper the doman of N s [30, 300]. (2) Crossover probablty P c: controls the frequency of crossover operaton. Generally t s between 0.25 and In ths paper between 0.6 and 0.8. (3) Mutaton probablty P m: s the second factor n ncreasng the dversty of populaton. Generally P m s between 0.01 and 0.2. 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: (1) through several operatons, the approxmate optmal ndvdual can be gotten stably; (2) contnue evolvng, the optmal ndvdual s not mproved obvously agan. IV. GNTIC ALGORITHM XPRIMNTS AND COMPARATIV XPRIMNTS 4.1 experments of genetc algorthm 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 1:250000, among them every map s composed wth nneteen layers ncludng hydrogen, road, vegetaton, boundary, and so on. The three topographc maps contan pont resdences 2511, 1651 and 2734 respectvely. From the evolvement experment on the map contanng 50~3000 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, at ths tme the algorthm should be termnated. Usually the map wth no more than 3000 pont features becomes matured wthn 300 generatons. Fgure 5. The labelng result of H4810 usng genetc algorthm The experment on three actual topographc maps, whch belong to the problems of moderate dffculty also be completed. Genetc algorthm can elmnate nearly all the conflcts (only 1 or 2 are not elmnated) n 20~30 seconds. Fgure 5 s a part of the labelng result of H4810 (2511 pont features). 4.2 comparson experments of genetc algorthm In order to verfy the performance of genetc algorthm ntroduced n ths paper, we make plenty of experments to compare genetc algorthm wth other representatve optmal algorthms such as smple random algorthm, hll clmbng algorthm, smulated annealng and neural network algorthm. 7
8 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 200~300 generatons n experments, namely let the program start to search n 200~300 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. It s kernel algorthm please refer to [Chrstensen, 1995]. Chrstensen has proved smulated annealng algorthm possess a lot of performance superor to tradtonal algorthms. The smulated annealng n ths paper adopts the processng flow and parameters followng Chrstensen s work. In order to guarantee the comparablty, we set up the number of teratons as 200~300. Neural network algorthm adopts the model put forward by Fan Hong and Zhang Zuxun [Fan Hong, Zhang Zuxun, 1997], after settng up the neural network of solvng pont labelng problem, let the network run teratvely, the runnng result s ntepreted as the labelng placement. In order to guarantee the comparablty, we also set up the number of teratons as 200~300. 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: (1) only consder conflct optmzaton; (2) consder both 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 200, 400, 600, 800, 1000, 1200, 1400, 1600 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. Whle consderng both conflct and poston prorty but not consderng overlap, for a randomly created map contanng 1500 pont features, the above fve algorthm( wth the same runnng condton and parameter) were used to get the best labelng placement for the map, dfferent results were obtaned, fgure 7 show ther dfferent results ( among ths fgure, black box represent the conflct of label remans after teraton of 300 ) respectvely. Fgure 6. Performance comparson among 5 knds of algorthms 8
9 (a) Random Algorthm(821 conflcts remans) (b) Hll Clmbng Algorthm(464 conflcts remans ) (c) Smulated Annealng( 194 conflcts remans) (d) Neural Network(80 conflcts remans) V CONCLUSION (e)genetc Algorthm(44 conflcts remans) Fgure 7. Comparson experment result for a randomly created map of 1500 pont features From the plenty of comparson experments we can draw two conclusons. (1) From fgure 7 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. 9
10 (2) Genetc algorthm ntroduced n ths paper s a knd of robust and expansble automated labelng algorthm wth well-performance. 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. ACKNOWLDGMNTS Thanks for the supportng from Natural Scence Fund of P.R.Chna (No ). References: Zbgnew Mchalewcz, 2000, evolutonary programmng, the press of scence. PanZhengun, KangLshang, ChenYupng,1998,evolutonary calculaton, the press of tsnghua Unv. Yoel,P.,1972, The logc of Automated Map Letterng,The cartographcal Journal, vol. 9(2),pp 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., 1(1): , Hersch,S.A., An Algorthm for Automatc Name Placement Around Pont Data., 1982, The Amercan Cartographer, vol 9(1) Imhof,., 1975, Postonng Names on Maps,The Amercan Cartographer, vol 2(2), pp James. Mower, 1993, Automated Feature and Name Placement On Parallel Computers, Cartography and Geographc Informaton Systems, Vol.20(2), pp Jefrey S. Doerschler and H. Freeman. A rule-based system for dense-map name placement. Comm.of the ACM, 35:68-79, Anthony C. Cook and Chrstopher B. Jones. A Prolog rule-based system for cartographc name placement. Computer Graphcs Forum, 9(2): , Jon Chrstensen, Joe Marks, and Stuart Sheber. An emprcal study of algorthms for pont-feature label placement. ACM Transactons on Graphcs, 14(3): , Lee R.bnger and M. Goulette,1990, Nonnteractve Automated Names Placement for the 1990 Decennal Census., Cartography and Geographc Informaton Systems, Vol. 17(1), pp Chrstopher B. Jones and Anthony C. Cook. Rule-based name placement wth Prolog. In Proc. Auto-Carto 9, pp , Davd S. Johnson, Umt Basoglu.,1989, The Use of Artfcal Intellgence n The Automated Placement of Cartographc Names, Proceedngs of Auto-Carto 9 Doerschler,J.,and H. Freeman,1989, An xpert System for Dense-Map Name Placement. Proceedngs of Auto-Carto 9,pp Freeman,H.,J.Ahn.,1984, AUTOMAP:An xpert System for Automatc Map Name Placement. Proceedngs of the Frst Internatonal Symposum on Spatal data Handlng, pp Davd S. Johnson, Umt Basoglu.,1989, The Use of Artfcal Intellgence n The Automated Placement of Cartographc Names, Proceedngs of Auto-Carto 9 Doerschler,J., H. Freeman,1989, An xpert System for Dense-Map Name Placement. Proceedngs of Auto-Carto 9,pp John Ahn and Herbert Freeman. AUTONAP - an expert system for automatc map name placement. In Proceedngs Internatonal Symposum on Spatal Data Handlng. pages ,
11 Fan Hong She s a professor of natonal laboratory of nformaton engneerng n surveyng, mappng and remote sensng of Wuhan Unversty She receved her B.S.degree n computer scence from Wuhan Unversty n , receved her M.S.degree n computer software engneerng from Wuhan Unversty n , and receved her Ph.D. degree of photogrammetry and remote sensng from Wuhan Unversty n Her maor research nterests ncludes GIS and Cartography, spatal mage processng, ntellgent algorthm theory and ts applcaton. Lu Kaun He s a doctor canddate of Management college of Huazhong Unversty of Scence and Technology. He receved hs B.S.degree n cartography from Wuhan Techncal Unversty n surveyng and mappng n , receved hs M.S.degree n Management college of Huazhong Unversty of Scence and Technology n Her maor research nterests ncludes GIS and applcaton, management nformaton system development, ntellgent algorthm applcaton. Zhang Zuxun He s a professor of Remote Sensng School of Wuhan Unversty. Member of Chnese Academc of ngneerng. Hs maor research felds ncludes remote sensng, cartography, dgtal photogrammetry system and ts applcaton. 11
AN EFFICIENT AND ROBUST GENETIC ALGORITHM APPROACH FOR AUTOMATED MAP LABELING
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
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