Research on Kruskal Crossover Genetic Algorithm for Multi- Objective Logistics Distribution Path Optimization

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1 , pp Research on Kruskal Crossover Genetc Algorthm for Mult- Objectve Logstcs Dstrbuton Path Optmzaton Yan Zhang 1,2, Xng-y Wu 1 and Oh-kyoung Kwon 2, a, 1 Chongqng Unversty of Posts and Telecommuncatons, Chongqng 465, Chna 2 Graduate School of Logstcs, INHA Unversty, Incheon 42751, Korea a scm@nha.ac.kr Correspondng - Author: Oh-kyoung Kwon Abstract To effectvely optmze mult-objectve logstcs dstrbuton path, the dstance and dstance related customer satsfacton factor are used as the objectve functon, a novel kruskal crossover genetc algorthm (KCGA) for mult-objectve logstcs dstrbuton path optmzaton s proposed. To test the optmzaton results, the termnal dstrbuton model and the vrtual logstcs system operatng model are bult. Experment results show that, compared wth basc genetc algorthm (GA), the run tme of KCGA takes a slghtly hgher. But the average dstrbuton dstance and the best dstrbuton dstance are reduced by 6%-8%. Acheve the goal of mult-objectve logstcs dstrbuton path optmzaton. Keywords: logstcs dstrbuton; mult-objectve; optmzaton; kruskal; crossover 1. Introducton Along wth the economc globalzaton and the development of natonal economy, logstcs ndustry gets a great development. Because our logstcs system s faultness, snce 25, the rato of logstcs cost accountng for Chnese gross domestc product (GDP) has been around 18% whch s hgher than Europe, Amerca and other developed countres (whch s around %) [1]. In logstcs system, a good dstrbuton path can drve to get a better transport result, save resources and reduce cost effcently. So far, the problem of logstcs dstrbuton path optmzaton has been a popular study pont. At present, the algorthms whch are appled n logstcs dstrbuton path optmzaton manly nclude ant colony algorthm (ACO) [2], genetc algorthm (GA) [3], partcle swarm optmzaton (PSO) [4] and smulated annealng algorthm (SA) [5] and so on. Contrastng the algorthms mentoned above, based on bologcal evoluton, GA starts searchng from group and t can compare multple ndvduals at the same tme. In other words, GA has potental parallelsm and hgh overall. Accordng to these advantages, GA s a good choce for logstcs dstrbuton path optmzaton. GA was frst presented by J.Holland n 1975 [6]. Except the advantages above, earlymaturng s the weakness of GA [7-8] and t can lead logstcs dstrbuton path not achevng optmal. To cure above problems, Ombuk [9] present a hybrd Tabu-search/GA algorthm. The number of vehcles was optmzed by GA and the dstance was optmzed by Tabu-search algorthm. The hybrd algorthm can obtan a better result than anyone of Tabu-search and GA. Tseng [] ntroduced the probablty theory nto GA. The probablty was regard as a parameter whch was used to adjust crossover and mutaton model. In the meantme, a two-way method was appled n global optmzaton search. Takng am at the problems of long dstrbuton path and tme by usng GA to optmze dstrbuton path, ths paper ntroduces kruskal algorthm nto GA. The delvery dstance ISSN: IJMUE Copyrght c 215 SERSC

2 and customer satsfacton whch are regard as objectve functon are present nto ths new method. Accordng to vehcle routng problem (VRP) model, order termnal dstrbuton model whch s used to verfy the proposed method s structured. So, ths method can be accomplshed n the dstrbuton model. 2. Mult-Objectve Logstcs Dstrbuton Path Optmzaton 2.1. Objectve Functon Total dstrbuton dstance objectve functon: n logstcs system, delvery paths are the routes of vehcles. The length decdes the dstrbuton qualty and cost. So the total dstrbuton dstance s the pror objectve functon for optmzng. Customer satsfacton objectve functon: on the premse of the mnmum total dstrbuton dstance, customer satsfacton s a very mportant ndcator. It can nfluence the clents drectly and then the competton ablty and economc beneft of enterprses [11]. In express logstcs ndustres, Customer satsfacton s manly decded by the arrval tme of goods. Customer satsfacton objectve functon Ft ( ) s shown n (2). F (2) ( t ) f( t )* X Where t s the arrval tme of goods, the satsfyng tme s range n [, L ]. LL presents the maxmum tme. As shown n Fgure 1, n [ L, LL ], Ft ( ) reduces to gradually. X s the number of orders. 1 ; t L LL t f ( t ) ; L t LL LL L ; t>ll (1) F( t ) F ( t ) f ( t )* X X L LL t Fgure 1. Customer Satsfacton Change Along wth the Goods Arrval Tme Total objectve functon: total objectve functon s composed of negatve Ft ( ) and total dstrbuton dstance objectve functon. Then mnmum value s obtaned by usng GA. Total objectve functon s shown n (3). F ( t ) ( F ( t )) F ( t ) (3) 1 Where Ft ( ) represents the total objectve functon, Ft ( ) represents the customer satsfacton objectve functon, Ft ( ) 1 represents the total dstrbuton dstance objectve functon. 368 Copyrght c 215 SERSC

3 2.2. Kruskal Algorthm Kruskal algorthm s a knd of greedy algorthm. It bulds a mnmum cost spannng tree by addng one edge to the cost spannng tree at every turn. Namely, kruskal algorthm can acheve global optmzaton accordng to local optmal choce [12]. Suppose that WN= (V, {E}) s a connected net whch ncludes n peaks. Then, the process of buldng mnmum spannng tree (MST) usng kruskal algorthm can be descrbed as follows. 1 Buld a sub graph whch only ncludes n peaks and ts fronter sets are empty; 2 Fnd one edge wth the smallest weght from the fronter set E of the sub graph. If the two peaks of the edge are belongng to dfferent trees, add the edge to the sub graph; 3 If the two peaks are part of one tree, gve up ths edge. Then fnd the next edge wth smallest weght and repeat 2 and 3 untl there are n-1 edges n sub graph. The pseudo code of kruskal algorthm s as follows. Begn T.V =n; T.E= {}; For (n-1 edges n the sub graph) Fnd the shortest edge (u, v)from WN.E; If(u, v local n two dfferent uncom components of T) Add(u, v)to T.E; Else Select the second shortest edge; End f; End for End 2.3. Termnal Dstrbuton Model In ths paper, combnng wth customer satsfacton objectve functon and VPR model, the termnal dstrbuton model, whch ncludes a dstrbuton center and multple dstrbuton termnals, s establshed. The VRP model can be descrbed as ths: n ths model, some trucks whch have a fxed load are used to delver cargoes from logstcs center to dfferent destnatons, and every destnaton has not only a fxed poston but also dfferent demands for goods [13]. In order to make the objectve functon mnmum or maxmum and to meet the followng constrant condtons, the path ought to be confgured reasonably. The constrant condtons are descrbed as below. 1 In some dstrbuton path, the total requrements of destnatons should be less than lorres` total loads; 2 The length of some dstrbuton path should be shorter than the maxmum mleages of vehcles; 3 Every destnaton's requrements should be met and the goods should be delvered by a truck only. 4 Durng the dstrbuton, every destnaton should be reached once. After that, cars can go back to dstrbuton center Kruskal Crossover Genetc Algorthm (KCGA) Because basc GA s easy to converge, when dstrbuton path are optmzed by ths method, a problem that the calculated path are always too long appears. Kruskal s a greedy algorthm whch establshes the fnal mnmum spannng tree by addng an edge nto the spannng tree every tme, and t has the characterstc that global optmzaton can be acheved through local optmzaton. Thus, n ths paper, the algorthm s ntroduced nto the crossover operator of basc GA to ncrease the dversty of populaton. Further, t Copyrght c 215 SERSC 369

4 s used to assure that the algorthm can fnd out the optmum of ndvduals durng the cross operaton and to solve the premature convergence problem n basc GA. The flow chart of KCGA s shown as Fgure 2. Start Generate ntal populaton Calculate the ftness Y Acheved the maxmum number of teratons? N Select operator Kruskal crossover operator Mutaton operator The optmal output End Fgure 2. The Flow Chart of KCGA KCGA s desgned as below. 1 Two parent ndvduals FA and FB are obtaned by selecton steps and two gene fragments FA1 and FB1 wth random length are selected from these two ndvduals as cross genes; 2 Use kruskal algorthm to search FA1 and FB1, and add the shorter and shortest sdes of FA1 and FB1 nto FA2 and FB2 respectvely, then remove the repettve parts of FA2 and FB2 to get the new FA2 and FB2; 3 Remove the FA`s repettve parts whch s contaned n FB2. So does FB by takng FA2 nto consderaton; 4 Exchange FA2 and FB2, then combne FA and FB2 to get the new offsprng SA. Smlarly, SB s obtaned by combnng FB and FA2 5 Introduce SA and SB nto the rest of basc GA to get the optmal soluton by teraton. Where step 2 s acheved by the followng pseudo codes. Begn Input FA1; FB1; If (FA1 meets the condtons of mnmum spannng tree) FA2= (FA1 (shortest edge), FA1 (shorter edge) ); //Establsh the mnmum spannng tree FB2= (FB1 (shortest edge), FB1 (shorter edge) ); Else Gve up the edges whch cannot meet the condtons and search for next edge; End f 37 Copyrght c 215 SERSC

5 Del (FA2); Del (FB2); //Remove repettve genes Return FA2; FB2; End For example, FA= ,FB= (1, 2, 3 are the gene ponts). Take out the gene fragment FB1=1487 of parental gene FB. Rand every edges of FB1 by ascendng counts,.e., (1,4),(4,7),(1,7),(4,8),(8,7),(1,8). As a result, FB2 can be gettng by step 2 n the followng way. a. FB2=(144748); //Establsh the mnmum spannng tree. Based on kruskal to examne every edge of FB1, condtons of (1,4) and (4,7)are ntroduced frst. When condton (1, 7) s ntroduced, the rules of mnmum spannng tree cannot be met. Therefore, nstead of gvng up edge (1, 7), we use the algorthm to search for next one (4, 8). As a result, the mnmum spannng tree s establshed by addng the new edge (4, 8). b. Remove the repettve genes, we get FB2=1478. The soluton of FA2 s smlar to that of FB2. Where step 4 s acheved by the followng pseudo codes. Begn Input FA; FB; FA2; FB2; Wpe out the same gene between FA and FB2 and also between FB and FA2; SA=(FA,FB2);SB=(FB,FA2); Return SA;SB; End Follow the above example, the result can be obtaned as follows. FB2=1478, FA= Thus, Step 4 can be realzed as follows. a. Wpe out the same gene between FA and FB2. FA=3265; b. SA=(FA,FB2)= The method to solve SB s smlar wth that of SA. However, after add kruskal algorthm to the basc GA crossover operator, ncreased the overall complexty of the algorthm, and the correspondng algorthm run tme consumng also ncreased. Therefore, ths paper makes a further optmzed to KCGA by the followng methods, whch wll effectvely reduce the algorthm runnng tme consumng. 1 Control algorthm computaton. Intal kruskal crossover extracts a random length of the parent applcaton kruskal algorthm. It s lkely to take the long gene segments of the parent generaton (e.g. more than 6% of the length). Thus, by the method of controllng the length of the gene, whch take no more than 2% of the total length of genes when the number of termnal cty pont s smaller (the number of termnals cty pont below 5), take no more than % of the total length of genes when the number of termnal cty pont s greater (the number of termnals cty pont above 5). It s n order to effectvely control the computatonal of algorthm. 2 Add ntal populaton eltst strategy and offsprng elte strategy. a. Intal populaton elte strategy s ntalze the ntal populaton for many tmes, take out the n ndvdual n the top ntalze objectve functon values every tme as the fnal part of the ntalzaton populaton, consttute the fnal ntal populaton the after repeated many tmes. For example, f the ntal populaton s set to 5 unts, t cans ntalzaton by tmes, reserve the 5 unts n the top objectve functon value, and consttute the fnal ntalzaton populaton after repeat tmes. b. The strategy of offsprng elte s after selecton, crossover and mutaton operaton, retan the best unt. Ths unt does not partcpate n crossover and mutaton operaton of the next generaton, whch only partcpates n the choce computng of the next generaton. It s n order to accelerate the algorthm convergence rate. Therefore, KCGA pseudo code as follows. Begn Copyrght c 215 SERSC 371

6 //Generate an ntal elte populaton ZQ (N) ZQ(N)=; For (Cyclc N / n tmes) Randomly generated N ndvduals, and choose out the N ndvdual objectve functon values n the top N ndvdual ZQ (N); ZQ(N)= ZQ(N)+ ZQ(n); Return (ZQ (N)); End for; //The man functon Iteratons = ; Whle (total teratons - teratons) Select operator; Kruskal crossover operator; Mutaton operator; Select the hghest ndvdual objectve functon values ZQ (m); ZQ (the next generaton) = ZQ (the next generaton) + ZQ (m); Iteratons++ Output optmzaton solutons; End; Select the ted for choce method to solve mult-objectve optmzaton, whch can provde multple parallel selecton methods. 1 The populaton s dvded nto three equal sub-populatons accordng to the number of objectve functon. 2 Assgned an objectve functon to each group. 3 New populaton wll complete crossover and mutaton operatons after each subobjectve functon complete selecton operaton ndependently n ther correspondng subgroups. 4 Iteratve to get optmal path. 3. Expermental Results and Analyss 3.1. Comparatve Experment of Usng Basc GA and KCGA to Solve the Order Termnal Dstrbuton Model, Whch Makes the Dstrbuton Dstance as the Objectve Functon Buld the order termnal dstrbuton model n one dstrbuton center and dfferent termnal ponts. Make the dstrbuton dstance as the objectve functon, and use the basc GA and KCGA to solve ths model ten tmes. At last, the result of the experment wll be analyzed. The operaton parameters of the two algorthms set as follows. The two algorthms are added wth ntal populaton elte strategy and offsprng elte retenton polcy. The locaton of test cty pont and the number of orders are generated by random. The populaton sze s 5. The evoluton algebra s. The crossover probablty s.8. The mutaton probablty s.1. The dstrbuton vehcle load restrant s 25kg. The dstrbuton vehcle dstance constrants are 8km. The experments were conducted on an Intel 2.17GHZ Wndows 7 platform wth 2GB RAM, and algorthm s mplemented n MATLAB. The expermental results are shown n Table Copyrght c 215 SERSC

7 Number of cty Algort hm Table 1. The Two Methods Expermental Results Dstrbuton dstance (Ten tmes, unt: km) Average tme (s) Average dstance (km) Optmal dstance (km) GA 71,71,68,7,68,68,68,69,69, KCGA 68,68,68,68,68,68,68,68,68, GA 124,118,114,117,126,122,12,12,117, KCGA 113,113,113,113,114,113,113,114,113, GA 139,135,134,135,141,141,133,139,149, KCGA 129,125,139,13,128,131,135,125,13, GA 155,151,16,156,151,159,166,162,156, KCGA 144,141,149,139,139,139,147,144,138, GA 2,29,24,198,212,189,199,195,193, KCGA 178,186,178,19,182,188,176,18,186, GA 261,264,248,251,264,259,269,267,26, KCGA 246,24,229,252,239,235,24,245,229, GA 357,361,369,345,345,34,343,351,353, KCGA 344,319,335,337,325,338,335,3,32, GA 558,543,566,563,555,548,558,57,55, KCGA 523,54,512,539,497,521,525,53,59, GA 71,717,69,682,737,734,711,72,695, KCGA 676,643,658,66,669,648,662,65,647, Table 1 show that the two algorthms were run tmes, compared wth basc GA, the run tme of KCGA takes a slghtly hgher (hgher than the range of %-8%). However, when comparng the results of the optmal dstance and the average dstance n ths ten tmes, KCGA s not nferor to GA. For example, wth 15 termnal cty ponts, the average dstance that solved by KCGA was reduced by 5.35%, and the optmal dstance was reduced by.88%. When there are 3 termnal cty ponts, the average dstance that solved by KCGA was reduced by 8.58%, and the optmal dstance was reduced by 8.81%. When there are 5 termnal cty ponts, the average dstance that solved by KCGA was reduced by 6.56%, the optmal dstance was reduced by 8.82%. When there are 75 termnal cty ponts, the average dstance that solved by KCGA was reduced by 6.18%, the optmal dstance was reduced by 7.79% Experment of Usng Basc GA and KCGA to Solve the Order Termnal Dstrbuton Model, whch Makes the Dstrbuton Dstance and Customer Satsfacton as the Objectve Functon Order termnal dstrbuton model s bult by a dstrbuton center and ffteen termnal ctes. Where, dstrbuton center s located n [8,8], the qualty of each accessory s randomly generated from to klogram, the rated load and speed of vehcles are 4kg and 3km/h (.5km/mn), and the server tme of dstrbuton vehcle s 15 mnutes n each dstrbuton pont, and the rest of parameters are consstent wth the prevous secton experment. Table 2. Termnal Pont Coordnates the Number of Orders and Tme Constrants Termnal pont Number of orders X (pece) Coordnates X Tme constrants [ L, LL ] Servce tme (mn) (mn) [6,8] [6,8] 15 Y Copyrght c 215 SERSC 373

8 [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] [6,8] 15 Experments are performed wth KCGA s appled nto the model. The experments were conducted on an Intel 2.17GHZ Wndows 7 platform wth 2GB RAM, and algorthm s mplemented n MATLAB. Results are showed as follows. 1 The shortest dstrbuton dstance a. Dstrbuton path: ; ; -1-3-; -7-; ; b. Number of vehcles: 5 c. Dstrbuton dstance: 82 d. Customer satsfacton (the shortest dstrbuton dstance): The hghest customer satsfacton a. Dstrbuton path: ; -7-; ; ; ; ; b. Number of vehcles: 6 c. Dstrbuton dstance (the hghest customer satsfacton): 97 d. Customer satsfacton: The comprehensve objectve functon optmal a. Dstrbuton path: ; ; ; ; ; b. Number of vehcles: 5 c. Dstrbuton dstance: 91 d. Customer satsfacton: The shortest dstance dstrbuton path The hghest customer satsfacton dstrbuton path A comprehensve optmal dstrbuton path Y(km) Y(km) Y(km) X(km) 2 X(km) 2 X(km) (a) (b) (c) Fgure 3. The Dstrbuton Path Chart of KCGA Solve the Model 374 Copyrght c 215 SERSC

9 Y(The value of dstance functon) The convergence of dstance functon 1 The value on average 5 The value on the bestest X(Update algebrac) Y(The value of customer satsfacton functon) The convergence of customer satsfacton functon The convergence of comprehensve functon The value on average The value on the bestest The value on average The value on the bestest X(Update algebrac) Y(The value of comprehensve functon) X(Update algebrac) (a) (b) (c) Fgure 4. The Objectve Functon Value Convergence Effect Chart of KCGA Solve the Model Combnng Fgure 3, 4 and the experment results, we could found that the dstrbuton dstance and customer satsfacton are lower than the sngle optmal value when the comprehensve objectve functon optmal. However, another objectve functon value s lower than the result of comprehensve objectve functon optmal when the sngle objectve functon s optmal. Therefore, dstrbuton path wll be closer to the real stuaton when the customer satsfacton objectve functon s added, and the dstrbuton plan of three dfferent advantages can be provded Dstrbuton Path Optmzaton Experment Under Vrtual Logstcs System Logstcs space model s composed by a logstcs center of ter one cty, a dstrbuton center of secondary cty, and a logstcs dstrbuton pont of termnal cty. In addton, order generate model, storage model, transport and termnal dstrbuton model are essental for the smple model of vrtual logstcs system. Ths model s mplemented n MATLAB/GUI. The operatng prncples are defned as follows: orders are dstrbuted from a startng pont, and sendng these orders to the dstrbuton center, whch s belongng to the cty of order creaton. Then, these orders wll be delvered from dstrbuton center to the prevous level that s logstcs center. After all knds of orders have been processed and classfed, sendng each order to the correspondng logstcs center of destnaton cty. Next, delverng orders from logstcs center to the next level that s dstrbuton center. At last, each order wll arrve to ther destnaton thorough dstrbuton center. Where, order termnal dstrbuton module s belongs to the smple model of vrtual logstcs system, and the successful delvery of orders from secondary cty to the termnal cty s the man functon for the module. Confgure the system parameters and generate the cty archtecture. Archtecture generated Fgure of the system man nterface as shown n Fgure 5. Copyrght c 215 SERSC 375

10 Fgure 5. The Man Interface Archtecture Chart of System As the Fgure 5 shows, the dotted lne n the Fgure s termnal cty ponts to secondary ctes, whch represents a runnng route between these two ponts. The sold lne s secondary ctes to ter one cty and between ter one ctes, t also represents a runnng route. Run the system and enter the termnal dstrbuton module, random selecton on January 2, 9th secondary cty for testng. The test results are shown n Fgure 6. (a) (b) 376 Copyrght c 215 SERSC

11 (c) Fgure6. The Dstrbuton Path Chart of System Termnal Dstrbuton Module As the Fgure 6 shows, the dstrbuton module can provde three knds of dstrbuton plan as follow. The frst s the shortest dstrbuton path, second s the hghest customer satsfacton, and the last s comprehensve dstrbuton. In Fgure 6(a), choose the frst dstrbuton plan, the dstrbuton dstance s 4.61km and the customer satsfacton s.2. In Fgure 6(b), choose the second dstrbuton plan, the dstrbuton dstance s 23.55km and the customer satsfacton s In Fgure 6(c), choose the last dstrbuton plan, the dstrbuton dstance s 4.92km and the customer satsfacton s The expermental results are same as the expermental 3.2 shows, whch the algorthm s proved effectve. 4. Concluson Takng am at the problems of long dstrbuton routes and tme by usng basc GA to optmze mult-objectve logstcs dstrbuton path, ths paper use the dstance and dstance related customer satsfacton factor as the objectve functon, and ntroduces kruskal algorthm nto basc GA to acheve the optmzng mult-objectve logstcs dstrbuton path. At last, to test the optmzaton results, the termnal dstrbuton model and the vrtual logstcs system operatng model are bult. Experment results show that, compared wth basc GA, the run tme of KCGA takes a slghtly hgher. But the average dstrbuton dstance and the best dstrbuton dstance are reduced by 6%-8%. Acheve the goal of mult-objectve logstcs dstrbuton path optmzaton. Acknowledgments Ths work s supported by Scence Foundaton Project of CQ (CSTC213yykfC65, cstc214jcyja64). References [1] Zhao D. M., The Quanttatve and Margnal Analyss of Reducng the Compasson between the Logstcs Costs and GDP, Logstcs Engneerng and Management, vol. 34, (212), pp [2] L Z., Chen X. H. and Wang H., Bucklng Optmzaton of Composte Lamnate Usng Modfed Ant Colony Optmzaton, J. Shangha Jaotong Unv. (Sc.), vol.46, (212), pp [3] Guo Y., Ln Y. and Zhang S., Interactve genetc algorthms based on frequent-pattern mnng, Proceedngs - 2 6th Internatonal Conference on Natural Computaton (ICNC), (2), pp [4] Wang T. Z. and Fan G. L., The research of buldng fuzzy C-means clusterng model based on partcle swarm optmzaton, Telkomnka - Indonesan Journal of Electrcal Engneerng, vol. 11, (213), pp Copyrght c 215 SERSC 377

12 [5] L Y., Jang J., Zhang Mn X., Automatc Word-Length Determnaton Tool Based on Smulated Annealng Algorthm, J. Shangha Jaotong Unv. (Sc.), vol.47, (213), pp [6] Holland J., Genetc Algorthm Theory and Applcaton, Translaton of L Mn-qang. Bejng scence and Technology Press, (23). [7] Kosnsk. W., Kotowsk S. and Mchalewcz Z., On convergence and optmalty of genetc algorthms, 2 IEEE Congress on Evolutonary Computaton (CEC), (2), pp.1-6. [8] Feng L., Chunyan Z. and K. C. Chang, Convergence rate analyss of alled genetc algorthm, 2 49th IEEE Conference on Decson and Control (CDC), (2), pp [9] B. Ombuk, M. Nakamura and M. Osamu, A Hybrd Search Based on Genetc Algorthms and Tabu Search for Vehcle Routng, In the 6th Internatonal Conference on Artfcal Intellgence and Soft Computng.Banff [C].Canada: ABC, (22), pp [] Tseng L. T., Genetc algorthm usng the bmodal operaton to prevent prematurty and reduce computatonal tme, Appled Mechancs and Materals, (212), pp [11] Sh L., Supply chan partnershp research based on customer satsfacton degree, Proceedngs of the 212 2nd Internatonal Conference on Busness Computng and Global Informatzaton, (212), pp [12] Ospov V., (Unverstät Karlsruhe (TH), Germany); Sanders P., Sngler J., The Flter-Kruskal mnmum spannng tree algorthm, 29 Proceedngs of the 11th Workshop on Algorthm Engneerng and Experments, (29), pp [13] Wu Q., VRP optmzaton of ntensve dstrbuton n enterprse sales logstcs, 2 Internatonal Conference on Management and Servce Scence, (2), pp.1-3. Author Yan Zhang, she was born n 1982 n Chongqng (Chna). In 27, she receved the master degree from the graduate school of logstcs, Inha Unversty. Now she s workng n Chongqng Unversty of Post and Telecommuncaton. Her research focus ncludes supply chan management, logstcs system optmzaton, vrtual envronment modelng. 378 Copyrght c 215 SERSC