Resource-Constrained Scheduling Optimization for Public Bicycles using Multi- Variety Ant Colony Algorithm

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1 Resource-Constraned Schedulng Optmzaton for Publc Bcycles usng Mult- Varety Ant Colony Algorthm Hatao XU, Hongwe ZHU, Nng ZHENG*, Jaxue PENG, Zhbe QI Hangzhou Danz Unversty, Zhejang Provnce, Hangzhou Zhejang, 3008, Chna Abstract Publc bcycle system has the problems of borrowng and returnng n practcal moton, the man reason beng the nter-staton bcycle schedulng s unreasonable and not tmely. The paper proposes a resource-constraned schedulng optmzaton algorthm for publc bcycles based on mult-varety ant colony algorthm. Frstly: ) we study schedulng optmzaton problems of publc bcycles, ) and gve schedulng optmzaton model under resourced-constraned condton, ) we consder schedulng vehcle capacty constrant and staton supply constrant. Secondly: ) we mprove the schedulng optmzaton model for publc bcycles by mang use of ant colony algorthm, such that ) all ant colones carry out search and decson ndependently based on seral schedule generaton mechansm to mprove optmal performance, and ) we deal wth the nteracton of pheromone that exsts between all ant colones to realze acceleraton search. Fnally, we verfy the effectveness of the proposed method by schedulng optmzaton experment of publc bcycles system n the area of Bnjang of Hangzhou Cty. Keywords- publc bcycle; ant colony algorthm; mult-varety; resource-constraned; pheromone I. INTRODUCTION Publc bcycle system (publc bcycle system,pbs) orgnates from Europe, mplementaton purpose s to solve the problem of last m from publc transportaton staton to places of resdence. From the end of 990s, many countres n Europe and Amerca ntroduce free bcycle lease servce; n nternatonal large ctes of Lyons, Pars, London, New Yor, Amsterdam, etc., free bcycle lease servce develops qucly; mplementaton effect shows PBS has postve functon to ease traffc pressure and promote energy conservaton and emsson reducton. Domestc PBS mplementaton s n startng stage; research n publc be plannng just begns; Yao Yao, Guo Mnhu and L Lhu have respectvely ntroduced PBS plannng n Hangzhou, Shangha and Wuhan; put forward respectvely statonng prncple, bcycles dstrbuton scale and layout plannng scheme for bcycle system servce pont accordng to condton of all ctes. After PBS mplementaton n recent years, urgent generalty problems occur n PBS of several domestc ctes, whch manly are the problems of dffcult borrowng and dffcult returnng. Man reasons nclude: unreasonable ste selecton of PBS staton; 2 unreasonable bcycle dstrbuton of PBS staton; 3 unreasonable and not tmely schedulng for bcycle between statons. Reasonable and tmely schedulng for bcycle numbers between statons of PBS can mprove effectvely turnover rate of bcycles and servce level of PBS. Travel route of schedulng vehcle between statons of bcycle s a typcal travellng salesman problem. Dffculty of solvng shortest travel return route ncreases obvously wth the ncrease of statons number. Therefore, the Paper puts forward a nd resourceconstraned schedulng optmzaton algorthm for publc bcycle based on mult-varety ant colony algorthm. Optmze schedulng optmzaton model for publc bcycle by mang use of ant colony algorthm. At last, verfy the effectveness of proposed method by experment. II. MATHEMATICAL DESCRIPTION OF MODEL Inter-staton bcycle schedulng s a specal sales man problem n PBS, shown as Fg.. Schedulng vehcle shall start from fxed startng pont and collect spare bcycles or provde and supply certan amount of bcycles when passng each staton; at last, t returns bac to startng pont and completes a bcycle schedulng. It s assumed n the research that bcycle schedulng s routne operaton; namely, carry out schedulng operaton accordng to practcal experence. Fgure. Publc bcycle system Accordng to partcularty of schedulng optmzaton, mathematcal descrpton to establsh model by mang use of gven dagram form s: G ( V, A) () DOI 0.503/ IJSSST.a ISSN: x onlne, prnt

2 Where, V s set of bcycle statons; A s fronter set that s consttuted by all statons. Supposed that D ( d j ) s dstance matrx that s consttuted by dstance between staton and staton j; supposed that B ( b ) s bcycle amount that shall be scheduled by all statons of bcycles; b 0 represents b spare bcycles n staton ; otherwse, t represents b bcycles needed to be suppled; staton of b 0 does not need schedulng; clear and remove these statons durng schedulng optmzaton. Sum of b for all statons needng schedulng shall be 0. In specal condton, f supply bcycles are ncreased, map spare bcycles number to a staton to ensure sum of all b s 0. Value b of all statons s obtaned by present actual bcycles number subtractng deal dstrbuton number calculated by hstory data. In Fg. G, t s requred that Hamlton loop T wth shortest length shall be confrmed; namely, start from a staton (startng pont), only one-tme shortest dstance L by passng all statons. For set V { v, v2,, v n } wth n statons, Hamlton loop access order s: T { t, t,, t,, t } (2) 2 Where, t V(,2,, n) and record as t n t. The tas of schedulng vehcle s to collect spare bcycles and supply needed bcycles by passng all bcycles statons. For startng pont, f there are spare bcycles n startng ponts, they can be put n schedulng vehcle; f startng pont lac bcycles, the second staton shall have spare bcycles. Afterwards, each staton shall have specal constrant condton: capacty constrant for schedulng vehcle; the constrant of maxmal loadng bcycle number Bcycle Max shall be consdered durng collecton of bcycles, namely, after collectng spare bcycles of next staton, the total number of bcycles on schedulng vehcle shall less than or equal to supply number of next staton. Otherwse, bcycle on schedulng vehcle wll be nadequate. 2 Supply constrant for next staton pont; consder whether the number of bcycles can meet supply demand of next staton pont when supplyng bcycles; namely, the number of bcycles on schedulng vehcle shall be larger than or equal to supply demand of next staton pont; otherwse, the number of bcycles on schedulng vehcles shall be nadequate. If the 2 constrant condtons are not satsfed, the staton cannot be selected as next staton. Record the number of bcycles on schedulng vehcle by ba durng schedulng process. Therefore, ba shall meet: n BeMax ba 0(,2,, n) (3) Mathematc model of nter-staton schedulng optmzaton problems of bcycle system s: mn L dt, t (4) Resource constrant condton s: Where, 2,3,, n bt, b 0 t ba 0, bt 0 t 0 (5) ba ba b (6) ba ba b BeMax (7) t III. MULTI-VARIETY ANT COLONY ALGORITHM A. Standard ant Colony Algorthm Ant colony algorthm s smulaton that ant colony forages by pheromone and s wdely used to optmzaton problem of varous combnatons. Generally speang, ant colony algorthm generates a complete and feasble project schedulng plan by adoptng schedule generaton system and by expandng local schedulng plan gradually. Receve best soluton by repeated research. See Fg. 2 for schematc dagram of smulaton of ant foragng. Fgure 2. Schematc dagram of smulaton of ant foragng In ant colony algorthm, ant searches from the frst tas and searches all tass; fnsh search n the jth tas. Durng gth search, after ant selects tas, feasble canddate tass set s recorded as D ; the set ncludes all schedules that are not arranged. At the same tme, schedule of all urgent tass have been arranged. Therefore, D not only excludes all selected tass, but also excludes all tass that cannot be arranged behnd tas logcally. Probablty of ant to select tas j from D s: Where, j a j j, j D a P ( ) h h j g (8) hd 0, j D s pheromone; j s heurstc nformaton; and are parameter to control 2 nds of nformaton weght. Heurstc nformaton generally represents perceptual ntuton that can be used n search decson. In RCPSP, DOI 0.503/ IJSSST.a ISSN: x onlne, prnt

3 heurstc nformaton s generally constructed by precedence rule. The most common s latest fnsh tme (late fnsh, LF); record latest fnsh tme of tas as L j ; therefore, heurstc nformaton can be represented as: j max Lh Lj (9) hd Updatng of pheromone s emphass of ant colony algorthm, whch ncludes volatlzaton and accumulaton of pheromone; volatlzaton and accumulaton of pheromone generally can adopt the followng mechansm: j ( g ) ( ) j (0) j / f () Where, s volatlzaton rate of pheromone; f s objectve functon value after completon of a complete search by ant. When ant searches from the frst tas to the tas Jth, t consttutes a complete tas lne. A feasble project schedule plan can be gotten by arrangng startng tme of all tass n order of the tas lne, on the premse of meetng resource constrant, accordng to early prncple. B. Search Decson Durng the process of search decson, represent the th ant n the l th colony by, ; the probablty of ant, to select tas j after selectng closely tas s: pj hd 0, j D j g, j D h g (2) Where, j g represents tendency degree that ant, contnues to select tas j after selectng tas : rd lr, l g{ [ g ] } (3) j j j r Where, parameter lr, decdes nfluence of pheromone between colony l and colony r. If value of lr, s postve, therefore, pheromone of colony r has postve promoton effect for search decson n colony l ; f lr, s negatve, pheromone of colony r has negatve suppresson effect; the larger the absolute value of lr, s, the stronger the postve effect or negatve effect of pheromone. If lr, s 0, there s no nteracton between colony l and colony r. s a decmal to prevent strength of pheromone s 0. l presents weght of heurstc nformaton n search decson of ant colony l. Supposed that objectve functon of the frst ant colony s mnmal total dstance of bcycle; adopt unverse latest completon tme precedence rule. Supposed that objectve functon of the second ant colony s weghtng tas mnmal delay; desgn the followng precedence prncple based on tas delay: Wj wj( Lj d j) (4) Heurstc nformaton of the second ant colony s: j maxwh Wj (5) hd C. Updatng Mechansm of Pheromone Pheromone of ant colony l can adopt the followng updatng mechansm: l ( ) l ( ) j g j g lj (6) Where, lj represents pheromone that released by ant, on vrtual route, j ; ts strength depends on qualty of receved soluton. For dfferent varetes, t can desgn dfferent pheromone updatng mechansm; for the frst colony, desgn the followng pheromone ncrement: lj (7) CT Where, s postve constant; CTJ represents total duraton of project schedule plan obtaned by ant,. For the second colony, desgn the followng pheromone ncrement: J 2 lj (8) WT Where: 2 s postve constant; WT represents weghtng tas delay of project schedule plan obtaned by ant,. D. Algorthm Steps In concluson, mult-varety ant colony algorthm desgned for mult-target resource-constraned project schedulng problems s as follows: Algorthm: mult-target resource-constraned multvarety ant colony algorthm of publc bcycle system nput RCPSP nstance ntalze coeffcents set pheromone matrx j 0 for every crcle for every ant colony for every ant DOI 0.503/ IJSSST.a ISSN: x onlne, prnt

4 for stage=:j estmate D ; select j from D ; set CT j as early as possbl evaporate pheromone j ; update pheromone j ; calculate devaton(s) f devaton(s)< devaton(s )then update S*; update pheromone j ; end f output S* IV. EXPERIMENTAL ANALYSIS A. Expermental Scheme and Data The Research selects PBS n an area of Bnjang of Hangzhou Cty. There are a schedulng center MO and 62 servce ponts of PBS; select 9 servce ponts that meet frstclass servce wndow condton as experment object. Heren, relevant lease requrement data s shown as Table. TABLE. INFORMATION DATA TABLE OF LEASE REQUIREMENT OF SERVICE POINT Loc stud n Servce Present bcycle Bcycle Bcycle servce pont pont No. number/unt loc rato number/unt number/unt Supposed d t 0 when servce pont need to send bcycles; d t 0 when servce pont need to transport nto bcycles. Maxmal number for loadng bcycles s 75 for actual schedulng vehcle. Cost of mleage s 2 Yuan/m; average travellng speed of schedulng vehcle s 36m/h; dstance between all servce ponts and the dstance between servce staton and schedulng center are shown as Table 2. Accordng to prevous schedulng experence, t needs 20s to set schedulng personnel to add or remove a bcycle; schedulng stoppng tme of schedulng vehcle n servce pont s d 3mn t ; t s 0.2d t m after transformng to travellng dstance; fxed cost for a round of schedulng s 80 Yuan. Change factor of users satsfacton s 0.36 c 0. B. Result Analyss Accordng to Table, the Research obtans schedulng plan by ant colony algorthm. In the process of experment and test, the 20 experments wth 200 teratons have been carred out. 8 optmal schemes wth the same performance; the optmal soluton s shown as Table 2. Algorthm Artfcal experence algorthm Algorthm n the paper Table 2. Optmzng Result Of The Optmal Soluton Schedulng lnes Mo->620- >67->63- >6027-> 602->6080- >6066->6097- >6205->Mo Mo->620- >6205->67- >63-> 6027->602- >6080->6066- Schedulng mleage/m Comprehensve schedulng cost/yuan >6097->Mo It can be gotten from Table 2 that total length of schedulng lnes obtaned from algorthm optmzaton of the paper s 26.3 m, whch s 4.9m less than path length f experence lnes. At the same tme, lnes after optmzaton have carred out precedent schedulng to mportant servce pont (620, 6205); try to mprove users satsfacton. Comprehensve schedulng cost of optmzng lnes s 9,6.8 Yuan (not actual cost and for reference only), whch saves 3.8 Yuan compared wth that of experence lnes and s about 22.7% of comprehensve schedulng cost before optmzaton. Fgure 3. Total length of schedulng lnes Fg. 3 shows convergence contrast condton of 5 nds algorthms; heren, algorthm s algorthm of the paper; algorthm 2 s partcle swarm algorthm; algorthm 3 s genetc algorthm; algorthm 4 s dfferental evoluton algorthm; algorthm 5 s standard ant colony algorthm. It can be seen that algorthm of the paper s superor to selected contrast algorthm on fnal convergence result and embodes effectveness of algorthm. DOI 0.503/ IJSSST.a ISSN: x onlne, prnt

5 V. CONCLUSIONS The paper puts forward a nd resource-constraned schedulng optmzaton algorthm for publc bcycle based on mult-varety ant colony algorthm; researches schedulng optmzaton of publc bcycle system; provdes schedulng optmzaton model n resource-constraned condton; carry out optmzaton to schedulng optmzaton model of publc bcycle by mang use of ant colony algorthm; fnally, carry out verfcaton to algorthm performance by experment. Research ey ponts for next step s to carry out hardware settng to actual system and further optmzaton of algorthm to decrease algorthm complexty and realze further mprovement of precson. ACKNOWLEDGMENTS Publc Projects of Zhejang Provnce(203C33082, 205C33067), State Key Program of Zhejang Provnce Natural Scence Foundaton of Chna(LZ5F020003). REFERENCES [] Wang J Q, Zhang S F, Chen J. Resource-constraned mult-project schedulng based on ant colony optmzaton algorthm[m]. IEEE, (200). [2] Lu, Y., Yang, J., Meng, Q., Lv, Z., Song, Z., & Gao, Z. (206). Stereoscopc mage qualty assessment method based on bnocular combnaton salency model. Sgnal Processng, 25, [3] Yang, J., Xu, R., Lv, Z., & Song, H. (206). Analyss of Camera Arrays Applcable to the Internet of Thngs. Sensors, 6(3), 42. [4] Lv, Z., Penades, V., Blasco, S., Chrvella, J., & Gaglardo, P. (206). Evaluaton of Knect2 based balance measurement. Neurocomputng. [5] Wu, W., L, H., Su, T., Lu, H., & Lv, Z. (206). GPU-accelerated SPH fluds surface reconstructon usng two-level spatal unform grds. The Vsual Computer, -4. [6] Gu, W., Lv, Z., & Hao, M. (205). Change detecton method for remote sensng mages based on an mproved Marov random feld. Multmeda Tools and Applcatons, -6. [7] L, X., Lv, Z., Wang, W., Zhang, B., Hu, J., Yn, L., & Feng, S. (206). WebVRGIS based traffc analyss and vsualzaton system. Advances n Engneerng Software, 93, -8. [8] Wang J Q, Zhang S F, Chen J. Resource-constraned mult-project schedulng based on ant colony optmzaton algorthm[c]// IEEE Internatonal Conference on Intellgent Computng and Intellgent Systems. IEEE, (200). [9] Lu Z G, Yan L I, Shu-Juan L I. Mult-resource Constraned Job-shop Optmzaton Schedulng Based on Ant Colony Algorthm[J]. Journal of System Smulaton, (2007), 9(): [0] Xue H Q, We S M, Wang Y E. Resource-constraned mult-project schedulng based on ant colony neural networ[c]// Internatonal Conference on Appercevng Computng and Intellgence Analyss. IEEE, (200): [] Zhang W C. Ant colony and partcle swarm optmzaton algorthmbased soluton to mult-mode resource-constraned project schedulng problem[j]. Computer Engneerng & Applcatons, (2007), 43(34): [2] Zhao J C, Zhang Y M, Qu H Y. Ant Colony Optmzaton for Resource-Constraned Mult-Project Schedulng[M]. (2009). [3] Zhang H. Ant Colony Optmzaton for Multmode Resource- Constraned Project Schedulng[J]. Journal of Management n Engneerng, (205), 28(2): [4] Merle D, Mddendorf M, Schmec H. Ant colony optmzaton for resource-constraned project schedulng[j]. Evolutonary Computaton IEEE Transactons on, (2002), 6(4): [5] Shan M, Wu J, Peng D. Partcle Swarm and Ant Colony Algorthms Hybrdzed for Mult-Mode Resource-constraned Project Schedulng Problem wth Mnmum Tme Lag[C]// Internatonal Conference on Wreless Communcatons, NETWORKING and Moble Computng. (2007): [6] Chang C W, Huang Y Q, Wang W Y. Ant colony optmzaton wth parameter adaptaton for mult-mode resource-constraned project schedulng[j]. Journal of Intellgent & Fuzzy Systems Applcatons n Engneerng & Technology, (2008), 9(4,5): DOI 0.503/ IJSSST.a ISSN: x onlne, prnt