Design of Toll Plaza Based on Genetic Algorithm

Transcription

1 d Iteratioal Coerece o Mechatroics Egieerig ad Ioratio Techology (ICMEIT 017) Desig o Toll Plaza Based o Geetic Algorith Jia Feg a, Wei Xiag b,* College o Electric ad Ioratio Egieerig, Southwest Uiversity or Natioalities, Chegdu , Chia a @qq.co, b @qq.co, Correspodig author: Wei Xiag Keywords: Toll Plaza, Geetic Algorith, Optial Value. Abstract. This paper studies the desig o toll plaza based o geetic algorith. Based o the idea o the uctio value o the geetic algorith, the area o the toll statio ad the traic accidet rate are take as the objective uctio, to id out the optial value o the costructio cost uder the iluece o the uber o toll statios, the gradiet rate, the width o the toll statio. 1. Itroductio With the rapid developet o the expressway, as a iportat part o the highway toll statio buildig egieerig is becoig ore ad ore iportat.toll statio is the bottleeck o the highway traic, it s operatio ake a direct ipact o the road capacity, but also a iportat part o the plaig ad costructio o toll statios.thereore, to solve the cogestio proble o toll statio is the basis o the desig o toll statio ad ecooic evaluatio.i the highway toll statio desig, ot oly to cosider the soothess o the highway, ad secodly, the shape o the toll statio area is ot to be uderestiated.i this paper, a geetic algorith is used to establish the odel o sooth ad reasoable cost, deteriig the optial solutio o toll statio.. Geetic Algorith Geetic algorith is a siulatio o the evolutio o orgaiss, start ro a iitial populatio, repeated selectio, crossover ad utatio operatios, a set o cadidate solutios is retaied i each iteratio. Accordig to soe speciied idex, the evolutio o populatio is gettig closer ad closer to a certai goal, so as to obtai the optial solutio or satisactory solutio.the geetic algorith uses the vicissitudes rule o probability to guide the search directio,searchig ro strig set,the coverage is large, which is avorable to the global optiizatio ad reduces the risk o beig trapped i the local optial solutio.at the sae tie, the algorith is easy to be parallelized, ad oly the itess uctio value is used to evaluate the idividual.o this basis, geetic aipulatio is to be used. 3. The Establishet o The Model 3.1 Model Establishet We will divide charge statio ito three parts, respectively is the etry sectio, waitig or the service period, leavig the toll statios, as show i Fig.1. I the desig o toll statio, based o the ipact o costructio costs ad traic luecy.the ost iportat thig is the desig o the toll area. The structure o the toll statio is built i the or o igure oe, the structure o a i ad a out area is basically the sae.ad the legth o the iterediate service area o each toll statio is the sae as that o the atioal road costructio law.thereore, this article oly take the a area o the chargig statio ito to cosider. The shape o the etrace area o the toll statio, as show i Fig.. Copyright 017, the Authors. Published by Atlatis Press. This is a ope access article uder the CC BY-NC licese ( 35

2 Figure 1. Toll statio overall ap Rate o chage o toll plaza Rate o chage o toll plaza: Figure. The a shape ta (1) Accordig to the literature search, get the uctioal relatioship betwee the rate o chage o toll plaza ad the uber o traic accidets [1] Y 1.431e () I the orula, Y-the uber o traic accidets correspodig to the gradual chage rate o toll plaza; - gradual chage rate o toll plaza. Matlab appig ca be used to clearly kow the relatioship betwee the two, as show i Fig.3. Figure 3. Relatioship betwee gradual chage rate ad traic accidets It ca be see ro the graph that the larger the gradiet rate is, the higher the requecy o traic accidets Calculatio o area o a etrace Accordig to the geoetric relatio i Figure two, the area o the a area ca be expressed as w w *l u (3) The area o the etrace area o the toll lae: s l *w 1 * * l (4) Speciies the width o each toll statio (icludig toll booths ad toll laes)is d, w d * (5) Accordig to deteriatio o the uber o toll statios, the value o toll lae ca be calculated, l a l (6) The coeiciets o a l used i the calculatio o l, values are geerally take ro 0.01 to 0.05, so take 0.0 kiloeter. The area o the etrace area o the toll lae: s a * d * l 1 * * (a ) (7) l 3. Highway Toll Plaza Desig Speciicatio Paraeters Accordig to the atioal highway toll plaza desig speciicatios, we ca deterie the local spatial rage, as show i Table 1. 36

3 Table 1. Desig paraeters o Expressway Toll Plaza Paraeter Nae Value Rage Chael width d 1.8~4.5 Toll islad width d.0~.7 Nuber o toll statios 8 Gradual chage rate 1/7~1/3 Copay uit 4. To Solve the Optial Value 4.1 Liit to the Optial Value I the uctioal relatioship, i we seek the optial value o ultivariate uctio, we ote use the let ad right liits o the uctio thought to id the optial solutio [].Below we will use the let ad right liit to id the optial solutio. Accordig to equatio (7) we kow that s is a ultivariate uctio or, ad d, i order that the s has a iiu value, we should ake s to get the iiu s.we should ake the aoresaid 0d iiu ad cosequet 00 axiu, the width o per uit o the toll statio back is 4.8, is 1/3.Siilarly, to get s has a axiu value, we should ake the axiu o aoresaid, iiu o cosequet, the width o per uit o the toll statio back is 7., is 1/0. The axiu s value o solutio is s Toll statio costructio area ad the uber o toll islad ito a o-liear relatioship. Accordig to state regulatios, whe is two, s Whe is eight, s Establishet o Geetic Algorith Paraeters Forula (7) is a ultivariate uctio, which ca be see that the a area is related to ay actors. Whe solvig the a i the area, the cost based o the atioal lad acquisitio is higher tha the costructio o chargig plator ad the cost o pavig, we aily cosider the iiu cost o the lad area. This paper puts orward the optial geetic algorith is used to solve the a i the area o value, toll statio uber is, the width o each toll statio (icludig toll booths ad toll lae width) is d, gradual chage ratio are served as three gees o the chroosoe. First o all, codig the idividual gee.the idepedet variables o the uctio ca be regarded as the represetatio or o the geetic algorith, ad the biary appig is used to ap the pheotype to geotype. I the iiu accuracy o the results is ot less tha 0.001, the biary strig o each variable ca be take up to 10 bits. Because the objective uctio is a uctio o three variables, so there are three gees o each chroosoe. The legth o each gee is 10, so the total legth o a sigle chroosoe is 30, at this poit, a 100 * 3 atrix is geerated. We ca produce a certai uber o idividuals to or a populatio, the size o the populatio is the uber o idividuals i the populatio. Secodly, to deterie the itess o this geetic operatio. I this paper, the s o the objective uctio value is used as the itess, the axiu o the costructio area is the axiu o the objective uctio, ad the itess is higher. The, select the better idividual. For the idividual selectio we use the roulette selectio ethod [3]. This algorith is siple, i order to select atig idividuals, it is ecessary to carry out ultiple rouds o selectio, each roud to produce a [0,1] uior rado uber, the rado uber as a selectio poiter to deterie the selected idividual. Fially, geetic aipulatio are take out. A idividual represeted by a atural biary ecodig ethod[4].i the cross variable usig the gray code or ecodig the idividual, i there is a bit dierece betwee the strig, the correspodig paraeter value is oly doig a sall dierece. i ax 5. Matlab Siulatio Accordig to the above algorith prograig uder the MATLAB eviroet, the siulatio waveor is show i Fig.4. 37

4 Figure 4 optial value o costructio area Fro the above chart shows, with the geetic operatio, the costructio area o the toll statio i the luctuatio o a deteried value ear, does ot appear large variatio values, through geetic algorith to id the optial value o , as the value o the solutio. Whe the optial solutio is obtaied by s, the optial value o each paraeter is show i Table. Table. Optial paraeters Optial Solutio o Fuctio Geetic Algorith Paraeter Nae Uit Relatio Optial Solutio s Costructio area Toll statio width d 4.8~ Toll statio plator Gradual chage rate 1/7~1/ Traic accidet 4.505~ case Fro the above table, the optial solutio obtaied by geetic algorith are i the rage o the optial solutio, ad the optial solutio is ot the estiatio rage, but the exact value i the case o the sallest error, has ore practical reerece value to the ipleetatio o the project, urther proo o the superiority o the algorith i this paper. 6. Coclusio I this paper, the geetic algorith is used to estiate the area o the toll statio ad the traic accidet rate, the superiority o geetic algorith ad the ratioality o the algorith are proved by Matlab siulatio, ad ake a eective assesset to the uber o toll statios, gradiet rate, toll statio width ad other actors. Ackowledgets This work was partially supported by Natioal Nature Sciece Foudatio ( ), SWUN Costructio Projects or Graduate Degree Progras (017XWD-S0805), Advace Research Pro-gra o Electroic Sciece ad Techology Natioal Progra(017YYGZS16) ad Sichua Youth Sciece ad techology iovatio research tea (017TD008), also was iacially supported by studets iovatio traiig project o SWUN(S ). Reereces [1] Zhag Mi,Che Hog,Wu Xiaowu. Saety evaluatio odel o expressway toll statio [J]. Chiese Joural o saety sciece, 009, (): [] Wag Shegju. Applicatio o uctio idea i the proble o paraeter estiatio [J]. sciece ad Techology Iovatio Herald, 016, (0): [3] Zhag Che, Zha Zhihui. Copariso o selectio strategies or geetic algoriths [J]. coputer 38

5 egieerig ad desig, 009, (): [4] Yag Xiaohua, Lu Guihua, Yag Zhieg, Li Jia Qiag. Gray codig geetic algorith ad theory research [J]. systes egieerig theory & practice, 003, (03):