A novel plant growth simulation algorithm and its application. Jun Lu, Yueguang Li

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1 Iteratioal Coerece o Advaces i Mechaical Egieerig ad Idustrial Iormatics (AMEII 05 A ovel plat growth simulatio algorithm ad its applicatio Ju Lu, Yueguag Li Gasu political sciece ad law istitute, Lazhou, gasu, , Chia Keywords: Plat growth simulatio algorithm; uctio; Iluece actors; Itelliget algorithm; est Abstract.his paper proposes a ovel plat growth simulatio algorithm. hrough the optimizatio experimetal o testig o the stadard uctio, the results show that the ovel plat growth simulatio algorithm has reliable covergece, high covergece rate ad solutio precisio.. Itroductio he optimizatio process o uctio problem is rom oe iitial state to the attractor i the easible regio o space []. Whe the uctio has a uique optimal solutio, equivalet to oly oe attractor i the space o easible regio, at this time the whole easible regio o space is the domai o attractio o the attractor, i order to solve this problem, brach boud method [], cuttig plae method [3], Motecarlo stochastic method ad a series o local or greedy algorithm are eective, they ca obtai the global optimal solutio [4]. However, the complex uctio problem has multiple global or local optimal solutios i the easible regio, which meas that the space exists multiple attractors, ad the optimizatio process evolutio to which attractor depeds o the iitial all i which space o easible regio, this eature causes the algorithm ito a local miimum poit ad ca ot be the udametal o the global optimal solutio [5]. Aimig at this problem how to jump out o a local miimum poit, i recet years, the category o bioic algorithm achieved attract people's attetio achievemets, its success lies i the algorithms the imitatio o ature i dieret biomes or eviromet adaptive optimizatio model, set up radom, positive eedback, coordiatio model. I may o the bioic model, essetial to simulate aimal ad isect, or some plat atural optimizatio model, such as phototropism dyamic mechaism, have ot give suiciet attetio. Rush J J Ki ad uri et al. Plat growth ad plat morphogeesis model o Lide Mayer ad Proulx Se Covic et al. he growth o brach model is maily aimed at the ield o computer graphics, ractal problems, the plat growth dyamics mechaism applied to solve uctio problems, there is o related research.. he plat growth simulatio algorithm Plat growth simulatio algorithm (PGSA is a evolutioary computatio techique through simulatig the growth processes i plats, which is based o the priciples o plat phototropism growth [6]. he algorithm has a good prospect i the applicatio due to requirig a simple o the parameters. It has gradually bee applied i the ield o egieerig by may scholars [7]. PGSA sets up several basic coceptio: root truk brach growth poit ad light source. he root o a plat expresses iitial solutio; the truk ad brach correspod to the search domai o possible solutios; the selected growth poit expresses the base o ext searchig process ad the light source represets the global optimal solutio. he key poit o PGSA is selectig oe growth poit to erupt ito brach, ad esurig the brach growig toward the light source. 05. he authors - Published by Atlatis Press 700

2 Plats ca be viewed as a system, which composes o a large umber o braches ad odes. It must be as soo as possible to strive or breedig more braches ad leaves or earig more surace areas, which ca obtai the greatest possible sulight. he orm o grammar that simulates the plat descriptio aalysis ad developmet had bee established sice liguistics was itroduced ito the biological, which based o a simple rewrite rules ad brachig rules, this is called L-system. Formal descriptio o plat growth ca be carried out as the ollowig:. he sectio o the site grow ew braches which irst emerged i a umber o stems is called the growth ode.. Most o the ew braches have grow updated braches, ad the process repeated o the old ad ew braches. 3. Dieret braches i the tree have similarities with each other, ad the etire plat has sel-similar structure. he Brachig model o plat growth is improved accordig to L-system combied with computer graphics ad ractal theory, the plat, as the orm o plat growth characteristics, ca be described as ollow: Supposed braches o plat growth occurred i the two-dimesioal plae, Each brach growig i uits legth every time, or rotatig a certai agle α, Startig rom the ode o truk or braches, he growth process were repeated through rewritig the rules o braches o plat growth i the two dimesioal plae. It was proved by biological experimets that a ew brach that is able to grow depeds o its morphacti cocetratio whe the plat has more tha oe ode. he ode which has larger value o morpheme cocetratio has more growth opportuities tha the smaller oe, morphacti cocetratio are ot pre-assiged to the odes, but ormed accordig to their locatio iormatio which we call that plat showed the eature o plat s Phototropism. Ater the ode has bee ormed, morphacti cocetratio will be readjusted accordig to chagig i the eviromet o a ew growth ode else. We could describe the characteristics o plat growth i term o the mathematical view basis o plat growth aalysis o the above. Suppose the legth o tree truk is, the legth o brach is L, ( there are W growig odes S S, S,..., SW ( odes is P P, P,..., PW i the truk, morphacti cocetratio o those S ( S S,..., Sq respectively. here are q growth odes, brach. Morphacti cocetratio o those odes is P ( P, P,..., Pq morphacti cocetratio which grow i the truk ad brach is calculated as ollows: i the respectively. he P i ( x0 ( Si W ( q ( ( x0 ( Si + ( x0 ( xq i j ( Where x0 represets the root o plat (the iitial ode, ( is the iormatio uctio o the ode i the eviromet, he smaller value o the uctio as possible shows the better eviromet where the ode located, it will help to grow ew brach. From ormula (, the value o morphacti cocetratio i every ode depeds o relative positio o the relative to the iitial root ad the locatio o the evirometal iormatio, the mechaism cosistet with the ormatio o the morphacti cocetratio i the plat cell. We ca deduced rom ormula ( as ollows: 70

3 q ( P i + P j i j We ca produce radom umber i the iterval [0, ]. he radom umber must all withi oe ( P, P P q o the state space,..., +, where the correspodig ode will have a prior right to grow ew brach. he value o morphacti cocetratio i all odes will chage ater the ew brach has grow up. Computatio ormula o the value o morphacti cocetratio i other odes will add the relevat ode o the ew brach, ad remove the grow ode, which basis o ormula (. he process will be repeated util there is o ew braches growig. 3. he aalysis o simulatio I order to veriy the eectiveess o the algorithm, this paper takes 5 bechmark uctios as a example to calculate, compared with reerece [8], literatures [9], literatures [0] ad literatures []. ( x i i i x i i j ( 00( x x + ( x 3 i+ i i xi 4 xi cos i i i 5 0exp 0. exp cos( exp( xi pxi i i I the experimet, the algorithm parameter settigs are as ollows. For uctios - 5, the populatio size is 0, the umber o iteratios is 50, the scope o the search or [-0, 0], dimesio N0. he ial testig results o the algorithm usig the average value o the idepedet operatio o 0 times. It ca be see, the covergece speed ad covergece accuracy o the algorithm is better tha AFSA ad SAFSA, the expected eect is reached or ovel plat growth simulatio algorithm. i 70

4 Fig. Fitess o the evolutioary curve o Fig. Fitess o the evolutioary curve o Fig.3 Fitess o the evolutioary curve o 3 Fig.4 Fitess o the evolutioary curve o 4 Fig.5 Fitess o the evolutioary curve o 5 4. Coclusios his paper presets a improved plat growth algorithm ad veriies through ive test uctios, the experimetal results show that this method is practical, simple ad easy to uderstad. Ackowledgmet his work is supported by Gasu Provicial College graduate tutor o scietiic research project (-09 ad Dea Fud o Gasu Normal College or Natioalities ( Reereces [] Huag Zhagca,Wu Fagcai,Hu Xiaoli. A evolutioary algorithm to iteger programmig problem based o pheromoe [J].Computer Applicatio Research, 00 (7:7-9. [] Zhu Wexig. A illed uctio method or iteger programmig[j]. Acta Mathematics Applicatio Siica, 000, 3(4: [3] Meg Zhiqig,Hu Qiyig,Yag Xiaoqi. A method o o-liear pealty uctio or solvig iteger programmig ad mixed iteger programmig [J].Cotrol ad decisio,00,7(3:

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