改进的粒子群优化控制算法及其仿真研究_英文_谭显坤.pdf

Oct 2012 机床与液压 Hydromechatronics Engineering Vol 40No 19 Received: 2012 08 22 * TAN Xiankun E- mail: txkcx11163 com DOI: 10 3969/j issn 10013881 2012 19 005 Improved Control Algorithm Based on Particle Swarm Optimization and Its Simulation Research TAN Xiankun* Polytechnic School，Chongqing Jiaotong University， Chongqing 400074， China Abstract:The performance of control system is determined by the control parameter of controller Aimed at the puzzle of parameter selection for particle swarm optimization ( PSO)control algo- rithm that the phenomenon of premature convergence made the basic PSO algorithms have been easy to get in local optimal solution，and resulted in impossible convergence to global extremum， as well as being not so high in search precision and slower in convergence speed， the paper pro- posed a sort of improved control algorithm based on particle swarm optimization In the paper，it discussed the particle swarm optimization algorithms with genetic thought ( GAPSO) ，researched on improved algorithm of PSO，and made the comparative study for proposed control algorithm by means of simulation experiment The response curve of simulation result demonstrated that it would be better in comparison with conventional method in dynamic and steady performance， and verified the reasonability and feasibility of the improved control algorithm The research result shows that the improved algorithm of PSO proposed by the paper is more effective for controller parameter tuning Key words:particle swarm optimization， genetic thought，parameter tuning， improved control al- gorithm of PSO 1 Introduction Particle swarm optimization ( PSO) 1and the genetic algorithm( GA)all are the evolutionary algo- rithm based on the theory of biology evolutionism and genetics etc for solving optimization problem，and each of them has own characteristic PSO algorithm has lots of advantages such as being faster in conver- gence rate，less in parameter tuning，simple and eas- ier in implementation，little in encoding compared with other algorithm and so on，and therefore it is widely used in many fields such as optimization of ob- jective function，modeling of biologic system，train- ing of neural network，control of fuzzy system and so on In engineering control fields，in order to enhance the speediness，accuracy and stability，the technolo- gy of advanced intelligent control has been obtained wide generalized application，and PSO algorithm has always been used in controller of intelligent control structure so as to make the parameter tuning 2 The genetic algorithm is a sort of search method based on principles of biology evolution，and it has better ability of global optimization and optimization strategy of randomization 3 4 Up to now，GA al- gorithm has been become a more mature analysis method，and it is widely used in many fields such as combination optimization，signal processing，machine learning，artificial life and adaptive control and so on Compared PSO with GA algorithm，there are some differences 5 For instance，firstly PSO algo- rithm owns better memory characteristics，and kept better solving particle GA algorithm only makes use of new population produced by current generation， and the new population produces through crossover and mutation Secondly for PSO algorithm，it is sim- ple in principle，less in control parameter and re- duced in computing load Thirdly PSO gave the evo- lution equation，the position and speed of particle is in quantification and modeling，and comparatively it is stronger in operability Both PSO and GA repre- sent as the simulation and research of biological world laws，and it is a sort of stochastic search technique and owns the global optimization characteristic and implicit parallelism And at the same time，in the face of complex control objective，it appears the dis- advantages of premature convergence and low conver- gence For this reason，the paper explored a sort of improved algorithm of particle swarm optimization based on genetic thought，and made the simulation research for the above mentioned 2 Particle swarm optimization based on ge- netic thought 2 1 Survey for genetic algorithm The basic thought of genetic algorithm 6 is that by means of encoding technology，it acts on chromosome ( binary digit string) ，and simulates the evolutionary process of population made up of chro- mosome，and is a sort of random search algorithm Genetic algorithm forms a new string population through the selection， crossover and mutation of chro- mosome in randomness and organization so as to solve，and makes evaluation for chromosome It se- lects the chromosome of better fitness to carry through the genetic reproduction The basic conception in the algorithm is briefly introduced as the following 7 1)Gene encoding，the biologic shape is deter- mined by gene coding- strand In the genetic algo- rithm，by use of binary system code each decoding of optimization objective forms a gene coding- strand， namely the individual， and also called as the chromo- some 2)Population，the population is a set of indi- vidual，namely it is a set of solution in solving prob- lem 3)Crossover，the reproduction in living nature is completed through chromosome crossover，and the GA makes it be an operator In the crossover opera- tion process，there exists random information ex- change，and the aim is that it produces the new gene combination and new individual 4) Mutation，the mutation operation usually takes mutation probability to execute NOT mutation of corresponding Bit，namely some gene value of chro- mosome changes from 1 to 0，or from 0 to 1，and thereby it gets the new individual The mutation op- erating operation can promotes the diversity of proge- ny individual，and expand the solution space The mutation operation decided the local search ability of genetic algorithm，and the combined action together with crossover operator completes the global and local search of optimal solution 5)Fitness，the survivability of biosome depends on fitness degree of environment The fitness reflec- ted the evolution law in nature of survival of the fittest and natural selection In the optimization problem， the corresponding function value of each solution presents the good or bad trend with solved problem And the evaluation value is called as the fitness of al- gorithm 6)Selection，also it is called as reproduction or copy operation，and the individual of high fitness would be put in a certain set so as to get ready for crossover and mutation operation It selects excellent chromosome of high fitness and performance as the parent individual，and therefore the excellent charac- teristic can widely distributed in the large scope of next generation population，thereby it can speedily solve the problem There are three sorts of crossover，mutation and selection operating operator，in which the crossover and mutation operation are used for producing the new individual so as to completes the reproduction operation The selection operation is used for comple- ting the copy operating 2 2 Basic step of genetic algorithm GA dominates the solution of problem to be as the chromosome inner the biosome，and it makes the selection according to individual of high fitness Through operating operator of crossover and muta- tion，it forms the new population from generation to generation so as to conjecture the improved set of searching optimization for next generation，thereby fi- nally it converges to an individual of most adaptive environment，and finds the optimal solution The ge- netic algorithm involves five essential factors，param- eter encoding，setting of initial population，and de- sign in fitness function，genetic operation and control parameter The above five key factors formed the core content of genetic algorithm The basic glow of algo- rithm is as the following 8 92 TAN Xiankun: Improved Control Algorithm Based on Particle Swarm Optimization and Its Simulation Research 1)Select encoding pattern and determine fitness function 2) Determine genetic strategy，and initialize population including population size，method of se- lection and crossover as well as mutation，parameters of crossover probability Pcand mutation probability Pmand so on 3)Compute the fitness of individual Bit string in the population after decoding 4)Make genetic operator act on current popula- tion according to the selected genetic strategy，inclu- ding that Selection，it charges in selecting some indi- viduals of high fitness directly to inherit into next generation population from current population Cross- over，it makes each individual in the match set after Selection operation randomly match into the pairs， and takes the crossover probability to carry through the exchange for partial gene of them so as to produce new individual Mutation，it makes specified popula- tion after crossover carry through the mutation with mutation probability 5)End the condition judgement If it satisfies the end condition then it stops the computing，and output the individual of maximum fitness to be as the optimal solution Otherwise it returns to step 3 Improved algorithm of PSO The wide space search and crossover- mutation a- bility can high efficiently search the global optimal solution By means of that，it can improve the PSO algorithm In the iteration process，the particle indi- vidual of one third of the best fitness makes selection operation directly go into the next generation，and then makes crossover between any two form particle of one third in next generation，and the final particle of one third forms through mutation operation for the selected particle By means of genetic crossover oper- ator operating，it increased the diversity of particle， and took full advantage of particle characteristic in best fitness so as to make better characteristic carry through the heredity，and it quickened the conver- gence speed of particle It enlarged the search area through mutation operation of partial particle，and a- voided the premature phenomenon of local optimiza- tion In the improved PSO algorithm，it adopts non- linear descending mode for the inertia weight in PSO algorithm，and it can improve the convergence per- formance of the original algorithm 3 1 Nonlinear descending of inertia weight The inertia weight system w determined the abil- ity of global and local search in algorithm If the w value is larger then the influence of particle subjected to previous speed of a moment also is larger It can avoid getting in least local extremum，and the global search ability would be stronger If the w value is less then the influence of particle subjected to previ- ous speed of a moment also is less，and the search a- bility of local particle would be stronger，and there- fore it would be propitious to algorithm convergence The formula ( 1)shows a sort of descending function of nonlinear inertia weight 9 ，and it has better con- vergence speed than linear inertia weight coefficient， and obtains better solving quality wi= wstart w () end ti t () max 2 + wstart w () end 2ti t () max + wstart( 1) In which，tmax， wstart， wendis respectively the most iter- ation number of times，maximum and minimum of in- itial inertia weight，and tiis the current iteration number of generation From formula ( 1) ，it can be seen that the iteration weight coefficient has maximum at the beginning of iteration，and in the process of it- eration it presents a sort of nonlinear descending， and at the last time of iteration process it reaches to the minimum So it can obtain the balance ability of global and local search 3 2 Operating realization of genetic operator 1)Realization of selection operation，adopting proportion selection operating，it first computes the summation of all individual fitness in the population， and then computes the proportion of individual fitness in the whole fitness summation To select one third particle of best performance makes selection operating directly go into the next generation so as to keep the heredity of best evolution ability in particle popula- tion，and it can better search optimal solution quick- ly 2)Realization of crossover operating，first it se- lects the particle of one third to put into a set，and pays a random crossover probability of each particle in the set，and then makes crossover operating be- tween any two Here it must pay attention to that it should ensure to produce next generation particle of the same number so as to maintain the number not to change of population particle The update formula of 03Hydromechatronics Engineering position and speed for new particle is shown as re- spectively the formula ( 2)and ( 3) Secondly it makes the fitness evaluation again for sub- particle of new generation produced，and makes the comparison with parent particle fitness If the fitness of sub- parti- cle is better than parent particle fitness then it would be replaced，and otherwise it keeps parent particle to go into the next generation X1() t= rand( ) X1( )t+1 rand () ( )X2( )t X2 t ( ) = rand( ) X2( )t+1 rand () ( )X1( ) t ( 2) V1() t = V1( )t+ V2( )t V1( )t+V2( )t V1( )t V2() t = V1( )t+ V2( )t V1( )t+V2( )t V2( )t ( 3) In which，X represents the position vector in D di- mension space，X( t)and V( t)is respectively the position vector and speed vector of the space used for selecting cross operating particle，and X ( t)and V ( t)is respectively the space position and speed vec- tor of new generation particle after cross Rand ()is a random vector of search space over interval 0， 1 3)Realization of mutation operating It first se- lects an anew initializing method in this paper so as to make initial mutation for partial dimension of selected particle，and it can avoid appear to get into the pre- mature convergence Secondly it makes the compari- son between fitness of new generation and parent par- ticle，and its process is similar to crossover operating in step 2 3 3 Algorithm flow The operation step of improved PSO algorithm is as the following 1)Initialize particle swarm Setting population size m，search space dimen- sion n，producing m particles randomly in space Rn， forming population matrix X = x1， x2， ， xi， ， xm ，producing speed value of each particle random- ly，forming speed change matrix of particle V = v1， v2， ， vi， ， v m ，setting learning factor c1and c2，inertia weight coefficient wstartand wend，encoding pattern，most iteration number of times tmax，and fi- nally setting iteration number of times in current gen- eration to be as 1 2)Update inertia weight coefficient according to formula ( 1) ，to make evaluation of population，and to compute fitness F( Xi)of each particle according to the objective function 3)Execute genetic operator operating First to compute fitness of each particle individual and make the order according to step 2，and to select optimal particle of one third directly to be as the next genera- tion particle Secondly to make cross operation for them，to produce the particle of one third of next generation，and the formula of position and speed cross is respectively the formula ( 2)and ( 3) Fi- nally to make random initializing operating for them so as to enlarge the parameter search area and jump out the local convergence 4)Update individual extremum of each particle in the population，and make comparison between current F( Xi)and itself individual extremum Pi If F( Xi)excels Pithen it would update the individual extremum Piby F( Xi) 5)Update the global extremum of population， and make the comparison among all Piproduced new- ly by each particle in the whole population with glob- al Pgin history If there exists that Pifitness value of particle excels Pgthen the global extremum Pgwould be updated by Pi 6)Update the speed and position of particle by formula ( 2)and ( 3) ，and produce the new popula- tion X( t +1) 7)Judge whether it satisfies the end condition ( usually it is set as the error precision or most itera- tion generation of times) If it is not satisfied then it would be returned to step 2，and otherwise it stops the search and outputs the result Fig 1 shows the flow of improved PSO algorithm of inertia factor nonlinear descending with fused ge- netic algorithm Fig 1Flow of improved PSO algorithm 13 TAN Xiankun: Improved Control Algorithm Based on Particle Swarm Optimization and Its Simulation Research 4 Simulation and its analysis 4 1 Design of control algorithm Here it takes two sorts of control algorithm to make the simulation for convenience of comparison， and they are respectively the improved PID control al- gorithm and human simulated intelligent control algo- rithm 1)Improved PID algorithm u = sgn( e) U， e () E u = Kpe + Ki t 0 edt + Kde e () E ( 4) In which，E is the error feature threshold level in the feature model，and the control parameter nee- ded tuning is respectively U，Kp，Kiand Kd Where U can be gotten from experience，and Kp，Kiand Kd can be gotten by means of parameter tuning method proposed in this paper 2)HSIC based control algorithm u = sgn( e) U， e E () 1 u = KP1e + KD1e e E1 e E () 2 u = KP2e + KD2e e E2 e E() 1 u = KP3e + KD3e e E2 eE1 e E3 eE() 2 u = un1 e E 3 e E() 2 ( 5) In which，E， is respectively the threshold level of error and its change rate in the feature model，and the control parameter is respectively U，Kp1，KD2， KP2，Kd2，Kp3and KD3Where U can be gotten through the experience，the other can be gotten by means of parameter tuning method proposed in this paper In order to get better control process and dy- namic characteristic，the objective function of im- proved PSO algorithm is selected as f