Analysis of pavement management activities programming by particle swarm optimization

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  • 1. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011 Analysis of pavement management activities programming by particle swarm optimization Navid Reza Tayebi Civil Engineering Department, Faculty Engineering , Islamic Azad University of Tehran-Science and Research branch Tehran,Iran navidtayebi62@gmail.com Fereidun Moghadasnejhad Dept. of Civil Engineering Amirkabir University of Technology, I. R. of Iran Tehran, Iran moghadas@aut.ac.ir Abolfazl Hassani Civil Engineering Department Technical and Engineering Faculty Tarbiat Modarress University Tehran, Iran hassani@modares.ac.irAbstract— The application of particle swarm optimization rehabilitation program at the network level would contain(PSO) to programming of pavement maintenance activities at the following information: (1) The time and type ofthe network level is demonstrated. The application of the PSO maintenance or rehabilitation (including the do-nothingtechnique and its relevance to solve the programming problem option) for every pavement segment over the entire planningin a pavement management system (PMS) are discussed. The time period;(2) the resource allocation by time and pavementrobust and quick search capability of PSO enable it to segment ;and (3)the total commitment of resources for eacheffectively handle the highly constrained problem of pavement time period [1]. These parameters made optimalmanagement activities programming, which has an extremely programming of PMS complicated.large solution space of astronomical scale. Examples arepresented to highlight the versatility of PSO in accommodating The common road-network system objectivedifferent objective function forms. This versatility makes PSO specified by highway agencies include the following :(1) Toan effective tool for planning in PMS. It is also demonstrated minimize the present worth of overall maintenance andthat composite objective function that combine two or more rehabilitation expenditures over the planning horizon ; (2)todifferent objects can be easily considered. PSO find near- minimize road-user costs by selecting and programmingoptimal solutions besides the “best” solution. This has practical maintenance and rehabilitation activities to reduce disruptionsignificance as it gives the users the flexibility to examine the and delays to traffic;(3)to maintain the highest possible levelsuitability of each solution when practical constraints and of overall network pavement condition with the resourcesfactors not included in the optimization analysis are considered. available [1] . It is also possible to combine two or more ofKeywords : Particle Swarm Optimization, Pavement these objectives by assigning an appropriate weight factorManagement System, Optimization to each object. The novel model in using PSO method for PMS is I.INTRODUCTION presented in this research and this is the first time that PSO is using in PMS. The purpose of this research is to determine The traditional methods of pavements management the best rehabilitation-maintenance activity with PSO , andsystem (PMS) programming activities based on ranking the cost of the activity is our decision parameter, so the inputmethods or subjective priority rules do not guarantee an data must be defined firstly after that PSO model calculatesoptimal or near-optimal utilization of available resources [2]. the pavement segment’s distress according to deteriorationThis is because the number of pavement management function and checks warning level, and finally with costactivities required to be carried out at the network level are function determine the minimal rehabilitation activity. Byinnumerous, and an optimization analysis is required to using FWA cost function [1] we verify our model with FWAidentify a pavement management program that would achieve model and the results was same and satisfying . In this paperan optimal or near-optimal utilization of available resources. four cost functions with different item were chosen. The The highway engineer responsible for maintaining minimal rehabilitation cost for hypothetical problem of roada road network is interested in identifying the pavement- network consisting of 15(3 km length for each) segmentmanagement program [1] that could be the best for PMS. pavement using particle swarm optimization is determined.Intelligent PMS Optimization method illustrated by FWA In section II the structure of particle swarmin 1996 with genetic algorithm[1]. They show that GA can optimization(PSO) is discussed, In section III the inputsatisfy PMS parameters and can be used as excellent operator parameter for PSO are illustrated, and is followed by thefor managing rehabilitation. A pavement maintenance- cost option presented in section IV, In section V the numerical© 2011 ACEEE 22DOI: 01.IJCom.02.01.126
  • 2. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011results of model are shown. Finally the results andconclusions of the study are reported and discussed in sectionVI. II.PARTICLE SWARM OPTIMIZATION (PSO) PSO is a global optimization technique that has beendeveloped by Eberhart and Kennedy in 1995[7], Theunderlying motivation of PSO algorithm was the socialbehavior observable in nature, such as flocks of birds andschools of fish order to guide swarm of particles towardsthe most promising regions of the search space. PSO exhibitsa good performance in finding solution to static optimizationproblems. It exploits a population of individuals tosynchronously probe promising regions of the search space.Each particle in the swarm represents a candidate solutionto the optimization problem. In a PSO system, each particlemoves with an adaptable velocity through the search space,adjusting its position in the search space according to ownexperience and that of neighboring particle, then it retains amemory of the best position it ever encountered, a particletherefore makes use of the best position encountered by itselfand the best position of neighbors to position itself towardsthe global minimum. The effect is that particles “fly” towardsthe global minimum, while still searching a wide area aroundthe best solution, [8,12,9]. The performance of each particle(i.e. the “closeness” of a particle to the global minimum) ismeasured according to a predefine fitness function which isrelated to the problem being solved. The iterative approach of PSO can be described bythe following steps: Step 1 initializing a population size, positions andvelocities of agents, and the number of weights and biases. Step 2 the current best fitness achieved by particle p isset as pbest . The pbest with best value is set as gbest and thisvalue is stored. Step 3 Compare the evaluation fitness value fp for each Figure.1 : The plan of PSOparticle. Step 4 Compare the evaluated fitness value fp of each III.THE INPUT PARAMETERSparticle with its pbest value, If fp <pbest then pbest= fp and bestxp Pavement network with 15 segments with 3 km= xp, xp is the current coordinates corresponding to particle length for each segments is assumed, the input parametersp’s best fitness so far. are summarized in table I [1]. The age of the pavement Step 5 The objective function value is calculated for new segments given in Fig 3 are randomly assigned by assumingpositions of each particle. If a better position is achieved by a normal distribution [1]. The age of pavement is computedan agent, pbest value is replaced by the current value. As in from the time the last structural overlay was laid, or fromstep 1, gbest value is selected among pbest values. If the new the time of construction if the pavement has never beengbest is better than previous gbest value, the gbest value is replaced overlaid. The total length of the study period is 15 years.by the current gbest value and this value is stored. If fp<gbest The unit planning period is one year.then gbest = p, where gbest is the particle having the overall In this research, the uncertainty of predictedbest fitness over all particle in the swarm. pavement condition is assumed to be associated with random Step 6 change the velocity and location of the particle traffic loads. It is assumed here that the uncertainty of futureaccording to Equation 1 and 2, respectively [7,10]. traffic loads are several magnitude larger than other sources Step 7 Fly each particle p according to Equation 3. of uncertainty. The predicted annual traffic load is a random Step- 8 If the maximum number of a predetermined variable so the predicted pavement performance, which takesiterations is exceeded then stop; otherwise loop to step 3 the effect of maintenance activity into account, becomes auntil convergence. In this work, 15 population of weights random variable as well, [3].were evolved for 100 generations with w=0.7. Distress parameters include the types of distress considered and their deterioration function. The deterioration© 2011 ACEEE 23DOI: 01.IJCom.02.01.126
  • 3. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011functions predict distress development with time or traffic Cracking C=21600*(N)(SN)-SN (3)loading. maintenance and rehabilitation parameters identify Rutting R=4.98*(Y)0.166(SN)-0.50(N)0.13 (4)the pavement repair methods used and their costs. Surface disintegration S=80*(e2.2677*N-1) (5)Unfortunately, the accuracy of the predicted pavement PSI=5.10-1.9*log(1+SV)-0.01*C0.5-0.00214R2 (6)condition could be influenced by the choice of prediction WhereSV=68.5*((N.106)/p)â +1.83 (6a)model,[4] as well as the accuracy of inputs of the Log(p)=9.36*log(SN+1)-0.20 (6b)deterioration model, [3] like the warning level. A warning â=0.4+1094/(SN+1)5.19 (6c)level refers to the pavement condition level that the pavement where C=total area cracked in m2/km/lane ;N=trafficrehabilitation activity must be performed before its specified loading in million passes of equivalent 80 KN single axle;warning level is reached, or at the latest, when the warning SN= structural number ;R=rut depth in mm ; Y=age oflevel is reached. Fig.2 presents the research process. pavement in years ; S=total surface disintegrated in m2/km/Regarding the input data, deterioration function and warning lane.levels, the program determine the essential rehabilitation The resource parameters defines what are commonlyactivity needed for each segment per year. Then according known as constraints in optimization problems. Typicalto cost function, the network rehabilitation cost is calculated planning constraints in pavement management areand finally, PSO determines the best rehabilitation activity availability of resources such as budget, manpower,(with minimal cost) in network level pavement for 15 years. materials, and equipment. Finally, The traffic parameters provide the necessary information for traffic loading to be computed for the entire planning period. The identifies alternative permitted parameters for repair activities is given in table II. [1] : IV.COST FUNCTION Figure.2 : General Methodology of Article A factor that directly influences the outcome of the maintenance-rehabilitation trade-off analysis is the relative costs of rehabilitation and maintenance activities. We have three maintenance activities considered in this study and we can have plenty of rehabilitation. In this paper we mention four rehabilitation strategy that is used in Iran and their cost is listed in table III (all cost values based on Iran exchange in US dollar (US$)). The discount rate used in the analysis is 6%. Fig.3 : Age Distribution of Pavement Segments For simplicity, only three main pavement distresstypes are considered. They are cracking, rutting, anddisintegration of pavement surface materials. [1] For the caseof structural damage requiring rehabilitation, the decisionto overlay construction is dependent on the presentserviceability index (PSI). [11]© 2011 ACEEE 24DOI: 01.IJCom.02.01.126
  • 4. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011 is problem dependent [14]. In this model we assumed w as 0.7 it means our particle started with 15 segments out of 100 which decreases over time to smaller values. At this time it is crucial to mention the important relationship between the values of w, and the acceleration constants. The choice of value for w has to be made in conjunction with the selection of the values for c1 and c2 [15,16] that showed in eq.7 ω>0.5∗(Χ1+Χ2)−1 (7) guarantees convergent particle trajectories. If this condition is not satisfied, divergent or cyclic behavior may occur. The solution to the four cases of the problem present interesting trade-off scenarios between rehabilitation and maintenance. These solution provide the complete program V.THE NUMERICAL RESULTS OF MODEL of repair activities by year and by pavements segment for the four cases. All solutions satisfy the pavement performance The purpose of this model is to find the requirements that distress conditions and pavement are keptmaintenance-rehabilitation program in pavement network. above their respective warning levels throughout the 15-yearIt shows the time and kind of rehabilitation with minimal analysis period. In table VIII the cost of rehabilitationcost. By using FWA cost function in the model , result activities in four cases are illustrated. Now with PSO modelsimilarity between PSO model and FWA model were we can make decision and choosing the best rehabilitation-achieved . Results of PSO model illustrate pavement maintenance strategy. In this research we use four costrehabilitation and maintenance program for 15 segments function with different activity such as cold asphalt, polymer,during 15 years . emulsion and hot mix asphalt according our budget, PSO calculated the cost of each part with cost manpower and resources we can use each of them. The costfunction and compare the costs with each other and selected of maintenance and rehabilitation program for the case 1the best of all. The model started the optimization with 100 and 2 is equal but its cost function treatment items areparticles and randomly selected 15 segments of them. For different (premix leveling in case 1 tack coat with asphaltthese segments distress will be calculated and controlled with emulsion but in case 2 asphalt emulsion) so one can bedistress level. After that the maintenance-rehabilitation selected base on performance situation and manpower.activity will be determined. Based on activity and table thecost function will be calculated, cumulated cost of eachsegment is set to Pbest and compared to Gbest, and the minimumof them is set to Gbest. This will be continued 600 times tofind the best Gbest. The last Gbest and related rehabilitationactivity is plotted. (see tables (IV-VII)) The inertia weight was introduced by Shi andEberhart [13]. As a mechanism to control the explorationand exploitation abilities of the particle, and as a mechanismto eliminate the need for velocity clamping [14].The inertiaweight, w, controls the momentum of the particle by weighingthe contribution of the previous velocity – basicallycontrolling how much memory of the previous flightdirection will influence the new velocity. VI.CONCLUSION The value of w is extremely important to ensure This paper presented the formulation of a PSO asconvergent behavior, and to optimally tradeoff exploration program for pavement management system in network level,and exploitation. For we”1, velocities increase over time, This is the first time that using PSO model for optimizingaccelerating towards the maximum velocity (assuming pavement system activities . Numerical examples werevelocity clamping is used), and the swarm diverges. Particles presented using four cases of a hypothetical problem, eachfail to change direction in order to move back towards with different relative costs of rehabilitation and maintenancepromising areas. For w < 1, particles decelerate until their activities, to demonstrate the trade-off relationship betweenvelocities reach zero. Large values for w facilitate pavement rehabilitation and maintenance activities and itexploration, with increased diversity. However, too small shows that PSO is suitable for pavement management invalues eliminate the exploration ability of the swarm. Little network level.Regarding the cost of rehabilitation andmomentum is then preserved from the previous time step, maintenance program in network level and according thewhich enables quick changes in direction. As with the performance limitation and manpower , the optimummaximum velocity, the optimal value for the inertia weight program can be selected.© 2011 ACEEE 25DOI: 01.IJCom.02.01.126
  • 5. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011 REFRENCES particle swarm optimization’, in International Joint Conference on Neural Networks, IJCNN 06, Vancouver, BC,[1] T.F. Fwa, W.T. Chan, and C.Y. Tan ,”Genetic-Algorithm Canada, pp.5088-5095, 2006. programming of road maintenance and rehabilitation”, Journal [9] N. Kwok,D. Liu , and K. Tan, “An empirical study on the of Transportation Engineering , Vol.122, No.3 ,pp 246-253, setting of control coefficient in particle swarm Optimization”, 1996. in Proceedings of IEEE Congress on Evolutionary[2] T.F. Fwa, W.T. Chan, and K.Z. Hoque ,”Analysis of pavement Computation (CEC 2006), Vancouver , BC , Canada, pp. management activities programming by genetic algorithm”, 3165–3172, (16-21 July 2006). Transportation Research Record 1643. pp.98-0019, 1998. [10] J.Lin, and T.Y. Cheng, “Dynamic clustering using support[3] P. Chootinan, “Pavement maintenance programming using a vector learning with particle swarm Optimization”, in stochastic simulation-based genetic algorithm approach Proceedings of the 18th International Conference on Systems “.Master Thesis,Department of Civil and Environmental Engineering, pp. 218–223, 2005. Engineering. Utah State University, Logan,UT.1991. [11] J.B. Rauhut , R.L. Lytton, and M.L. Darter, Pavement damage[4] P.L. Durango, M. Madanat, “Optimal maintenance and repair functions for cost allocation, Rep No FHWA/RD-82/126, policies in infrastructure management under uncertain facility Federal Hwy. Admin Washington ,DC. deterioration rates: an adaptive control approach”. [12] T.J. Richer, and T.M. Blackwell, ‘When is a swarm Transportation Research 36A, pp. 763–778, 2002. necessary?’, in Proceeding of the 2006 IEEE Congress on[5] R. Eberhart, and J. Kenedy, A New Optimizer Using Particles Evolutionary Computation ,eds. Swarm Theory, Proc. Sixth International Symposium on Micro [13] Y. Shi, and R.C. Eberhart, A Modified Particle Swarm Machine and Human Science (Nagoya, Japan), IEEE Service Optimizer. In Proceedings of the IEEE Congress on Center, Piscataway, NJ, pp 39-43, ,1995. Evolutionary Computation, pp. 69–73, 1998.[6] R.C. Eberhart, and Y. Shi, Particle Swarm Optimization: [14] Y. Shi, and R.C. Eberhart,” Parameter Selection in Particle Developments, Applications and Resources. In Proceedings Swarm Optimization” .In Proceedings of the Seventh Annual of the IEEE Congress on Evolutionary Computation, volume Conference on Evolutionary Programming,1998, pp.591–600. 1. pp.27–30 , May2001. [15] F. Van den Bergh, “An Analysis of Particle Swarm[7] J. Kennedy and R. C. Eberhart, “Particle swarm optimization”, Optimizers”. PhD thesis, Department of Computer Science, Proceedings of IEEE International Conference on Neural University of Pretoria, Pretoria, South Africa,2002. Networks (Perth, Australia),IEEE Service Center, Piscataway, [16] F. Van den Bergh, and A.P. Engelbrecht, “ A Study of Particle NJ, 5(3),pp. 1942–1948,1995. Swarm Optimization Particle Trajectories”. Information[8] R. Kiran , S.R. Jetti, and G. K. Venayagamoorthy, ‘Online Sciences, 176(8), pp.937–971, 2006. training of generalized neuron with particle swarm optimization’, in International of generalized neuron with© 2011 ACEEE 26DOI: 01.IJCom.02.01.126
  • 6. ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011© 2011 ACEEE 27DOI: 01.IJCom.02.01.126