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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Volume XXXVIII, Part 8, Kyoto Japan 2010 .Particle Swarm Optimization in Emergency Services H. Hajaria, M. R. Delavara a GIS Division, Department of Surveying and Geomatics Engineering, College of Engineering, University of Tehran, Tehran, Iran - h.hajari@ut.ac.ir KEYWORDS: Particle Swarm Optimization, Disaster Management, Geospatial Information System, Emergency Services ABSTRACT: Particle Swarm Optimization (PSO) is motivated by the social behaviour of organisms, such as bird flocking and fish schooling. Each particle studies its own previous best solution to the optimization problem, and its group s previous best, and then adjusts its position (solution) accordingly. The optimal value will be found by repeating this process. PSO can be useful in different applications. PSO can be used in Multi Modal Optimization (MMO), Multi Objective Optimization (MOO) and Vehicle Routing Problems (VRP). This paper presents a solution representation and the corresponding decoding method for solving the emergency services problems using PSO. PSO algorithm can be used to solve the emergency problem, because different and outspread solutions can be generated in PSO. It means that the generated solutions by particles spread in entire search space of the problem. PSO algorithm can also keep the best solution until the iteration stops. The solution representation is a -dimensional particle for emergency services with injured. The decoding method for this representation starts with the transformation of particles into a priority list of injured to allocate an ambulance and a hospital to each injured according to the constraints of the problem. For assigning each ambulance to each injured, time is considered as a constraint. Also assigning hospitals to the injured is done according to hospital's capacity. The proposed solution is applied using PSO algorithm with star topology, and tested on a small district in Tehran Metropolitan Area (TMA). 1. INTRODUCTION PSO, individuals, referred to as particles, are flown through hyperdimensional search space. Changes to the position of particles within the search space are based on the social- PSO can be used in multimodal optimization and multiobjective psychological tendency of individuals to emulate the success of optimization problems (VRP) (Alexander and Darrell, 2006; other individuals. The changes to a particle within the swarm Carlos et al; Fernandes and Ismael, 2005). Also different are therefore influenced by the experience, or knowledge, of its applications like Vehicle Routing Problems (VRP) can use PSO neighbours. The search behaviour of a particle is thus affected algorithm (Jung, Haghani, 2005; Wanliang and Yanwei, 2006). by that of other particles within the swarm. The consequence of The Emergency Services problem is a problem to design a set of modelling this social behaviour is that the search process is such ambulance routes in which a fixed fleet of ambulances with that particles stochastically return toward previously successful same capacity must service known injured demands for an regions in the search space (Engelbrecht, 2007). ambulance from an emergency center and carry them to Each particle has the following properties: specified hospital at minimum cost. Set of injured requires a Each agent was attracted towards the location of the number of ambulances from an emergency center. A fleet of roost (Engelbrecht, 2007). identical ambulances with same capacity is stationed at the Each agent remembered where it was closer to the emergency center. The emergency center, injured and hospital roost (Engelbrecht, 2007). locations are known; the travel distance or travel costs between Each agent shared information with its neighbors locations are also known. The distances between locations are (originally, all other agents) about its closest location calculated by Dijkstra algorithm. The speed of ambulances is to the roost (Engelbrecht, 2007). assumed to be constant during the trip. Therefore, the travel time between locations can be calculated. This problem consists The research on the application of PSO to emergency services is of designing a set of at most routes such that (1) each route a new subject which is focused on this paper. starts at the emergency center and ends at the specified hospital, In order to make PSO applicable to emergency services, the (2) each injured is carried to the nearest hospital according to relationship between particle position and ambulance routes the hospitals capacity, (3) each injured is serviced by an must be clearly defined. The definition of particle as an encoded ambulance in shortest possible time, (4) the total routing cost is solution is usually called a solution representation and the minimized. method to convert it to problem specific solution is usually Studying the emergency services problem and its method for called a decoding method (Jin and Voratas, 2008). This paper finding solution of the problem is necessary to protect the health proposes a solution representation and its corresponding and safety of the injured people. It is known that this problem is decoding method to convert position in PSO into emergency an NP-hard problem, in which finding the optimal solution is services solution. This solution representation is a new proposed very hard and requires very long computational time. representation which is an extension of the work of Ai and Kachitvichyanukul (Jin and Voratas, 2008). PSO is an optimization technique which first developed by The reminder of this paper is organized as follow: Section 2 James Kennedy (social psychologist) and Russell Eberhart reviews PSO framework for solving emergency services. (electrical engineer) in 1995 (Kennedy and Eberhart, 1995). In Section 3 explains the proposed solution representation and 326 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Volume XXXVIII, Part 8, Kyoto Japan 2010 decoding method. Section 4 is computational result and finally, section 5 summarizes the result of this study and suggests further directions in this research. 2. PSO FRAMEWORK FOR SOLVING THE EMERGENCY SERVICES The PSO framework for solving emergency services is based on + 1 > gbest PSO, an algorithm with star topology (Marco and Montes, max 2007). This algorithm is designed for the minimization problem, x id ( t 1) X , v id ( t 1) 0 since the emergency services problem is to minimize total route cost and allocating nearest ambulance and hospital to each injured according to the constraints. + 1 < The notation and the description of the algorithm are given as x id ( t 1) X min , v id ( t 1) 0 follows (Voratas, 2007). (1) Notation 7. If the stopping condition is met, go to step 8. , = 1,2, , , = 1,2, , Otherwise, and return to step 2. , = 1,2, , 8. Decode as the best set of patient and compute the [0,1] fitness. Velocity of the ith particle at the ddimension in the t iteration This framework is starting with particles, which corresponds Position of the i particle at the d dimension with different set of ambulances and hospitals that are in the t iteration allocated to the injured. Then the particles are moved in the Personal best position pbest of the i particle at search space and the fitness of each particle is evaluated. The fitness of each particle is calculated by Dijkstra algorithm. the d dimension Whenever a better allocation of ambulances and hospitals to the Global best position (gbest) at the d dimension injured is found, its corresponding pbest information is updated. Inertia weight in the t iteration This movement process is iterated with an expectation to find Personal best position acceleration constant better allocations. Finally the particle with best fitness (gbest) Global best position acceleration constant decodes. Vector position of i particle, [x , x , , x ] Vector velocity of i particle, [v , v , , v ] Vector personal best position of i particle, [P , P , ,P ] 3. SOLUTION REPRESENTATION AND THE Vector global best position, [P , P , , P ] DECODING METHOD Fitness value of Minimum position value At first, the program crates Table 1 to assigns specified Maximum position value hospitals to each injured according to the distance between each injured to each hospital. For example, the nearest hospital to P1 1. Initialize particles as a population, generate the is H 1 , the next nearest hospital is H3 and the utmost hospital particle with random position in the range from the first injured is H 2 . For example, Table 1 represents and initial velocity and the allocated hospitals to each injured corresponding to distance pbest on the network. Then decoding of each particle begins. The dimension of each particle in this problem with injured is 2. equal to . Each particle dimension is encoded as a float number. The decoding method for this representation begins with extracting the values of each dimension and after sorting the numbers in ascending order, make a priority list of injured. Schematic example of the whole decoding procedure for the 3. problem is shown in Figure 1. 4. 5. Table 1. The allocated hospitals to each injured that is calculated by Dijkstra algorithm 6. Injured ID Hospitals ID 327 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Volume XXXVIII, Part 8, Kyoto Japan 2010 P1 H1 H3 H2 T nd Table 3. Final decoded particle an its fitness P2 H1 H2 H3 P3 H2 H1 H3 P4 H3 H1 H2 P5 H1 H2 H3 P6 H2 H3 H1 distances are cal All of the d jkstra algorithm. Then lculated with Dij p values of pbest, gbest, d update and the process iterates. Solution represen Figure 1. S oding steps ntation and deco UTATIONAL R 4. COMPU RESULT atient priority lis is decoded acc Finally, the pa st e cording to Table f l A set of computational result is con st nducted to tes the 2 2. ce ion performanc of the PSO with the soluti representatio for on he solving th emergency se ata ervices. The da set is in a small ing Table 2. Decodi of a particle T n district in Tehran shown in Figure 2. The Projected Coorrdinate System is WGS_1984_UT TM_Zone_39N and the Project tion is Transverse e_Mercator. Hos ed es spitals are marke by blue square and d the injured are marked by green squares. Hospitals and innjured domly in the whole area. The cir in people are distributed rand rcle s Figure 2 shows the emer rgency center w es where ambulance are originally tthere. N I e ch In decoding the particles, the capacity of eac hospital as a c nsidered. Also, in assigning eac ambulance to constraint is con i ch o 0 Scale 1:65000 e me d . each injured, tim is considered as a constraint. For example, if f w we have amb erving injured bulances, after se d, d injured i ch e is served by the ambulance whic arrives to the location sooner r t s. ll r than the others In this smal instance, for clarifying the e s pacity of each ho solution, the cap ed ospital is assume equal to 2 and d is 3. Accordi ing to the expl lanations, sh d hould be carried to , because th capacity of t he is full. Also, are e District 6 for imp Figure 2. D plementing the solution represen ntation c fied th carried to specifi hospitals wit ambulances e to . But the n the hat next injured, , is carried with t ambulance th arrives to the e The algoritthm is implemen on a PC wit Intel core 2 Duo 2.5 nted th l t location sooner than the others. he GHz - 4 GB RAM. Th PSO parame ber eters are: Numb of At the end, the fitness or cost of each particle is calculated by A o y I=100; Number of Iteration, T=500; Numb Particle, I r ber of D hm o and Dijkstra algorith according to Equation 2 a the result is s ambulance ber es, =13; Numb of injured Numb of ber s e showed in Table 3. i hospitals is five; the cap o; pacity of each hospital is two the of capacity o each ambula ance is one; I Inertia weight W=4; est personal be position acce nt, eleration constan al globa best cceleration const position ac tant, (2) 328 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Volume XXXVIII, Part 8, Kyoto Japan 2010 The computational results of the solution representation are 5. CONCLUSION presented in Table 3. Table 3. Computational Result This paper presents a solution representation and the corresponding decoding method for solving the emergency INJURED ID HOSPITAL ID AMBULANCE ID services using particle swarm optimization (PSO). The 14 90 1 representation is a dimensional particle for the problem with 293 251 2 ambulances and injured. The computational result shows that 115 90 3 proposed PSO framework with the solution representation is 28 90 4 effective for solving the emergency services. 143 215 5 Some further research for applying the proposed method is to use PSO algorithm with Ring topology and compare the results 227 251 6 with the proposed algorithm. Also the emergency services can 32 90 7 be solved with other evolutionary computing methods like Bee 158 201 8 colony. 150 215 9 94 90 10 References 19 90 11 298 251 12 [1] Alexander and Darrell., 2006. A generalized MultiObjective 66 215 13 PSO solver for spreadsheet. 96 134 4 [2] Engelbrecht A., 2007 Computational Intelligence An Introduction. 81 134 3 [3] Carlos A. Coello, Gregorio Toscano Pulido, Maximino 272 251 5 Salazar Lechuga., 2004. Handling Multiple Objectives With 310 215 6 Particle Swarm Optimization. [4] Fernandes and Ismael., 2005. PSO for multi-local 241 215 9 optimization. 184 201 11 13 134 10 [5] Jung and A. Haghani., 2005. A dynamic vehicle routing problem with time-dependent travel times. 225 201 8 [6] Kennedy, J. and R.C. Eberhart,., 1995. Particle swarm 296 215 13 optimization. Proc. IEEE Int'l. Conf. on Neural Networks, IV, 73 134 7 1942-1948. Piscataway, NJ: IEEE Service Center. 22 134 1 [7] Marco A. de Oca Montes., 2007. Particle Swarm 317 215 2 Optimization - Introduction [8] Jin A. and K. Voratas., 2008. Particle Swarm Optimization Total Fitness = 28712.2639201484(m) and Two Solution Representation for Solving the Capacitated Vehicle Routing Problem. [9] Voratas K., 2007. Particle Swarm Optimization: Recent Advances and Applications. Table 3 shows that the injured with ID=14 should be carried to [10] Wanliang and Yanwei., 2006. Particle Swarm Optimization hospital with ID=90 by ambulance with ID=1. Figure 3, shows for Open Vehicle Routing problem with Time Dependent that the more the algorithm iterates, the lower the cost becomes. Travel Time. Fitness Value (Km) Iteration Figure 3. The fitness values across iteration 329

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