Combined A*-Ants Algorithm: A New Multi-Parameter Vehicle Navigation Scheme

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1 Combined A*-Ants Algorim: A New Multi-Parameter Vehicle Navigation Scheme Hojjat Salehinejad, Hossein Nezamabadi-pour, Saeid Saryazdi and Fereydoun Farrahi-Moghaddam Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran h.salehi@mail.u.ac.ir, nezam@mail.u.ac.ir, saryazdi@mail.u.ac.ir, ffarrahi@mail.u.ac.ir Abstract: In is paper a multi-parameter A*(Astar)-ants based algorim is proposed in order to find e best optimized multi-parameter pa between two desired points in regions. This algorim recognizes pas, according to user desired parameters using electronic maps. The proposed algorim is a combination of A* and ants algorim in which e proposed A* algorim is e prologue to e suggested ant based algorim.in fact, is A* algorim invigorates some pas pheromones in ants algorim. As one of implementations of is meod, is algorim was applied on a part of Kerman city, Iran as a multi-parameter vehicle navigator. It finds e best optimized multi-parameter direction between two desired junctions based on city traveler parameters. Comparison results between e proposed meod and ants algorim demonstrates efficiency and lower cost function results of e proposed meod versus ants algorim. Keywords: Ants algorim, A* algorim, Multiparameter optimization, Vehicle navigation. 1. Introduction The development of e vehicle navigation systems started since early The vehicle navigation system is an information system in substance. Therefore it is necessary of e frame structure, organization and management of electronic map data, as all powerful system functions must be run based on it [2]. Electronic map data should include information such as medical treatment, entertainment, number of traffic lights, traffic flow and accidents occurred history [1,2], useful for finding pas. Pafinding plays an important role in many modern games. It is usually a state-space search applied to a two-, or ree-dimensional map where each state describes a position on e map [3]. One of e most game programmers popular algorims is A* (A-star) algorim. This is due to e fact at it is often e algorim of choice. It is also popular because of easy implementation, efficiency and huge body of experience [6]. On e oer side, ants algorim has plenty of applications in pafinding and networ problems such as transportation networs [10] and communication networs [9]. Alough real ants are blind, ey are capable of finding e shortest pa from food source to eir nest by exploiting information of a liquid substance called pheromone, which ey release on e route transiting in. The idea of employing e foraging behavior of ants as a meod of stochastic combinatorial optimization was initially introduced by Dorigo in his PhD esis [4]. In is paper, an A*-ants based algorim is proposed in order to find e best optimized multiparameter direction between two desired points using electronic maps. As e problem is complex, e proposed A* algorim is e prologue to e proposed ants algorim. In oer words, A* algorim is run before ants algorim and updates (increases) pheromones of its resulted pas in ants algorim. This algorim is applied on a part of Kerman city, Iran, for multi-parameter desires. Comparison results between e proposed meod and e ants algorim demonstrates efficiency and lower cost results of e proposed meod versus ants algorim This paper is organized as follows. The next section reviews e basic principles of e A* and 154

2 ants algorim. Section 3 represents e details of e proposed meod and experimental results are demonstrated in section 4. Finally, e paper in concluded in section A review on A* algorim and Ant colony system 2.1 A* algorim A* was e result of two decades of research into state-space algorims [3]. A simple form of A* algorim is described briefly in is section. The search area is a two-dimensional square grid area wi an obstacle between two desired points X and Y as in Figure (1). Assume an agent is looing for shortest direction from point X to point Y. The steps are as follow. Fig.1 A simple two-dimensional square grid area a) The start point, X, is labeled as parent square and is added to e open list wi walable squares adjacent to e starting point. b) The point X is dropped from open list and added to e closed list. c) A square is chosen from e open list by means of e Equation (1). f = g + h ( 1) Where g is e movement score from parent to its adjacent walable squares; h is e heuristic movement score from e origin to e destination using Manhattan meod. In ese procedures, scores are calculated by considering each vertical or horizontal movement score 10-unit, and each diagonal movement score 14-unit. d) The lowest f score square is dropped from e open list and is added to e closed list. The mentioned procedure is repeated until arrival to e destination. The squares in e closed list are e direction. 2.2 Ant colony system Ant colony optimization (ACO) is a class of algorims, whose first member, called Ant System (AS), was initially proposed by Colorni, Dorigo and Maniezzo [8]. The AS strategy developed by Dorigo attempts to simulate e behavior of real ants wi e addition of several artificial characteristics: visibility, memory and discrete time to solve many complex problems successfully such as e traveling salesman problem (TSP) [5], vehicle routing problem (VRP) [11] and best pa planning [7]. Even ough many changes have applied to ACO algorims during past few years, but eir fundamental ant behavioral mechanism which is positive feedbac process demonstrated by a colony of ants, is still e same. Different steps of an ant colony system algorim (ACSA) are e followings. - Problem graph representation: As problems which could be solved by ACSA are often discrete, ey could be represented by a graph wi N nodes and R routes, G = N, R. - Initializing ant distribution: A number of ants are placed on e origin nodes. - Node transition rule: The node transition rule specifies ants movement from node to node which is probabilistic. The probability of displacing ant from node i to node j is calculated by Equation (2). p α ( τ ) ( η ) β if j tabu = α β ( τ ) ( ) h tabu ih η ih 0 ( 2) Where τ and η are respectively e intensity of pheromone and e visibility of direct rout from i to j. α and β are parameters which control e relative importance of τ and η respectively. tabu is set of unavailable routes for ant. - Update Global Trail: A cycle of ACO algorim is completed when every ant has assembled a solution. At e end of each cycle, e intensity of pheromone is updated by a pheromone trail updating rule as in Equation (3). m τ new = 1 ρ τ old + τ ( 3) ( ) ( ) ( ) Where ρ = 1 is a constant parameter ( 0 < ρ < 1) named pheromone evaporation and τ is e amount of pheromone laid on route ( i, j) by e ant and could be given by Equation (4). 155

3 Q if route (i, j) be traversed by τ = ( 4) f e ant (at e current cycle) 0 Where f is e cost value of e solution found by ant K. - Stopping criterion: The end of e algorim could be achieved by a predefined number of cycles, or e maximal number of cycles between two improvements of e global best solutions. 3. Proposed meod In is paper an A*-ants based algorim is proposed. This algorim is a multi-parameter navigator using electronic maps in which finds e best optimized direction between two desired points based on users needs. This algorim is exclusively applied on a part of Kerman city as a vehicle navigation algorim. In is meod, A* algorim finds some candidate directions by solving e problem. Afterwards, e results are entered into e ants algorim. In fact, e A* algorim influences e ants algorim by updating (increasing) pheromone of resulted directions. It was attempted to mae a collection of all parameters important for travelers taing journey in cities. These parameters are distance, wid, traffic load, road ris, medical treatment, entertainment, number of traffic lights, traffic flow and history of accidents occurred. An algorim named ant-based vehicle navigation (AVN) algorim was proposed in [1] which finds e best optimized directions based on ants algorims. However, e algorim proposed here is an upgrade version of AVN algorim. As it was mentioned before, is algorim consists of two algorims itself. These algorims are A* algorim and ants algorim. A* algorim is a prologue of e ants algorim. It invigorates some produced directions by itself in order to help ants algorim, recognize best direction wi higher reliability and lower cost an ants algorim. This is done by updating (increasing) pheromone amount of directions founded in e A* algorim. A pseudocode of is algorim is presented in Figure (2). Procedure A*-ants algorim Initialize Activate A* algorim Update pheromone list Active ants algorim Express best optimized direction End A*-ants algorim 156 Fig 2.The proposed A*-ants algorim pseudocode Updating pheromone amount for resulted direction from intersection i to j ( τ ) in e proposed A* algorim is done by e Equation (5). new = τ + τ old 5 ( ) ( ) T τ τ ( ) Where 1 is e ants algorim pheromone updating constant parameter adjusted by try and error. The proposed A* algorim produced directions are recorded in e listt. The proposed A* algorim is discussed in more details in e following subsections Proposed A* algorim The pseudocode of e A* algorim used in e proposed algorim is presented in Figure (3). Procedure A* algorim Add start to open While open is not empty Let n=first nod on open Drop n from open & add it to closed Add adjacent walable squares to open Compute scores Select next square Add parent to closed If parent=destination Search is succeed Else if open is empty and destination is not find Search is fail End End Fig.3 The proposed A* algorim pseudocode As is pseudocode is clear and some of its steps were defined in e last section, brief descriptions of some of its steps are presented as follow. - Compute scores: In is stage, all adjacent squares to e n square, except impossible and ose in e closed list scores are calculated. The selected square is named parent. - Select next square: If e g score for any left square in e open list is better an e current square, e parent is changed to is square. Afterwards, h and g scores are calculated again for e new parent. This algorim is successful when open list is empty and destination is found Proposed ants algorim This subsection discusses e employed ants algorim in details. The pseudocode of is

4 algorim used in e proposed algorim is presented in Figure (4). Procedure ants algorim Initialize For each loop Locate ants For each iteration For each ant If ant be alive Construct probability Select route Update tabu list End Next ant Next iteration Value ants Update pheromone Next loop Select best optimized direction End ants algorim Fig.4 The proposed ants algorim pseudocode. This pseudo code is contained of e following steps. - Initialize: It consists of algorim parameters initial values such as number of ants, evaporation coefficient, and average velocity of vehicle. - Locate ants: Ants are located on e start point in is stage. Alive ant refers to an ant which has not arrived to e destination yet and is not bloced in an intersection. An ant is bloced in an intersection is a situation where has no opportunity to continue its transition toward e destination as ere is no possible route to continue or transiting bacward [1]. - Construct probability: In is step, e probability of each possible direct route is calculated based on its cost function for each alive ant. The probability of displacing from intersection i to intersection j for ant is calculated by Equation (6) α 2α l cost p τ = τ h tabu ih l parameters l parameters 0 l cost 2αl ihl j tabu Where τ is e direct route pheromone intensity from intersection i to j. α controls e importance of τ and tabu is set of direct bloced routes. Parameters set consists of distance, wid, traffic load, road ris, road quality and oer useful parameters [1]. Cost of each parameter (l ) is ( 6) -2α l cost where significance of each l is adjustable l byα l. Data is entered into e algorim by an electronic map [2]. - Select route: A random parameter q wi uniform probability in [ 0,1 ] is compared wi a parameter Q ( 0 Q 1). The result pics up one of two selection meods for e alive ant to continue its route to next intersection. Selection meods are mentioned in Equation (7). arg max p q > Q 7 j = Roulette ( ih ) ( ), ( ) Wheel p ih If q > Q alive ant selects e route wi highest probability, else Roulette Wheel rule will be selected to choose e next intersection rough probabilities. - Update tabu list: In is step, e route which ant has chosen is added to tabu list in order not to be selected again and its probability will not be calculated anymore. If ant arrives to e destination or be bloced in an intersection, it is omitted from alive ant list. In oer words, is step ills e bloced or arrived ant in e current iteration. Value ants: The tcost is summation of cost from intersection i to intersection j for alive ant, since it has started its journey from origin until its arrival to destination. Based on tcosts average ( avg. tcost ) of all e ants, each ant will be added to one of e AWA or PLA lists base on e Equation (8). AWA tcost < avg. tcost ( 8) PLA Where avg. tcost is e average of all arrived ants tcosts. If tcost of alive ant be more an avg. tcost, it will be added to AWA list, it will be added to PLA list. - Update pheromone: This stage consists of local and global pheromone updating sections. The pheromone amount of route between intersections i and j is updated by Equation (9) for ant. ( ) ( ) av τ new = τ old + if AWA tcost ( 9) τ ( new) = τ ( old) pv if PLA Where pv ( 0 < pv <1) and av ( > 1) av are respectively punishment and awarding amounts. The last step of each completed loop is global pheromone updating using Equation (10). ( new ) ρτ ( old ) τ = ( 10) 157

5 Fig.5 A part of Kerman city, Iran, adapted for experiments. Where ρ ( 0 < ρ < 1) is evaporation coefficient. Select best optimized direction: After m loops, e optimized direction wi e lowest cost function from origin to destination is e result. Section 4 presents e simulation results of e proposed algorim. 4. Experimental results In is section, e proposed algorim and ants algorims are compared for finding e best optimized multi-parameter direction in a part of e Kerman city This procedure is run for two separated parameters importance rates. The selected part of Kerman city is consisted of 27 intersections as in Figure (5). Suitable parameters used in is algorim were determined based on trial and error as follows: α = 2, Q = 0.9, pv = 0. 9, av = 950 and ρ = 0.9. In e bo experiments, e average velocity of vehicle is assumed 40Km/h and start time is 6:00 PM as default. The parameters important rates for bo experiments are presented in Table (1) for e origin and destination number 24 and 23 respectively. The resulted directions from ants algorim and A*-ants algorim are as follow respectively. Table 1 No. Parameter Experience1 Experience2 1 Distance Wid Traffic load Road ris Road quality Traffic lights ( 12 ) The cost of directions (11) and (12) are and respectively. It should be noticed at e directions from intersection 6 to 7 and 7 to 3 are one-way. Therefore, e proposed algorim found anoer direction based on e desired parameter importance rates. In e second experiment, e resulted directions from ants algorim and A*-ants algorim are as follow respectively ( 13 ) ( 14 ) The cost of directions (13) and (14) are 99.2 and 52.6 respectively. Because e experimental region is simple, e proposed meod found similar directions in e bo experiments. As it is illustrated in Figures (6,7), e proposed meod has less cost average an [1] which is due to e pheromone updating (increasing) of A* algorim. This figure illustrates efficiency of e proposed meod. ( ) 158

6 References Fig.6 Costs average in e first experiment. Fig.7 Costs average in e second experiment. 5. Conclusion In is paper a combination of A* and ants algorim is proposed in order to find e best optimized multi-parameter direction between two desired points. The proposed A*-ants algorim is a new meod where A* algorim is run before ants algorim and updates (increases) pheromones of its resulted pas in e ants algorim. This algorim was applied on a part of Kerman city, Iran as a vehicle navigation algorim and e results were encouraging in comparison of ants algorim. This meod could also be useful for emergency services, taxi drivers, tours and etc. as it is a fast access, low-cost and easy vehicle navigator algorim. Acnowledgements This paper was supported by Shahid Bahonar University of Kerman Young Researchers Society. [1] H. Salehinejad and F. Farrahi-Moghaddam, An Ant Based Algorim Approach to Vehicle Navigation, Proc. First joint cong. on eight conf. of intelligent systems and seven conf. of fuzzy systems, Iran, [2] CHEN, Dawei, LIU, Zhuo, ZHOU, Chuanming, WANG, Bo, Research of GIS Application in e Vehicle Location and Navigation System, Traffic and Computer, Vol.18, No.96, pp (6). [3] D. Higgins, Generic A* Pafinding. AI Game Programming Wisdom, Charles River Media, pp , 2002 [4] M. Dorigo, Optimization, learning, and natural algorims. PhD Thesis, Dip Electronica e Informazione, Politeccnico di Milano, Italy, [5] M. Dorigo and LM. Gambardella, Ant colony system: a cooperating learning approach to e traveling salesman problem IEEE Trans. Evol. Compute Vol. 1, No.1, pp.1-24, [6] P.E. Hart, N. J. Nilsson and B. Raphael, Correction to a formal basis for e heuristic determination of minimum cost pas, SIGART Newsletter, 37: pp.28-29, 1972 [7] C.L. Liu, Best pa planning for public transportation systems, Proc. of e IEEE fif International Conf. on Intelligence Transportation Systems. pp , [8] M. Dorigo, V. Maniezzo, and A. Colorni, The ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems. Man and Cybernetics. Vol. 26, No.1, pp.1-13, [9] M. Dorigo, Ant foraging behavior, combinatorial optimization, and routing in communication networs, Swarm intelligence: From natural to artificial systems. Santa Fe Institute Studies in e Sciences of Complexity, pp , [10] Z. Guo, X. Song and P. Zhang, The ACO algorim for container transportation networ of seaports, Proc. of e Eastern Asia Society for Transportation Studies, pp , 2005 [11]M. Dorigo, MACS-VRPTW: A multiple ant colony system for VRP. McGraw-Hill, pp.63-76, [12] David V. Pynada and Michael P. Wellman, Accounting for context in plan recognition, wi application to traffic monitoring,. Proc eleven conf. on Uncertainty in Artificial Intelligence, Montreal,