Conflict-Based Multi-Capacity Constraint Route Planning

Transcription

1 IAENG International Journal of Computer Science, :, IJCS Conflict-Base Multi-Capacity Constraint Route Planning Daniel Siahaan, Muhamma Rusli, Salamun Nuin, Ahatus Solichah Abstract Planning an scheuling mass eparture is critical for tsunami isaster management. Algorithm that can generate effective evacuation plan an scheule is require. The evacuation plan an scheule have to ensure that the whole population can be move to safety areas before the calamity of tsunami takes its impact on the lan. Current heuristic solutions fail from computational complexity by assuming that the network s elements, such as noes an eges, have infinite capacity. Their approaches generate lazy evacuation route an evacuation plan as one instance. They fail to ensure their scalability when ealing with a real problem, i.e. huge transportation networks. This paper introuces a refinement of a multi-capacity constraine heuristic routing algorithm, which embee a conflict-base path generation for evacuation scheuling. The algorithm is exercise on tsunami scenario in a capital city (northern coast of North Sulawesi, Inonesia which has the population of more than, lives. The propose algorithm improves the computation time significantly (8%) while maintaining the time require for executing the evacuation plan the previous solution Inex Terms Capacity Constraint, Conflict-Base, Evacuation Route Planning an Scheuling I INTRODUCTION Planning evacuation route an scheule are a critical process for tsunami mitigation activities in a coastal area. An efficient an yet scalable computational algorithm is require to generate evacuation route an scheule that ensure zero life lost when the event of great tsunami actually takes its impact on the lan. Some solutions focus on solving the problem as a linear programming problem [, ]. The computational complexity of the solutions is exponential, which are not suite for a huge network such as in urban area. A number of heuristic solutions are propose to solve the problem of exponential complexity of the computation [,, ]. The solution was inspire by the work of Goochil et al. [], which suggest the use of Manuscript receive January 9 th, ; revise March,. This work was supporte in part by the Higher Directorate General of Eucation, Inonesia Ministry of Eucation an Culture, uner Grant Unggulan PT. D. Siahaan is with the Institut Teknologi Sepuluh Nopember, Surabaya, Inonesia (phone: +-99; fax: +98; e- mail: aniel@ if.its.ac.i). M. Rusli is with STIMIK-STIKOM Denpasar, Inonesia ( rusli@stikom-bali.ac.i). S. Nuin is with the Eucation Technology Dept, Universitas Negeri Surabaya ( salamunrn@gmail.com) A. Solichah is with the Institut Teknologi Sepuluh Nopember, Surabaya, Inonesia ( closelicha@gmail.com) geospatial information for generating optimal evacuation routes. The solution propose by Sarshar et al. utilizes the Volunteere Geographic Information (VGI) create by community []. This ecision was taken ue to the fact that of formal agencies (Environment System Research Institute) can only provie limite resources, which cannot match the rate of which the community proucing the geospatial information [8]. Thus, the aforementione solutions use a heuristic approach to generate optimal routes an or scheule. They reuce the computational time compare to the linear-programming approaches. These solutions generate the evacuation route with the assumption that any group of evacuees that transits at an evacuate noe may be irecte to take ifferent evacuation path than other groups starte from the evacuate noe or also transits from that evacuate noe but from ifferent source noe. They also assume that each group of evacuees from an evacuate noe may be irecte to take a ifferent evacuation path than other group from the same noe. These assumptions are not feasible when applie to the fiel. During the evacuation time, it is ifficult to organize evacuees to join their esignate group an to take their esignate path. This is because the tsunami event may occur anytime an panic may isorient evacuees in choosing their esignate evacuation path. Sarshar et al. introuces a ynamic moel base on Bayesian Network to preict the probability of congestion occurrences uring evacuation process in ship []. The algorithm consiers a number of variables, such as passengers panic, passengers gener, an the structure of the ship. It preicts the probability of trapping in congestion for evacuees an the extension of evacuation time given an evacuation moel. Nonetheless, it oes not consier the ynamic of the evacuation routes. Other research by Kinugasa an Nakatani focuses on proviing a tool that analyzes the behavior of visitors, such as tourists, uring an evacuation process [9]. The work compares an evaluates the effectiveness of various evacuation guiance methos. The case for the stuy is Kyoto city, especially the tourism area. It focuses on the event of an earth quake. It uses a static evacuation plan, where the state (availability) evacuation paths are consiere unchange. The research by Ogunlana an Sharma evaluates an evacuation moel which is base on intelligent agent []. It evelops a visualization tool for that purpose. The tool helps in envisaging the time of evacuation. It also helps analyzing evacuation moel base on the what-if scenario. It incorporates ata on human emotions an movements. (Avance online publication: July )

2 IAENG International Journal of Computer Science, :, IJCS T l P Po l l l (a) Evacuation Scenario (,) P T l algorithm is calle Conflict-Base Multi-Capacity Constraine Route Planning (CBMCCRP). The algorithm separates the process of generating the evacuation route an the evacuation scheule an elays as long as possible the evacuation scheule. It aopts the lexicographic function to minimize the number of casualties. This algorithm was teste on real-scale tsunami case in Manao, which lies on the coast of North Sulawesi. It has to eal with evacuating more than. lives on more than noes an eges. The rest of the paper is organize as follow. The next section paper escribes how the problem of tsunami evacuation is moele. Then, it escribes the propose algorithm calle Conflict-Base Multi Capacity Constraine Route Planning. The paper then presents the experimental result an its analysis. The last section provies the conclusion of the paper. (,) (,8,) P (,8,~) T Po (,,) (,,) An enhance algorithm base on Multi-Capacity Constraine Route Planning was evelope. The P T (b) Evacuation Graph Fig.. Evacuation Problem Moel (,) (,,8) II. TSUNAMI EVACUATION PROBLEM Evacuation route planning can be best escribe as a graph as seen in Fig.. The figure in Fig..a shows an evacuation scenario with evacuate noe (P, P, an P ) an two safe noes (T an T ). In this scenario, the population in each evacuate noe has to be evacuate in given time. In this example, all evacuees in P, P, an P have to be evacuate within hours, hours, an hours respectively after the first warning given. The eges (roas) l, l, an l connect two noes an may be unavailable within ifferent time after the first warning. For example, after hours, l will be isconnecte because tsunami takes its impact on that ege. This evacuation scenario can be represente as a graph G = (N = P T; A ), where P an T are the set of evacuate noe (an/ transit noe) an safe noe respectively, an A is a set of eges l. Each evacuate noe i has a set of attributes ( i, f i ), which consist of a t P o v o P P T v t T 8 Fig. Time-Expane Graph of an Evacuation Scenario (Avance online publication: July )

3 IAENG International Journal of Computer Science, :, IJCS number of evacuees an the ealine time for evacuation respectively. Each ege l has a set of attributes (s e, u e, f e ), which inclues istance of the ege (with respect to time neee for evacuees to travel from source noe to estination noe), ege capacity (a maximum number of evacuees that can be in the ege at an evacuation time unit), an the time when the ege become unavailable respectively. III. CONFLICT-BASED MULTI-CAPACITY CONSTRAINT ROUTE PLANNING Since the CBMCCRP aopts the conflict-base approach in generating the evacuation path of a specific noe, CBMCCRP moels the evacuation problem as a time-expane graph by iscreite the planning in time steps with ientical length. Fig. illustrates the timeexpane graph of the previous scenario. Graph G = (N = P T, A ) is generate by uplicating each noe in N an ege in A for each time t. For each time t, any unavailable noe in N an ege in A shoul be remove. From the scenario, we can see that after t=, evacuate noe P is remove because it is estroye by the tsunami. A super-source v s an a super-sink v t are ae to moel the inflow an outflow of evacuees respectively. The algorithm has to fin a set of evacuation routes from v s to v t that ensure all evacuees reach the safe noes within the minimum evacuation time. The pseuo coe of evacuation route algorithm is as follow: The following are rules which are applie in this propose algorithm:. All groups of evacuees of an evacuate noe p shoul take the same evacuation route c. This is to ensure that there will be no chaos uring the evacuation process ue to panic evacuees. Panic evacuees coul cause conflicte flow of evacuation among groups of evacuees an ineffective evacuation route taken by groups of evacuees ue to confusion an other group provocations.. An evacuation route p of a group of evacuees that starte from an evacuate noe p is a subset of any evacuation route of a group of evacuees that passes the evacuate noe.. An evacuation route p shoul only contain ege l at most one. Input: - Evacuation graph G = (N = P T, A ), where N is a set of evacuate noes P an safe noes T, an a set of irecte-eges A that connect a noe with another noe. - For each noe n N, n comprises of ( i, f i,), where i is the ealine for evacuation an f i is the amount of population that nees to be evacuate. - For each ege l A, l comprises of (s e, u e, f e ), where s e is travel time, u e is the capacity, an f e is the time when the ege becomes unavailable. Output: - Ω is an evacuation plan, which contains a set of evacuation routes, with the shortest evacuation time. - S is the evacuation scheule with the maximum number of evacuees. Algorithms: Sort noe in P by its istance to a nearest safe noe. Foreach noe p sorte P, generate c <n, n,, n k > with the shortest path for each pair of p an t, (,) (,) P l (,,) P l (,,) P (,) (,) P P l (,8,) l (,,) (,) (,) P l (,8,) l 9 (,,) (,) P 8 l l (,,) (,,) P (,8) l l (,,) (,,) (,,) l (,9) 8 P T T P (,) (,) Fig.. Experimental Network Topology l (,,) l P 9 (,,) (Avance online publication: July )

4 IAENG International Journal of Computer Science, :, IJCS where p P, t T generate While there is an evacuate noe p P where fi,> { flow = min(fi,>, available_ege_capacity(all ege on route c), available_noe_capacity (all noe on evacuate noe to safe noe on route c), ) for i= to k- o { t = t + fe(e(ni,ni+)); available_ege_capacity (e(ni,ni+),t) - flow; available_noe_capacity (ni+, t) flow; t = t ; } Ω = Ω (G, Ω, c,s); S = (Ω, G, G ) Fig. illustrates the network topology of a coastal area use in the experimentation. The network comprises of noes which are member of N, that is evacuate noes P an safe noes T. The generation process of evacuation plan (Ω ) an evacuation scheule (S ) are one iteratively until there is no evacuee left in any evacuate noe (ue to all evacuees have been evacuate or the evacuate noe have been rawn by tsunami). When an evacuate noe still has evacuees left by the time it was rawn by the tsunami, then a penalty is given. Fig. visualizes the evacuation plan generate by the algorithm. Table shows the evacuation plan prouce by CBMCCRP given the network topology given in Fig..The first two groups of evacuees that starte from P an P were the first groups of evacuees that reach the safe noe t an t respectively. Evacuees which starte from noe P were ivie into two smaller groups (groups of an evacuees) which starte the evacuation at the same time (t=) an through the same evacuation route. The first group reache the safe noe at t=, while the secon group reache the safe noe at t=. This is because the secon group has to wait unit of time at noe P ue to ege capacity of unit l that connect P an T. The evacuees that starte from evacuate noe P are also ivie into two groups of evacuees (groups of an evacuees). The first group eparte at t=, while the secon group eparte at t=. Both groups took the IV. EXPERIMENTAL RESULT The following are assumptions which are applie in this propose algorithm:. Decision maker instructs where an when each group of evacuees from certain evacuate noe must leave an which route shoul be taken.. There shoul be only one scenario is use at a time.. The objective of the ecision maker is only to ensure that all evacuees are evacuate to the safe noe within a feasible time. P t vo P P P P P P P9 P T T P P8 Fig. Generate Evacuation Route of Given Scenario (Avance online publication: July ) vt

5 IAENG International Journal of Computer Science, :, IJCS same evacuation route. The first group that starte earlier reach the safe noe T at t=. The secon group that starte later joine by another group of evacuees that starte from T.reach the safe noe T at t= The evacuees that starte from in evacuate noe T were ivie into groups (groups of,, an evacuees). All groups took the same evacuation route, i.e. P-l-P-l-P-l-T. The first two groups starte at t=, while the thir groups starte at t=. At P, the first group together with the first group (group of ) that starte from evacuate noe P8 joine the secon group of evacuees (group of ) that starte from P, which arrive unit of time earlier, an immeiately continue travelling to safe noe P. At the same noe, after waiting for unit of time ue to l were fully occupie, the secon group together with the secon group (group of ) that starte from evacuate noe P8 were joine by the thir group of evacuees an continue travelling to safe noe P. Given this result we can see not only the algorithm make sure one route for each evacuate noe, but also ensure that an evacuation route a of an evacuate noe pa where pa is in evacuation route of evacuate noe pb, then b a. Given the problem in Fig., the algorithm prouces four paths for generating evacuation routes, that is: - P- l-p- l-p- l-p- l-p- l-t - P- l-p- l-p- l-p- l-p- l-t - P- l-p- l9-p- l-t - P8- l8-p9- l-p- l-t The result shows the ifferent between previous algorithm, i.e. MRCCP, an the propose algorithm. First, CBMCCRP aopts [] to generate evacuation path an evacuation scheule separately while ensuring that one evacuate noe shoul only be assigne to one evacuation route. Secon, instea of generating route uring the generation of scheule, the algorithm starte the process by sort the evacuate noe by its istance to the sinknoe. The iea is to ensure that the scheuling process start from the closest-to-sink evacuate noe. The allocation of evacuees group into the scheule is as follow:. Group of evacuees starte from the current evacuate noe.. Group of evacuees which arrive earlier in the current evacuate noe.. Group of evacuees from the closest evacuation noe which arrive in the current evacuate noe. Thir, the propose algorithm splits evacuees base on the capacity of an ege that connect starte noe to esignate noe. When a group of evacuees arrive at an evacuate noe, where next evacuation ege has less number of available capacities than the number of evacuees to be evacuate, then the group is split into two smaller groups. Last, MRCCP maintains all routes of each evacuee groups an the capacities of all eges within the routes in every iteration. This is because the algorithm generates new routes base on the capacity of eges at time t. The propose algorithm oes not have to maintain all evacuation routes of all evacuation groups, but the algorithm only has to maintain the main evacuation routes. Given evacuate noes, safe noes, eges, an evacuees, the algorithm require t= to evacuate all evacuees to safe noes. In orer to calculate the cost moel of the propose algorithm, we assume that n is the total number of noes in graph G with np is the total number of evacuate noes an ng is the total number of evacuee groups generate uring evacuation scheuling. TABLE I EVACUATION SCHEDULE FROM THE SCENARIO # Group of Evacuees Number of pi Evacuees p p p p9 p p p p8 p p p p8 p p p p p p Start Time Route P-T P-T P-T P9-P-T P-P-T P-P-T P-P-ile-T P8-P9-P-T P-P-P-T P-P-P-T P-P-P-ile-T P8-P9-P-ile-T P-P-P-T P-P-P-P-T P-P-P-P-P-T P-P-P-P-P-T P-P-P-ile-P-P-T P-P-P-ile-P-P-T (Avance online publication: July ) Exit Time

6 IAENG International Journal of Computer Science, :, IJCS Num of evacuees Network capacity Testing Dataset (Generating network topology) Initial num. of evacuees in each evacuate noe Initial State from Network Topology Generator Num. of noes an eges Coverse Noe-Ege Moel Fig.. Evacuation Time vs. Ratio Noes MRCCP Algorithm MRCCP Algorithm Analysis Fig.. Scalability Testing Design The computation moel of MRCCP is characterize as iterative problem. In each iteration, an evacuation route of each noe is selecte an capacities of all eges along the routes are preserve. The number of iterations is etermine by the number of groups generate uring the evacuation scheuling process. In each iteration, the route with the earliest estination arrival time from starte evacuate noe is recalculate with the cost of. Reservation is mae for the noe an ege capacities along the chosen route with the cost of. The cost moel of MRCCP algorithm is as follows: () The cost moel of CBMCCRP is less complex. The evacuation route is generate once an separate from the calculation of evacuation scheule. Furthermore, the evacuation routes are generate for all evacuation groups that starte or passe an evacuate noe. Therefore, it ecreases the complexity an ensures its scalability for a bigger network topology. The cost moel of MRCCP algorithm is as follows. () The number of iteration uring the evacuation route generation of CBMCCRP is equal or less than MRCCP algorithm. It is because CBMCCRP ensures that any evacuate noe that precees another evacuate noe within the path to sink-noe has an evacuation route that inclues the evacuation route of precee evacuation noe. Therefore, the path of preceing noe shoul be the aition of evacuate noe, connecting ege, an evacuation route of the following noe. Fig shows the testing methoology use for evaluating the scalability of the algorithm. This Total Running Time CBMCCRP MRCCP 8 9 Source Noe Ratio (%) Fig.. Running Time vs. Ratio Noes methoology was aopte from the one use by []. The ata set use in this testing was aopte from Google Map of Manao area, which lies on the North Coast of North Sulawesi Province, Inonesia. The network consists of 9 eges, 8 evacuate noes, an safe noes. The population to be evacuate is,8 lives. The istribution of evacuees was base on the number of population in each 8 sub-regions. The test was conucte on Intel i-core bit, Portege Z8, GB RAM, Winows Operating System. Fig an show the result of the scalability testing on MRCCP an CBMCCRP. On one han, Fig inicates that there is no significant improvement by CBMCCRP with respect to evacuation time. The evacuation time prouce by CBMCCRP tens to be longer (. minutes in average) than MRCPP. The evacuation routes generate by CBMCCRP o not change with respect to the changes in the number of evacuees at a certain evacuate noe at given time t. During the generation of evacuation routes, CBMCCRP as a penalty to a route that contains evacuate noe which becomes unavailable at time t while still has evacuees. In MRCCP, the evacuation routes are regenerate in each iteration. When an evacuate noe has become unavailable at time t, a new column is generate to revise the current route. Two groups of evacuees which start from the same noe, at some transit evacuate noe may take ifferent paths to the sink-noe. (Avance online publication: July )

7 IAENG International Journal of Computer Science, :, IJCS Therefore, the total evacuation time of MRCCP in average is shorter than the one prouce by CBMCCRP. Accoring to Lumbroso et al. [], the situation uring the event of the tsunami isaster is consiere times chaotic. Communication tens to be ifficult an the comman hierarchy structure is fragile an easily fails. This is the result of logistic failure an the nature of the human behavior which is very ifficult to preict an control uring an emergency situation. This means that it is har (not to say impossible) to irect various groups of evacuees to take ifferent routes accoringly. Scare an confuse evacuees may become misirecte ue to various miss irection they receive from other evacuee groups that they encounter along the route. Stepanov an Smith [] suggest a clear an easy instruction or information of evacuation route shoul be given to ensure the optimal result of the evacuation effort. With respect to computation time, Fig inicates a significant improvement by CBMCCRP compares to MRCCP. It can reuce more than 8% of computation time require by MRCCP. This is because the CBMCCRP prouces evacuation route separate from evacuation scheule. The process of generating evacuation routes is relatively linear to the number of evacuate noes. The generation of evacuation routes is one once, before the generation of evacuation scheule. This approach reuces the complexity significantly. Separating evacuation route generation an evacuation scheule generation can reuce the time require to prouce the evacuation routes for it accelerates the formation of new evacuation route as a remey to conflicte evacuate route. The separation of evacuation route generation an evacuation scheule generation can reuce the time require to prouce the evacuation routes. It accelerates the formation of new evacuation route as a remey to conflicte evacuate route. The result of this research can be use by various stakeholer of tsunami isaster in orer to prouce a tangible an measurable evacuation plan an evacuation scheule of evacuees when an event of big tsunami occurs, especially in a coastal area such as Manao. A goo planning can reuce the probability of casualties uring the real evacuation event, especially for a coastal area that has ense population such as Manao, Ambon, Jayapura, an Denpasar. V. CONCLUSION The propose algorithm, Conflict-Base Multi-Capacity Constraine Route Planning (CBMCCRP), lowers the computation time require by the previous algorithm, MRCCP, by reucing the complexity of evacuation routes generation. CBMCCRP reuce the complexity by separating the generation of evacuation route from evacuation scheule.. It accelerates the formation of new evacuation route as a remey to conflicte evacuate route with respect to the ynamic changes of evacuation path availability. Thus, the total evacuation time is not improve in CBMCCRP. It prouce a slightly longer (i.e..%) evacuation time than MRCCP. Nevertheless, the assumption use in generating the evacuation route is safer, with respect to the chaotic situation uring the tsunami event. It can be expecte that the evacuation route can work better in real situation. Further research shoul be irecte to consier other aspects that is relevant to urban areas, such as ynamic population istribution with respect to time (working hours, rushing hours, rest hours, etc.) an ay (working ays an weekens), builing structures, the role of social network applications an evices, etc. Complex variables may improve the moel precision to the near-real life situation. REFERENCES [] R. Francis an L. Chalmet, "A Negative Exponential Solution To an Evacuation Problem," 98. [] T. Kiosko, R. Francis an C. Nobel, "EVACNET User's Guie," Universtiy of FLoria, Minneapolis, 998. [] L. Qing, Y. Huang an S. 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