Moth Search Algorithm for Drone Placement Problem

Transcription

1 Moth Search Algorthm for Drone Placement Problem IVANA STRUMBERGER Sngdunum Unversty Faculty of Informatcs and Computng Danjelova 32, Belgrade DUSAN MARKOVIC Sngdunum Unversty Faculty of Informatcs and Computng Danjelova 32, Belgrade MARKO SARAC Sngdunum Unversty Faculty of Informatcs and Computng Danjelova 32, Belgrade NEBOJSA BACANIN Sngdunum Unversty Faculty of Informatcs and Computng Danjelova 32, Belgrade Abstract: Ths paper presents mplementaton of the moth search algorthm adjusted for solvng statc drone locaton problem. The optmal locaton of drones s one of the most mportant ssues n ths doman, and t belongs to the group of NP-hard optmzaton. The objectve of the model appled n ths paper s to establsh montorng all targets wth the least possble number of drones. For testng purposes, we used problem nstance wth 30 unformly dstrbuted targets n the network doman. Accordng to the results of smulatons, where moth search algorthm establshed full coverage of targets, ths approach shows potental n dealng wth ths knd of problem. Key Words: moth search algorthm, metaheurstcs, NP hardness, swarm ntellgence, optmzaton 1 Introducton The applcatons of flexble flyng drones have ncreased wth the emergng of low energy consumpton machnes, processng devces wth hgh performance and avalablty of lght materals. Drones can be used n a wde varety of applcatons, such as vehcle trackng, the traffc management, fre detecton, mltary operatons,etc. [1]. Drones are mostly used to montor targets, whch are consdered as ponts that can be statc or moble, dependng on the scenaro. Smlar to anchor nodes targetng unknown nodes n wreless sensor network, drones deployment must be placed n a way to cover multple targets, where each target must be covered by at least one drone [2]. The optmal placement of drones s one of the most mportant challenges n ths doman and belong to the group of NP-hard problems [3]. For solvng NP-hard problems, metaheurstcs can obtan satsfyng results, whle standard, determnstc methods can not be appled. One of the most promsng group of metaheurstcs approaches s swarm ntellgence. Swarm ntellgence smulate group of organsms from the nature, such as flock of brds and fsh, herd of elephants, groups of bats and cuckoos, etc. Artfcal bee colony (ABC) models the behavor of honey bee swarm [4], and proved to be robust optmzaton technque [5], [6]. Frefly algorthm (FA) emulates lghtng behavor of frefles [7], and has been mplemented for a wde varety of problems [8], [9], [10]. Cuckoo search (CS) metaheurstcs [11] s based on smlar prncples as FA and has also been appled to dfferent real-world tasks [12], [13]. Frework algorthm (FWA) was nspred by the process of freworks exploson [14], and became on of the most popular algorthm wth many versons [15], [16], [17], [18], [19]. Bat algorthm (BA) smulates group of bats and ther characterstcs of echolocaton [20], and shows outstandng performance [21], [22], [23]. Bran storm optmzaton algorthm s based on the human dea generaton process and t was appled to real world problem[24], [25], [26]. In ths paper, we propose moth search (MS) algorthm adopted for solvng statc drone locaton problem. MS algorthm was proposed n 2016 by Wang for global optmzaton problems [27]. The structure of ths paper s as follows: after Introducton, n Secton 2, we show mathematcal formulaton of statc drone placement problem, MS metaheurstcs s presented n Secton 3, Secton 4 show emprcal results, whle Secton 5 concludes ths paper. ISSN: Volume 3, 2018

2 2 Formulaton of statc drone locaton problem Ths secton presents mathematcal formulaton of the statc drone locaton problem (SDLP). In our mplementaton, we used smlar problem formulaton as n [28]. Rectangular two-dmensonal terran wth length x max and wdth y max represents the flyng regon of the drone u. The radus r and 2D coordnates (x, y) determne the poston of each drone u n the montorng doman. Set of avalable drones can be denoted as U, whle T can be used to ndcate the set of targets to be montored by the avalable drones. Wth the assumpton that the drone u wth radus r u s located n the terran at coordnates (x u, y u ), and that there s a target t wth coordnates (Y t, Y t ), the dstance D xu,yu t between u and t can be calculated as: D xu,yu t = (X t x u ) 2 + (Y t y u ) 2 (1) Moreover, Each drone u wth radus r u s characterzed wth the vsblty θ, that exemplfes a dsk n the plane. In mathematcal formulaton of drone coverage of targets, two man ssues should be consdered. In order to montor the targets, coordnates (x u, y u ) of each drone u U wth radus r u should be determned. Wth known locaton (x u, y u ) of the drone u U wth radus r u, we need to determne whch target t T s montored by the drone u U. The mathematcal formulaton of two above mentoned ssues can be represented as decson varables [28]: δ u xy = and { 1, f the drone u s located at (x, y) 0, otherwse (2) { γt u 1, f the target t s observed by the drone u = 0, otherwse (3) The objectve functon of the mathematcal model employed n ths paper s to montor all targets wth the least possble number of drones. Ths model can be expressed as follows [28]: mn f(δ) = δxy u (4) (x,y) u U s.t. δxy u 1 x,y γ u t (x,y) δ u xy ( r u D uxy t ) γt u 1 u U u U (5) u U, t T (6) t T (7) δ u xy {0, 1}, (x, y), 1 x x max (8) 1 y y max, u U (9) γ u t {0, 1}, t T, u U (10) The objectve functon showed n Eq.(4) deals wth the mnmzaton of the number of employed drones. Assurance that the drone u s postoned n at most one locaton s provded by usng constrant showed n Eq. (5). Condton showed n Eq. (6) s used to set the value of decson varable γ u t. The varable γ u t takes the value of 0, f the radus of drone u s lesser than the dstance between the target t and the drone u, and vce-versa. Condton that the each target t s beng montored by at least one drone s specfed n Eq. (7), whle constrants (8) - (10) determne the doman of the varables. 3 Moth search algorthm MS algorthm was nspred by the the phototaxs and Lévy flghts of the moths. Ths relatvely new algorthm was developed n 2016 by Wang [27]. MS algorthm belongs to the group of swarm ntellgence metaheurstcs, and was prmarly mplemented for global optmzaton problems [27]. In order to demonstrate the performance of MS algorthm, ts very frst mplementaton was compared wth fve state-of-the-art metaheurstcs through an array of experments on fourteen basc benchmarks, eleven IEEE CEC 2005 complcated benchmarks and seven IEEE CEC 2011 real world problems [27]. The results of comparatve analyss have shown great potental of the MS algorthm for tacklng global optmzaton tasks [27]. Moths have two dstngushng characterstcs that dfferentate them from other smlar speces. Frst characterstc of moths, phototaxs, represents a phenomena, where moths tend to fly around the lght source [29]. The other characterstc of the moths, ISSN: Volume 3, 2018

3 Lévy flghts, as one of the most mportant flght patterns n natural surroundngs, was consdered for MS algorthm [27]. Lévy flghts defne the type of random walk whch step length s drawn from Lévy dstrbuton. The Lévy dstrbuton whch can be modeled n the form of a power-law formula [27]: L(s) s β, (11) where β [0, 3] denotes an ndex. Accordng to the analyss of moths fly patterns [30], moths use Lévy flghts movements wth β 1.5. For that reason, n our experments, we set the value of parameter β to 1.5. Some other swarm ntellgence approaches also use Lévy flghts search, lke cuckoo search (CS) [11], FA [7] and krll herd (KH) [31] metaheurstcs. Two above mentoned characterstcs of moths (phototaxs and Lévy flghts) were used to model two steppng stones of every swarm ntellgence metaheurstcs - ntensfcaton and dversfcaton. The moths that are closer to the lght source (best moth n the populaton) tend to fly around the best moth n the form of Lévy flghts. Ths type of behavor s presented n the followng equaton [27]: x t+1 = x t + αl(s), (12) where x t+1 s the updated poston of moth and x t s the orgnal poston of moth n current generaton t, respectvely. Step drawn from Lévy dstrbuton s denoted as L(s), and the parameter α s scale factor whose value depends on the optmzaton problem. In the orgnal MS s mplementaton, α was gven as [27]: α = S max /t 2, (13) where S max s the maxmum walk step whose value also depends on the problem n hand. Lévy dstrbuton gven n Eq. (12) can be calculated as [27]: L(s) = (β 1)Γ(β 1) sn( π(β 1) 2 ) πs β, (14) where Γ s the gamma functon and s s greater than 0 [27]. Moths that are far from the lght source (best moth n the populaton) wll fly towards the lght source wth trajectory of a lne.ths type of fly can be mathematcally expressed as [27]: x t+1 = λ (x t + φ (x t best xt )), (15) where x t best denotes best moth n generaton t and φ and λ are acceleraton and scale factors, respectvely. The moth can fly n drecton of the fnal poston that s beyond the best moth n the populaton (lght source). Ths flght pattern s descrbed as [27]: x t+1 = λ (x t + 1 φ (xt best xt )) (16) In the orgnal research [27], the entre moth populaton s separated nto two equvalent subpopulatons based on ther ftness. In subpopulaton 1 (moths wth greater ftness), postons of ndvduals are beng updated usng Lévy flghts (Eq. (12)), where moth postons n the subpopulaton 2 (moths wth lower ftness) are beng updated by usng Eq. (15) or Eq. (16) wth possblty of 50% [27]. 4 Expermental results In ths secton, we brefly show network topology used n experments, parameters setup, and results of emprcal tests. In the emprcal tests, we used statc drone locaton problem nstance wth 30 unformly dstrbuted targets. Scenaro wth randomly dstrbuted targets s harder to solve than scenaro wth clustered targets. Workng doman of the network was set to 100 m by 100 m. For all drones n the populaton, radus r was set to 15 m, smlar lke n [28]. The number of moths n the populaton N was set to 40, and the maxmum number of generatons MaxGen was set to 2,000 yeldng total of 80,000 objectve functon evaluatons. The rest of parameters were adjusted as: the number of moths kept n each generaton to 2, ndex β = 1.5, max walk step S max = 1.0, and acceleraton factor φ = (5 1/2 1)/2 = For testng purposes, we developed software framework usng Vsual Studo 2017 wth.net Framework 4.7. Algorthm was tested n 30 ndependent runs on Intel CoreTM HQ wth 32GB of RAM memory. For expermental purposes, n order to analyze how MS algorthm behaves, we conducted experments wth dfferent number of drones (startng wth only one drone). In the employed scenaro, mnmum number of 9 drones s necessary to cover all targets. Expermental results for 30 unformly dstrbuted targets are shown n Table 1. In the presented table, we show results for dfferent number of drones for absolute and targets coverage n percentles, and for executon tme of the MS algorthm. As performance ndcators, we used best and mean results obtaned n ISSN: Volume 3, 2018

4 From the results presented n the Table 1, we conclude that the MS algorthm generates optmal values, and establshes full coverage of targets wth 9 drones. Results wth 9 drones are vsualzed n Fgure 1. Fgure 1: Examples wth one drone (left), and four drones (rght) n clustered target set 30 ndependent runs of the algorthm. In Table 1, T.C., T.C.% and E.T. are abbrevatons for target coverage, target coverage n percentles and executon tme, respectvely. Table 1: Expermental results Drone No. Indcator T.C. T.C % E.T. 1 Best 6 20% 1.5 Mean % Best % 4.3 Mean % Best 15 50% 6.6 Mean % Best 18 60% 7.6 Mean % Best 21 70% 10.0 Mean % Best 24 80% 14.2 Mean % Best 26 86% 17.3 Mean % Best 28 93% 21.9 Mean 27 90% Best % 29.4 Mean % Concluson In ths paper we showed moth search (MS) algorthm adjusted for solvng statc drone locaton problem (SDLP). MS s novel swarm ntellgence metaheurstcs proposed by Wang n 2016, and t was not tested on ths problem before. The MS algorthm was tested on problem nstance wth 30 unformly dstrbuted targets. In ths case, MS algorthm obtaned coverage of all targets wth 9 drones, whch s optmum soluton. As a concluson, we state that the MS algorthm shows good performance when tacklng NP-hard problems such s statc drone locaton problem. Acknowledgements: Ths research s supported by the Mnstry of Educaton, Scence and Technologcal Development of Republc of Serba, Grant No. III References: [1] H. Chen, X. mn Wang, and Y. L, A survey of autonomous control for uav, n Proceedngs of the 09 Internatonal Conference on A Artfcal Intellgence and Computatonal Intellgence (AICI 09), pp , IEEE, November [2] D. Zorbas, L. D. P. Puglese, T. Razafndralambo, and F. Guerrero, Optmal drone placement and cost-effcent target coverage, Journal of Network and Computer Applcatons, vol. 75, pp , November [3] M. Youns and K. Akkaya, Strateges and technques for node placement n wreless sensor networks: A survey, Ad Hoc Networks, vol. 6, pp , June [4] D. Karaboga, An dea based on honey bee swarm for numercal optmzaton, Techncal Report - TR06, pp. 1 10, [5] N. Bacann, M. Tuba, and I. Brajevc, Performance of object-orented software system for mproved artfcal bee colony optmzaton, Internatonal Journal of Mathematcs and Computers n Smulaton, vol. 5, no. 2, pp , ISSN: Volume 3, 2018

5 [6] N. Bacann, M. Tuba, and I. Strumberger, RFID network plannng by ABC algorthm hybrdzed wth heurstc for ntal number and locatons of readers, n th UKSm-AMSS Internatonal Conference on Modellng and Smulaton (UKSm), pp , March [7] X.-S. Yang, Frefly algorthms for multmodal optmzaton, Stochastc Algorthms: Foundatons and Applcatons, LNCS, vol. 5792, pp , [8] E. Tuba, M. Tuba, and M. Beko, Moble wreless sensor networks coverage maxmzaton by frefly algorthm, n 27th Internatonal Conference Radoelektronka, pp. 1 5, IEEE, [9] E. Tuba, M. Tuba, and M. Beko, Two stage wreless sensor node localzaton usng frefly algorthm, n Smart Trends n Systems, Securty and Sustanablty, LNNS, vol. 18, pp , Sprnger, [10] M. Tuba and N. Bacann, JPEG quantzaton tables selecton by the frefly algorthm, n Internatonal Conference on Multmeda Computng and Systems (ICMCS), pp , IEEE, [11] X.-S. Yang and S. Deb, Cuckoo search va levy flghts, n Proceedngs of World Congress on Nature & Bologcally Inspred Computng (NaBIC 2009), pp , [12] I. Brajevc and M. Tuba, Cuckoo search and frefly algorthm appled to multlevel mage thresholdng, n Cuckoo Search and Frefly Algorthm: Theory and Applcatons (X.-S. Yang, ed.), vol. 516 of Studes n Computatonal Intellgence, pp , Sprnger Internatonal Publshng, [13] N. Bacann, Implementaton and performance of an object-orented software system for cuckoo search algorthm, Internatonal Journal of Mathematcs and Computers n Smulaton, vol. 6, pp , December [14] Y. Tan and Y. Zhu, Freworks algorthm for optmzaton, Advances n Swarm Intellgence, LNCS, vol. 6145, pp , June [15] E. Tuba, M. Tuba, and E. Dolcann, Adjusted freworks algorthm appled to retnal mage regstraton, Studes n Informatcs and Control, vol. 26, no. 1, pp , [16] N. Bacann and M. Tuba, Freworks algorthm appled to constraned portfolo optmzaton problem, n Proceedngs of the 2015 IEEE Congress on Evolutonary Computaton (CEC 2015), May [17] M. Tuba, N. Bacann, and A. Alhodzc, Multlevel mage thresholdng by freworks algorthm, n th Internatonal Conference Radoelektronka (RADIOELEKTRON- IKA), pp , Aprl [18] E. Tuba, M. Tuba, and M. Beko, Node localzaton n ad hoc wreless sensor networks usng freworks algorthm, n Proceedngs of the 5th Internatonal Conference on Multmeda Computng and Systems (ICMCS), pp , September [19] E. Tuba, M. Tuba, and D. Sman, Wreless sensor network coverage problem usng modfed freworks algorthm, n Internatonal Wreless Communcatons and Moble Computng Conference (IWCMC), pp , IEEE, [20] X.-S. Yang, A new metaheurstc bat-nspred algorthm, Studes n Computatonal Intellgence, vol. 284, pp , November [21] E. Tuba, M. Tuba, and D. Sman, Adjusted bat algorthm for tunng of support vector machne parameters, n IEEE Congress on Evolutonary Computaton (CEC), pp , IEEE, [22] M. Tuba and N. Bacann, Hybrdzed bat algorthm for mult-objectve rado frequency dentfcaton (RFID) network plannng, n Proceedngs of the 2015 IEEE Congress on Evolutonary Computaton (CEC 2015), May [23] E. Tuba, M. Tuba, and D. Sman, Handwrtten dgt recognton by support vector machne optmzed by bat algorthm, Proceedng of the WSCG 2016, Computer Scence Research Notes, pp , [24] E. Dolcann, I. Fetahovc, E. Tuba, R. Capor- Hrosk, and M. Tuba, Unmanned combat aeral vehcle path plannng by bran storm optmzaton algorthm, Studes n Informatcs and Control, vol. 27, no. 1, pp , [25] E. Tuba, R. Capor-Hrosk, A. Alhodzc, and M. Tuba, Drone placement for optmal coverage by bran storm optmzaton algorthm, n Internatonal Conference on Health Informaton Scence, Advances n Intellgent Systems and Computng, vol. 734, pp , Sprnger, ISSN: Volume 3, 2018

6 [26] E. Tuba, E. Dolcann, and M. Tuba, Chaotc bran storm optmzaton algorthm, n Intellgent Data Engneerng and Automated Learnng, LNCS, vol , (Cham), pp , Sprnger Internatonal Publshng, [27] G.-G. Wang, Moth search algorthm: a bonspred metaheurstc algorthm for global optmzaton problems, Memetc Computng, Sep [28] D. Zorbas, T. Razafndralambo, D. P. P. Lug, and F. Guerrero, Energy ecent moble target trackng usng yng drones, n Proceedngs of the 4th Internatonal Conference on Ambent Systems, Networks and Technologes (ANT 2013), Proceda Computer Scence, vol. 19, pp , Sprnger, [29] P. S. Callahan, Moth and candle: The candle flame as a sexual mmc of the coded nfrared wavelengths from a moth sex scent (pheromone), Appled Optcs, vol. 16, no. 12, pp , [30] A. Reynolds, D. Reynolds, A. Smth, G. Svensson, and C. Lfstedt, Appettve flght patterns of male agrots segetum moths over landscape scales, Journal of Theoretcal Bology, vol. 245, no. 1, pp , [31] A. H. Gandom and A. H. Alav, Krll herd: A new bo-nspred optmzaton algorthm, Commun Nonlnear Sc Numer Smulat, vol. 17, pp , ISSN: Volume 3, 2018