Cuckoo Optimization Algorithm for a Reliable Location-Allocation of ...

Internaational Journal of Indusstrial Engineering & Prroduction Research (201 16) December 2016, Volum me 27, Numberr 4 pp. 309-3320

DOI: 110.22068/ijieepr.27.4.309

htttp://IJIEPR..iust.ac.ir/

Cuckooo Optimiization Algorith A m for a Reliable R e Locatioon-Allocation of Hubs aamong th he Clientts Mohamm mad Mehd di Nasiri*, Nafiseh Shamsi S Gamchi & Seeyed Ali Torabi T Mohammadd Mahdi Nasirri, School of Industrial I Eng gineering, Colllege of Engin neering, Univeersity of Tehraan Nafiseh Shaamsi Gamchi,, School of Inddustrial Enginneering, Colleege of Engineeering, Universsity of Tehrann Seyed Ali Torabi, To School of Industrial Engineering, College of Enngineering, University U of Tehran Te

RDS KEYWOR Hub locationn, Allocation, Reliable Patth, Fully Intercoonnection, COA.

ABSTRACT A T H Hubs are criitical elemennts of transpo ortation netw works. Locattion of hubs a and allocatiion of demaands to them m are of high h importaance in the n network dessign. The most m importa ant purpose of these models m is to m minimize thee cost, but path p reliabiliity is also annother important factor w which can in nfluence the location of hubs. h In this paper, we propose a Pc center hub location l moddel with full interconnection among hubs, while t there are diff fferent pathss between origins and deestinations. The T purpose o the model is to determ of mine the reliaable path witth lower costt. Unlike the p prior studiess, the number of hubs in the path is not n limited to t two hubs. T This paper presents a bi-objectivee model whhich includees cost and r reliability too determine the t best loca ations for huubs, the finesst allocation o the demannds to hubs, and of a the mostt efficient paath. In order to illustrate t proposedd model, a nuumerical exaample is pressented and solved the s using t Cuckoo Optimization the O n Algorithm. © 2016 IUST T Publication,, IJIEPR. Voll. 27, No. 4, All A Rights Resserved

1.

In ntroduction n1

Public traansportation is a veryy challenging problem inn many deeveloped annd developing countries. In I addition, hubs are criitical elemennts of telecoommunicatioon and transportation networks because b they y play an impportant role in controlling the traffic. Hubs are sppecial facilitiies in many-too-many distrribution systems, and thhey are used to connect the origins and destinations in i of coonnecting eaach a network. Therefore, instead a pair of origin-destinaations directtly, hubs are located bettween them to consolidaate, route, and distribute thhe traffic in order to take advantage of economies of scale on o inter-hubb connection ns. ms arise in most of the t Hub locatiion problem network ddesign problems. The hub location *

Correspondin ng author: Moha ammad Mehdi Nasiri N

Email: [email protected] Received 4 Maay 2015; revised d 4 March 2017;; accepted 10 Appril 2017

prroblem is co oncerned with h locating huub facilities annd allocatingg demand no odes to hubs in order to rooute the trafffic between origin-destinnation pairs. Thhis area is riich and incluudes many models m most off which are aimed a to minnimize the coosts and just diiffer in theirr constraintss. Capacity constraints, seervice level constraints, c me, single or delivery tim m multiple alloccation, etc. are a the mainn constraints inn the modeels. Howeveer, the impportance of coonsidering th he reliability of the netwoorks is often neeglected andd few paperss discuss it. In hub and sppoke networkks, any malffunction at thhe path may caause degradaation of the whole w netwoork’s ability too transfer floows; moreovver, due to thhe fact that thhe current networks are quite vulnerable, deesigning moore reliable networks in hub-andsppoke systemss is a critical issue. C Campbell [1] classified hub locationn problems acccording too the optiimization criteria: c (i) m minimization of the totall transportattion cost in thhe p-hub med dian problem m (which is the original

International Journal of Ind dustrial Engineeering & Producttion Research, December D 2016, Vol. V 27, No. 4

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M. M. N Nasiri, N. Sha amsi Gamchi & S. A. Toraabi

model propposed in [2]); (ii) minim mization of the t total transpportation coost and the fixed cost of establishingg hubs (un-ccapacitated/capacitated huub location pproblem); (iiii) minimizzation of the t maximum transportatiion cost (p-hub ( centter problem); (iv) minimiization of thhe number of hubs whiile serving each paair within a predeterminned bound (h hub coveringg problem). Alumuur, Nickel [3 3] introducedd a multimod dal hub locatioon and netw work design with differeent possible ttransportation n modes. They jointtly considered transportatiion costs annd travel tim mes parately in different huub which are studied sep location prooblems. Theey also considdered differeent service levvels for diffferent types of customers. Contreras, Fernández [4] presentedd a model for f m, where the t hubs are a hub locatiion problem connected by means of a treee. The mod del ork combines several aspeects of locaation, netwo design, andd routing problems. Oktal and Ozger [5] developed the tradition nal model of uun-capacitateed multiple allocation huub location pproblem. Thhe new coonstraints are a consideringg the value and compoonents of coost including ddirect operaating cost, total t operating cost, fixedd and variiable costs for aircraffts. Alumur annd Kara [6] reviewed r thee network huub location pproblems. Since S hubs are special facilities thhat serve ass switching, transshipmeent and sortingg points in many-to-man m ny distribution systems, thhey classifieed and survveyed netwo ork hub locatioon models. They categoorized the huub location models m as follows: p-hub p mediian problem, huub location problem p withh fixed cost, phub center problem, and hub coveriing problem. Kim and O'Kelly [7] discussed reliable p-huub in teleccommunication location problems nted a new w hub location networks. They presen which focuses on maxim mizing netwo ork problem w performancce in terms of reliabilitty by locating hubs for deelivering flow ws among citty nodes. Zhou and Liu [88] formulateed a capacittated locatioonallocation problem with w stochaastic demannds expected value moodel, channce-constrainned annd deppendent-channce programmiing, programmiing accordinng to diffe ferent criterria. Their objecctive is to minimize m the transportation cost. Melkkote and Dasskin [9] com mbined faciliity location/neetwork desiggn problem. In this moddel, the capacitty of facilitiees is limited to the amouunt of demand they can seerve. Klose and a Drexl [1 10] on networkk which is a designed a distributio strategic isssue. In thiis model, thhey developped continuous location moodels and network location models. Daskin, Snydder [11] presented faciliity

Cuckooo Optimization n Algorithm for f a Reliablee …

loocation decissions in a suppply chain ddesign. They reeviewed cllassical mo odels incluuding the traditional fix xed charge faacility locatiion problem d to annd the conteext of facilitty location decisions inncorporate addditional feattures of a suppply chain. Bashiri, Mirzzaei [12] discussed the qualitative paarameters whhich have crritical roles to locate the huubs in thee best placces. They considered paarameters, such s as quaality of serrvice, zone traffic, enviroonmental isssues, and caapability for deevelopment, in the futuree, in additionn to cost and tim me. Alumu ur, Yamann [13] prroposed a hiierarchical multimodal m h location problem in hub w which two typpes of hubs and hub linkks are to be esstablished. In this modeel, they connsidered the tim mer-definite deliveriess. de Cam margo, de M Miranda [14]] worked on o the MM MHLRP and coombined tw wo models: the vehiccle routing prroblem and the single-hhub location problem to deevelop a new formulatiion for the problem of frreight industtry in a paarcel deliverry network deesign. In thhis problem, several faacilities are reesponsible foor assemblinng flows froom origins, ree-routing, dissassembling, and deliverring them to thhe final desttinations. Geelareh and Nickel N [15] prresented a MIP M hub loccation modell for public transport. In their moddel, several levels of ( locating deecisions are made simulltaneously: (1) huub nodes; (2) ( choosing the connnecting hub eddges to havee a connecteed hub-levell graph; (3) roouting the floows through the cheapestt paths. R Razmi, Zahed di-Anaraki [16] [ proposeed a model foor reliable warehouse network deesign. They prresented a bi-objective stochastic s miixed-integer linnear program ming modell to minimiize average coosts of prod duction, trannsportation, relocation, annd capacity extension and to maaximize the cooverage perccent of custo omer demannd delivered w within preferrred delivery y lead time. Eghbali, A Abedzadeh [ [17] propossed a mullti-objective m model which consists of cost minim mization and m minimization i of the total number of intermediate linnks (betweeen all origgins and deestinations). A Although theey considereed a constrraint which asssured that the t reliabilityy of a routee is not less thhan a specifieed value. A mathematicaal model for thhe dynamic single alllocation hubb covering prroblem was proposed by b Zare Meehrjerdi and H Hosseininasab b [18], which w consiidered the coovering radiius of hub nodes as one o of the deecision variaables in order to save tthe costs of esstablishing additional hub nodees. Davari, Zarandi [19] presented an a HLP whiich aims to m maximize thee reliability of the rooutes. They


Cuckoo Optiimization Algoorithm for a Reliable R ……

considered the reliabiility of eacch arc in the t network off hub-and-spooke as fuzzy variables. m to design a reliab ble Kim [20] ddiscussed a model and survivaable hub netw work. Kim [19] considerred the substanntial aspectss of the cuurrent netwoork systems suuch as locaations demannding servicce, their interaactions, the role r of hubs,, and inter-huub links. Karim mi, Eydi [21] presented a model for the t capacitatedd single allocation a hub location problem with a approcch. hierarchiccal Tavak kkoli-Moghaaddam [2 22] Mohammaddi, presented a mixed-intteger prograamming mod del mproved metta-heuristic algorithms to and two im solve a cappacitated sing gle allocationn hub covering location pproblem. Ghodratnama G a, TavakkooliMoghaddam m [23] comppared three proposed p mettaheuristics to solve a new p-hhub locatio onallocation problem. Yahyaei, Bashhiri [24] ussed m undder multi-criterria decisionn making methods criteria weights uncertaainty to solvve logistic huub Moghaddam, Gholipouurlocation. Tavakkoli-M osed a multi-objecti m ive Kanani [[25] propo imperialist competitivee algorithm for f solving the t capacitatedd single-alllocation hhub location problem. Z Zarei, Mahhdavi [26] presented the t multi-level capacity approach too specify the t t appropriatee link typess to be insstalled on the network eddges leadingg to deteminnination of the t correct opptimum hu ub locationn and spooke allocation. Tavakkoli-M Moghaddam m, Baboli [227] proposed a new robust mathematiccal model forr a p-hub coveering probleem, which coped with the t intrinsic unncertainty of some param meters. Cuckoo seaarch (CS) is an optimizaation algorithhm developed by Yang and Deb [228]. A mulltiw objective ccuckoo searrch (MOCS)) method was formulatedd to deaal with multi-criterria ms. This appproach usses optimizatioon problem random weeights to combine multiiple objectiv ves to become a single objeective. As the weights vaary nts can be found, so the t randomly, Pareto fron t points cann be distribbuted diverssely over the fronts. The signifiicant shortcooming of the papers in thhis scope is thhat the researrchers considder one or tw wo hubs betweeen the origiins and destiinations, while there may bbe more thann two hubs inn the path. The T situation arrises when thhe cost of ussing three huubs in a path iss less than using two hubbs, such as the t non-Eucliddean TSP. Therefore, T in this paper, we w propose a P P-center hub b location model m with full fu interconnecction amon ng hubs, annd there are a different paaths between n origins and destination ns. In this model, m we consider c thee cost to be minimized and the relliability to be b maximizeed.

M. M. Nasiiri, N. Sham msi Gamchi, S. A. Torabi

311

ws between Thhe model finnds the best path for flow orrigins and deestinations. Thhe remainder of the paper p is orrganized as foollows. We would have the nottations and asssumptions of o the model in Section 2. 2 The main boody and form mulation of the problem is i presented inn Section 3. 3 Section 4 discussees a short deescription of o COA. Numerical N e example is diiscussed in Section 5 to t illustrate the model. Fiinally, Secttion 6 conccludes the paper and prresents the potential areaa for further studies. s

2. Nottations and d Assumptiions Thhis section n introducess the notaations and foormulations of our model. m Here,, we state deecision varriables, inpput parameeters, and asssumptions underlying u ou ur models. 2--1. Input parameterrs and deecision

vaariables Inn this paper, we introducce two diffeerent sets of pootential hubss. One of them m is a subsett of demand noodes potentiaal for constiituting a hubb. The other onne is a subseet of non-dem mand nodes. Therefore, w define the following seets: we : Set of Cllients; This set includess all of the cuustomers in the t problem. : Set of pottential hub locations within demand noodes ( ⊆ ) : Set of potential p hubb locations within w nondeemand nodess ( ∩ ∅) Inn this moddel, we connsider diffeerent costs, inncluding fixeed cost of esstablishing huubs, cost of alllocating the customers to t the hubs, and cost of transportationn. The notattions of diffferent costs arre as follows: : Fixed costt of installing g hub at nodee ∈ : Fixed costt of installing g hub at nodee ∈ : The cost of o allocating node i to huub j. : Unit cosst of transpo ortation amonng clients k annd l via path a Each demand d node has a flow to annother node nt of this flow w is an inputt parameter. annd the amoun : Demand flow betweeen nodes k annd l Thhe capacity of each hub b is distinctiive and the am mount of demand d cannnot be moree than this caapacity. : Capacityy of hub i Siince a P-ccenter hub location problem p is suupposed, it is necessary to locate P hubs in the neetwork and allocate a the customers c to these hubs. : Number off hubs Inn this modell, there are different d patths between orrigins and destinations, d and also eacch path has diifferent reliab bility as folloows:


312


: Reliaability of path h a among cllient k and l We consideer that it is possible p to have h more thhan one hub in a path betweeen two dem mand nodes. : Set off hubs in pathh a between clients k andd l In additionn, the decisioon variables are defined as follows. 1 0 1 0 1 0

2-2. Assum mptions The propossed model inn this paper is i based on the t following aassumptions:: 1. Thhere are P hubbs to be locaated. 2. Eacch client is just allocateed to one huub (single alloocation). 3. Thhe hubs are fu ully interconnnected. 4. Thhere are diffferent paths between tw wo clients bassed on the number off hubs in the t determinedd path. The total t numberr of paths is as follows:  | N |  | N p' TNP   p  P 

| P   i !  i 1

( (1)

we would hav ve: 1, 2, 2 …, . and then, w 5. Thhe number off hubs in eacch path is leess than the tottal number of hubs. | ∈ ((2) , , | where | .

3. The Pro oposed Mod del There are many paperrs, including hub locatio onhe main shhortcoming of allocation models. Th t determ mine a speciffic these models is that they e path, and they juust number off hubs in each consider thhe cost, but as in realityy, maximizing the reliabiility of the path is as important as t minimizingg the cost off establishingg hubs and the cost of trannsportation between two clients. c Here, we have a bi--objective fuunction whiich consists off minimizingg the cost annd maximizing the reliabiliity. Min OB1 



 C y   C y   C z    C i

iN p

i

i

iN 'p

i

ij ij

i

j

Max OB 2    Rkla xkla k

l

a



yi  P



zij  1, j  N

kla

k

l

a

iN p  N 'p

zij  yi  0, i  N p  N p' , j  N

xkla k  yi  0, i  Fkla

xkla k 



(8)

ziki  0, i  Fklaa

(9)

k N  N p  N 'p

wkl xkla  capi , i  Fkla xkla k , yi , zij  {0,1}

(10) (11)

Thhe first objecctive functioon minimizess the cost of innstalling hubs in demand nodes and non-demand n noodes, the cosst of allocatinng a node too a hub, and thhe cost of flo ow between origin and destination. Thhe second one o maximizes the reliabbility of the paath, which is i selected to transport the flows. C Constraint (1)) shows the number of hubs in the m model. We haave a single allocation a in this model, i.ee., each dem mand node should be allocated a to onnly one huub. This concept c is shown by coonstraint (2).. Constraintss (3) allow a node to be alllocated to a hub only if i that hub is installed. C Constraints (4 4) guarantee that the pathh between k annd l includees hub i if that t hub is established. C Constraints (5 5) show that the path bettween k and l can exist if k and l are assigned to the t existing huubs in that path. p Since each hub haas a limited caapacity, the amount a of floow cannot be more than itss capacity. This T constrainnt is shown in (6).

4. Cucko oo Optimizzation Algoorithm Thhe model is solved by the t cuckoo optimization o allgorithm (CO OA) which iss suitable forr continuous noonlinear optiimization prooblems. COA A has some addvantages in n comparisonn to other metaheuristic m m methods such as rapidd convergennce, higher acccuracy, and ability of loocal search inn addition to gllobal search.. Applying MOCS, M we use u random w weights to coombine two objectives to a single obbjective. In this algorithhm, cuckooss with their egggs are initiaalized and loccated in diffe ferent places ass the initiaal solution. Some of the initial soolutions (egggs) are detected d as infeasible soolutions, annd thus rem moved. Theen, a new geeneration of cuckoos is produced p annd the profit vaalues and in nfeasible solutions are ddetected. At laast, the beest places for the cuuckoos are deetermined as a the opptimum soluution. The flowchart of thhis algorithm m is as in Figg. 1 [29].

4--1. Solution n representtation

w

(3)) (4)) (5))

iN p  N 'p


Thhe random key representation iss used for enncryption annd the smalleest position value v (SPV) ruule is appliied to decrrypt and caalculate the obbjective funcctions.

(6)) (7))




3133

Main Effects Plo ot for Means Data Me eans No. of cuckk os

MaxNo of Eggs

MaxIter

2.5000E+14 2.4800E+14

Mean of Means

2.4600E+14 2.4400E+14 2.4200E+14 1

2

1

No of Clusters

2 3 Mottion Coefficient

4

1

4

1

2 3 Ma axNo of cuck oos

4

2.5000E+14 2.4800E+14 2.4600E+14 2.4400E+14 2.4200E+14 1



2

3

4

1

2

3

2

3

4

Fig. 2. Result R of thee Taguchi method m

5.. Numericaal Example

Fig. 1. Flow wchart of CO OA [29] meter tuningg 4-2. Param We designn different experiments e t based on the important factors f of CO OA such as the number of cuckoos, tthe maximu um number of eggs, the t maximum number of iterations, the t number of n coefficiennt, and the t clusters, the motion o to set the t maximum nnumber of cuckoos. In order parameters, the Taguch hi method is used for the t design of experimentss. The levells of differeent T 1, and the results are a factors are shown in Table Fig. 2. shown in F Tab. 1. Levels L for diifferent facttors of COA A M Ma x No. Maax No. of Motion Max No. No. of of Cucko Cooeffici Iterati o of Cuckko Clust ent os on E Eg oss ers ggs 4 1 5 0 100 10 10 6 12 2 2 6 120 20 8 14 4 3 7 140 10 16 6 4 8 160 We have also variedd populationn size n and probabilityy . We have used n = 15, 20, 50, 1000, 150 and = 0, 0.1, 0.115, 0.2, 0.25,, 0.3, 0.35. The T simulationss show that n = 20 and = 0.25 are a suﬃcient fo for this optim mization probblem.

Suuppose that a country with w 24 citiess and all of thhem are potential locationns for hubs among a nondeemand and demand d nodees. Also, supppose that a 5--center hub location-alloocation probblem. There w would be at most m 5 hubss in each paath between tw wo clients, and a the purppose is to deetermine the loocation of hu ubs and alloccate the clieents to them (ssee Appendixx A). Then, the t path betw ween origins annd destinattions wouldd be deteermined to m maximize thee reliability and minimizze the cost. Thhe model is solved by the t cuckoo optimization o allgorithm (CO OA), and the results are as a follows: Tab. 2. Hubs H selecteed by the prooposed algorithm B locationns for hubs Best Tehraan, Mashhad,, Isfahan, Keerman, Tabrriz

T Tab. 3. Alloccation of citiies to the selected hubs Huub Tehran Mashhad Isfahan

Kerman Tabriz

Allocated City C Mazandaaran, Gilan, Ghazvin, Zanjan, Z Hamedan, Karaj Golestann, Semnan, Khorasan__N Ghom, M MarKazi, ChaharMahhalVaBakht iari, Yazd Hormozggan, SistanVaBaluchestan, Khorasan__S Urmia, Kordestan, K Ardabil

o hubs and By solving thhe model, thee locations of d cities are determined d a in Tables as thheir allocated


314


2 and 3. They show that the cost c would be ble minimized by using these hubs. The reliab d as well. For example, paths are determined consider thhat someone in Yazd wannts to travel to Urmia. Usiing this moddel leads to the following path: “Yazd- Isfaahan- Tehran n- Tabriz- Urmia” Ur with the t reliability oof 0.9234 which w is moree reliable thhan the path “Y Yazd- Isfahan n- Tabriz- Urmia” Ur with the t reliability oof 0.7302. The paths between thhe hubs are different, and since we hhave 20 citiess and five huubs, we wouuld have lots oof paths whiich are deterrmined by the t model.


b strategy a bi-objective model to find out the best t demand foor establishinng the hubs,, allocating the noodes to the hubs, h and deetermining thhe best path beetween two clients c in ordder to minim mize the cost annd maximizee the reliabiliity. The moddel is solved byy Cuckoo Opptimization Algorithm A foor a country w with 31 citiees and diffeerent reliablee paths are deetermined beetween origiin and destinnation. The sttochastic dem mand for thee customers or different loocation-allocaation probleem with reeliable path appproach can be consideered for futuure research sttudies. Furth hermore, onee can study a hub-tree neetwork insteaad of fully innterconnectedd hubs.

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Fig.. 3. Iran map p by determ mined hubs

Figg. 4. Converggence of the proposed algorith hm (

6. Conclusion Public traansportation is a veryy challenging problem inn many deeveloped annd developing countries. In I addition, hubs are criitical elemennts of telecoommunicatioon and transportation networks, bbecause they y play an im mportant role in controlling the traffic. In I this paperr, we propossed



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M. M. Nasirii, N. Shamsi Gaamchi, S. A. Torabi

Cuckoo Optimization O Algorrithm for a Reliable ……

31 17

Appendix A A- Daata Gathering

Tab.. A. 1. Cost of transshipment t from hub k to hub l City

Tehran

Mashhad Isfahan Karaj

Tabriz

Tehran

100000

883

446

51

626

939

967

151

502

3333

Mashhad

883

100000

1,252

940

1,514

1,344

1,762

953

1,378

1,2222

909

Isfahan

446

1,252 100000

462

936

480

522

316

641

6645

734

462 100000

579

944

1,004

187

524

2287

1,084

579 100000

1384

1,097

766

778

4492

1,662

1,384 100000

527

798

1,021

1,1127

595

1,561

527 100000

831

638

1,1160

1,170

1,272

443

4472

906

907

100000

5549

1,364

636

1,368

633

1,,915

100000

1,806

537

Karaj

51

940

Tabriz

626

1,514

901

Shiraz

939

1,344

570

944

Ahvaz

967

1,762

522

1,004

1,097

Shiraz

Ghom

151

953

316

187

766

798

Kermanshah

502

1,378

641

524

778

1,021

Rasht Kerman Urmia

Ahvaz

Ghom

831 100000 638

443

333

1,222

645

287

492

1,127

1,160

472

1,047

909

734

1,084

1,662

595

1,170

906

Kermanshah Rashht

549 1000000 1,364

1,3368

Kerman Urmia 1,047

768

Zaheedan Arak

Bandar B e Ghazvin Ardabil Abbas A

Zanjan

Khoram Abad Sanandaj Gorgan Sari

S Shahrekord Bushehr Bojnu urd Birjand Ilam

1,,579

288

321

626

152

592

1,530

334

629

492

414

280

538

1,068

1,657

943

1,087

1,198

917

1,042

1,482

1,634

1,222

1,505

1,369

567

730

1,333

1,079

1,,275

333

530

313

471

904

988

651

768

702

852

718

123

722

1,,631

309

343

662

106

546

1,567

287

651

514

423

319

574

152

2,,210

726

597

1,241

471

277

1,891

295

905

455

1,032

898

989

1,,102

815

1,012

439

953

1,386

580

1,133

909

1,183

1,333

1,200

1,,677

753

797

812

987

1,358

1,245

972

550

866

1,367

1,233

1,,447

135

321

484

291

731

1,389

474

570

492

544

1,,904

313

199

942

418

660

1,620

486

193

229

911

493

384

946

178

247

1,726

200

692

483

1,049

1,180

419

1,190

1,631

496

1,370

1,487

1,351

768

1,657

1,079

722

152

1,561

1,272

907

636

6633

1,579

943

1,275

1,631

2,210

1,102

1,677

1,447

1,904

1,9915

537

2,348

Arak

288

1,087

333

309

726

815

753

135

313

4493

1,049

719

1,,590 100000

Hamedan

321

1,198

530

343

597

1,012

797

321

199

3384

1,180

533

1,,722

188

Yazd

626

917

313

662

1,241

439

812

484

942

9946

419

1,380

960

Ghazvin

152

1,042

471

106

471

953

987

291

418

1178

1,190

610

Ardabil Bandar Abbas

592

1,482

904

546

277

1,386

1,358

731

660

2247

1,631

2,030

1,530

Zahedan

Hamedan Yazd

1,806 100000

Semnaan Yasuj

82 25

1,120

670

21 17

783

1,645

26 62

1,645

1,547

66 68

1,303

615

1,19 90

900

810

58 86

330

1,104

87 79

1,172

692

27 71

819

1,518

1,45 52

1,751

757

84 48

1,233

523

287

1,34 49

1,071

960

1,06 68

252

478

436

1,70 01

1,429

601

1,09 93

425

410

397

926

89 92

1,184

612

28 84

641

777

527

906

1,31 17

1,607

167

70 08

833

500

366

735

1,263

80 06

1,456

734

55 52

979

1,141

1,128

879

850

1,00 08

581

1,525

97 74

815

2,,348

719

533

1,380

610

2,030

2,119

436

769

411

1,171

1,037

1,128

1,657

1,59 96

1,890

713

98 88

1,372

100 0000

1,590

1,722

960

1,735

2,175

710

1,917

2,026

1,893

1,300

1,423

1,375

1,346

1,10 08

453

2,067

1,36 64

1,311

188

628

317

690

1,416

434

437

362

698

564

309

953

1,02 25

1,323

479

41 17

668

100000

764

242

566

1,595

305

312

175

735

601

464

1,132

1,13 36

1,431

353

52 28

847

628

764 10 00000

766

1,206

916

949

1,060

927

752

740

463

730

93 38

638

1,101

58 81

388

1,,735

317

242

766

100000

435

1,550

179

545

409

558

424

560

1,089

98 80

1,277

587

37 72

804

2,,175

690

566

1,206

435

100000

1,982

261

811

538

746

612

954

1,483

1,05 53

1,715

911

81 12

1,198

00000 1,982 10

e 1,634

1,078

1,567

1,981

670

1,245

1,389

1,620

1,7726

496

2,119

710

1,416

1,595

916

1,550

1,730

1,574

1,780

1,555

1,543

1,120

952

1,71 19

1,174

1,162

1,38 88

932

Zanjan Khoram Abad

334

1,222

608

287

296

1,091

972

474

486

2200

1,370

436

1,,917

434

305

949

179

261

1,599 100000

613

285

740

606

697

1,226

1,16 60

1,459

654

55 56

941

629

1,505

768

651

905

909

550

570

193

6692

1,487

769

2,,026

437

312

1,060

545

811

1,574

613

100000

357

905

771

354

818

1,44 44

1,297

292

83 35

660

Sanandaj

492

1,369

702

514

455

1,183

866

492

229

4483

1,351

411

1,,893

362

175

927

409

538

1,780

285

357

100000

898

764

647

1,062

1,30 07

1,593

303

69 99

1,010

Gorgan

414

567

852

423

1,032

1,333

1,367

544

911

5500

1,141

1,171

1,,300

698

735

752

558

746

1,555

740

905

898 100000

132

935

1,464

30 05

850

1,071

30 05

1,180

Sari

280

730

718

319

898

1,200

1,233

410

777

3366

1,128

1,037

1,,423

564

601

740

424

612

1,543

606

771

764

132 100000

804

1,334

43 36

968

940

19 97

1,049

Shahrekord

538

1,333

123

574

989

523

478

397

527

7735

879

1,128

1,,375

309

464

463

560

954

1,120

697

354

647

935

804

100000

554

1,27 71

1,017

697

66 63

269

Bushehr

1,068

1,645

615

1,104

1,518

287

436

926

906

1,2263

850

1,657

1,,346

953

1,132

730

1,089

1,483

952

1,226

818

1,062

1,464

1,334

554

100000

1,80 01

1,478

914

1,19 93

454

Bojnurd

825

262

1,190

879

1,452

1,349

1,701

892

1,317

8806

1,008

1,596

1,,108

1,025

1,136

938

980

1,053

1,513

1,160

1,444

1,307

305

436

1,271

1,801

10000 00

650

1,485

60 06

1,516

Internationall Journal of Industriall Engineering & Production Research, Deceember 2016, Vol. 27, N No. 4

318 Birjand Ilam

M. M. M Nasiri, N. Sham msi Gamchi & S. A. A Torabi

Cuckoo Optimization O Algorrithm for a Reliab ble …

1,120

1,645

900

1,172

1,751

1,071

1,429

1,184

1,607

1,4456

581

1,890

453

1,323

1,431

638

1,277

1,715

1,174

1,459

1,297

1,593

850

968

1,017

1,478

670

1,547

810

692

757

960

601

612

167

7734

1,525

713

2,,067

479

353

1,101

587

911

1,162

654

292

303

1,071

940

697

914

65 50 100000 1,48 85

1,781

90 05

1,146

1,781 100000

87 77

858

10000 00

908

Semnan

217

668

575

271

847

1,058

1,093

284

708

5552

974

988

1,,364

417

528

581

372

812

1,566

560

835

699

305

197

663

1,193

60 06

905

877

Yasuj

783

1,303

330

819

1,233

252

425

641

833

9979

815

1,372

1,,311

668

847

388

804

1,198

932

941

660

1,010

1,180

1,049

269

454

1,51 16

1,146

858

Tab. A. 2. Cost of transp portation betweeen origin and destination Ban Khora nda Mashh Isfaaha Kerma Kerma Ghazv Ardabi r m Sanann Gorga Semna Zahed Hame Shahre Bushe Bojnur Birjan e City Tehran ad n Urmia an in l bas Zanjan Abad daj Ilam I n Yasuj Karaj Tabriz Shirazz Ahvaz Ghom nshah Rasht n Arak dan Yaazd Abb n Sari kord hr d d 10000 Tehran 460 510 6260 939 90 9670 1510 5020 3330 10,470 7680 15,790 288 3,210 6260 1,520 5920 15,3 300 3340 6,290 4920 4,140 2800 5,380 10,680 8250 11,200 6,700 2170 7,830 00 8830 44 10000 Mashhaad 8830 00 12,5 520 9400 15,140 13,44 40 17,620 9,530 13,780 12,220 9,090 16,570 9,430 1,087 11,980 9 9,170 10,420 14,820 16,3 340 12,220 15,050 13,690 5,670 7,300 13,330 16,450 2,620 16,450 15,470 6,680 13,030 100 000 6,450 7,340 10,790 12,750 8,520 7,180 1,230 6,150 11,900 9,000 8,100 5,860 3,300 Isfahan 4460 12,520 00 5,220 3,160 6410 333 5,300 3 3,130 4,710 9,040 9,8 880 6,510 7,680 7,020 00 4620 9,360 4,80 10000 2870 10,840 7220 16,310 4,230 3190 5,740 11,040 8790 11,720 6,920 2710 8,190 Karaj 510 9400 46 620 00 5790 944 40 10,040 1870 5240 309 3,430 6620 1,060 5460 15,6 670 2870 6,510 5140 10000 6260 15,140 90 010 5790 00 1384 40 10,970 7660 7,780 2,410 4,710 2,770 18,9 910 2,950 9,050 4,550 10,320 4,920 16,620 1,520 22,100 8,980 9,890 15,180 14,520 17,510 7,570 8,480 12,330 Tabriz 726 5,970 12 1000 00 5950 15,610 11,020 5,230 2,870 13,490 10,710 9,600 10,680 2,520 9390 13,440 57 700 9440 13,840 00 0 5270 7980 10,210 11,270 815 10,120 4 4,390 9,530 13,860 5,8 800 11,330 9,090 11,830 13,330 12,000 Shiraz 10000 4,780 4,360 17,010 14,290 6,010 10,930 4,250 Ahvaz 9670 17,620 5,2 220 10,040 10,970 527 70 00 8,310 6,380 11,600 11,700 12,720 16,770 753 7,970 8 8,120 9,870 13,580 12,4 450 9,720 5,500 8,660 13,670 12,330 10000 4,720 9,060 9,070 14,470 5,440 4,100 3,970 9,260 8,920 11,840 6,120 2,840 6,410 Ghom 1510 9,530 3,1 160 1870 7660 798 80 8,310 00 4,430 135 3,210 4 4,840 2,910 7,310 13,8 890 4,740 5,700 4,920 10000 5,490 13,640 6,360 19,040 9,110 7,770 5,270 9,060 13,170 16,070 1,670 7,080 8,330 Kerman 6,380 4,430 00 nshah 5020 13,780 64 410 5240 7,780 10,210 313 1,990 9 9,420 4,180 6,600 16,2 200 4,860 1,930 2,290 10000 00 13,680 6,330 19,150 5,000 3,660 7,350 12,630 8,060 14,560 7,340 5,520 9,790 Rasht 3330 12,220 6,4 450 2870 4,920 11,27 70 11,600 4,720 5,490 493 3,840 9 9,460 1,780 2,470 17,2 260 2,000 6,920 4,830 10000 00 18,060 8,790 8,500 10,080 5,810 15,250 9,740 8,150 Kerman n 10,470 9,090 7,3 340 10,840 16,620 595 50 11,700 9,060 13,640 13,680 5,370 1,049 11,800 4 4,190 11,900 16,310 4,9 960 13,700 14,870 13,510 11,410 11,280 10000 6,330 18,060 00 23,480 7,130 9,880 13,720 9,070 6,360 Urmia 7680 16,570 10,7 790 7220 1,520 15,610 12,720 719 5,330 13 3,800 6,100 20,300 21,1 190 4,360 7,690 4,110 11,710 10,370 11,280 16,570 15,960 18,900 10000 5,370 23,480 4,530 20,670 13,640 13,110 Zahedan n 15,790 9,430 12,7 750 16,310 22,100 11,02 20 16,770 14,470 19,040 19,150 9 9,600 17,350 21,750 7,1 100 19,170 20,260 18,930 13,000 14,230 13,750 13,460 11,080 00 1,590 17,220 10000 4,930 10,490 7,190 15,900 6,980 5,640 3,090 9,530 10,250 13,230 4,790 4,170 6,680 Arak 2880 10,870 3,3 330 3090 7,260 8,15 50 7,530 1,350 3,130 0 1,880 6 6,280 3,170 6,900 14,1 160 4,340 4,370 3,620 10000 3,840 11,800 5,330 17,220 7,350 6,010 4,640 11,320 11,360 14,310 3,530 5,280 8,470 3,210 11,980 5,3 300 3,430 5,970 10,12 20 7,970 3,210 1,990 188 00 7 7,640 2,420 5,660 15,9 950 3,050 3,120 1,750 Hamedaan 10000 9,460 4,190 13,800 7,520 7,400 4,630 7,300 9,380 6,380 11,010 5,810 3,880 Yazd 6260 9,170 3,1 130 6620 12,410 4,39 90 8,120 4,840 9,420 9,600 628 7,640 160 9,490 10,600 9,270 00 7,660 12,060 9,1 10000 1,780 11,900 6,100 17,350 5,580 4,240 5,600 10,890 9,800 12,770 5,870 3,720 8,040 Ghazvin 317 2,420 n 1,520 10,420 4,7 710 1,060 4,710 9,53 30 9,870 2,910 4,180 7 7,660 00 4,350 15,5 500 1,790 5,450 4,090 10000 2,470 16,310 20,300 21,750 7,460 6,120 9,540 14,830 10,530 17,150 9,110 8,120 11,980 Ardabil 5920 14,820 9,0 040 5460 2,770 13,86 60 13,580 7,310 6,600 690 5,660 12 2,060 4,350 00 19,8 820 2,610 8,110 5,380 Bandar 100 e 000 4,960 21,190 9,520 17,190 11,740 11,620 13,880 9,320 Abbas 780 15,670 19,810 6,70 00 12,450 13,890 16,200 17,260 7,100 1,416 15,950 9 9,160 15,500 19,820 15,300 16,340 10,7 00 17,300 15,740 17,800 15,550 15,430 11,200 10000 2,000 13,700 4,360 19,170 7,400 6,060 6,970 12,260 11,600 14,590 6,540 5,560 9,410 3340 12,220 60 080 2870 2,960 10,910 434 3,050 9 9,490 1,790 2,610 15,9 990 00 6,130 2,850 Zanjan 9,720 4,740 4,860 10000 Khoram m 6,920 14,870 7,690 20,260 9,050 7,710 3,540 8,180 14,440 12,970 2,920 8,350 6,600 Abad 680 6,510 9,050 9,09 90 5,500 5,700 1,930 437 3,120 10 0,600 5,450 8,110 15,7 740 6,130 00 3,570 6,290 15,050 7,6 10000 4,830 13,510 4,110 18,930 8,980 7,640 6,470 10,620 13,070 15,930 3,030 6,990 10,100 Sanandaaj 4920 13,690 7,0 020 5140 4,550 11,83 30 8,660 4,920 2,290 362 1,750 9 9,270 4,090 5,380 17,8 800 2,850 3,570 00 10000 5,000 11,410 11,710 13,000 00 1,320 9,350 14,640 3,050 8,500 10,710 3,050 11,800 Gorgan 4,140 5,670 8,5 520 4,230 10,320 13,33 30 13,670 5,440 9,110 698 7,350 7 7,520 5,580 7,460 15,5 550 7,400 9,050 8,980 10000 3,660 11,280 10,370 14,230 1,320 00 8,040 13,340 4,360 9,680 9,400 1,970 10,490 Sari 2800 7,300 7,1 180 3190 8,980 12,00 00 12,330 4,100 7,770 564 6,010 7 7,400 4,240 6,120 15,4 430 6,060 7,710 7,640


90 08 100000

M. M. Nasirii, N. Shamsi Gaamchi, S. A. Torabi

Cuckoo Optimization O Algorrithm for a Reliable …… Shahrek kord

31 19

5,380

13,330

1,2 230

5,740

9,890

5,23 30

4,780

3,970

5,270

7,350

8,790

11,280

13,750

309

4,640

4 4,630

5,600

9,540

11,2 200

6,970

3,540

6,470

9,350

8,040

10000 00

10,680

16,450

6,1 150

11,040

15,180

2,87 70

4,360

9,260

9,060

12,630

8,500

16,570

13,460

953

11,320

7 7,300

10,890

14,830

9,5 520

12,260

8,180

10,620

14,640

13,340

5,540

5,540 10000 00

12,710

10,170

6,970

6,630

2,690

14,780

9,140

11,930

4,540

14,850

6,060

15,160

9,050

11,460 8,580

Bojnurd d

8250

2,620

11,9 900

8790

14,520

13,49 90

17,010

8,920

13,170

8,060

10,080

15,960

11,080

1,025

11,360

9 9,380

9,800

10,530

15,1 130

11,600

14,440

13,070

3,050

4,360

12,710

18,010

18,010 10000 00

Birjand

11,200

16,450

9,0 000

11,720

17,510

10,710

14,290

11,840

16,070

14,560

5,810

18,900

4,530

1,323

14,310

6 6,380

12,770

17,150

11,7 740

14,590

12,970

15,930

8,500

9,680

10,170

14,780

6,500

6,500 10000 00

Ilam

6,700

15,470

8,1 100

6,920

7,570

9,60 00

6,010

6,120

1,670

7,340

15,250

7,130

20,670

479

3,530

11 1,010

5,870

9,110

11,6 620

6,540

2,920

3,030

10,710

9,400

6,970

9,140

14,850

17,810

17,810 10000 00

Semnan n

2170

6,680

57 750

2710

8,470

10,58 80

10,930

2,840

7,080

5,520

9,740

9,880

13,640

417

5,280

5 5,810

3,720

8,120

15,6 660

5,600

8,350

6,990

3,050

1,970

6,630

11,930

6,060

9,050

8,770

8,770 10000 00

Yasuj

7,830

13,030

3,3 300

8,190

12,330

2,52 20

4,250

6,410

8,330

9,790

8,150

13,720

13,110

668

8,470

3 3,880

8,040

11,980

9,3 320

9,410

6,600

10,100

11,800

10,490

2,690

4,540

15,160

11,460

8,580

9,080

Bushehrr

Tab. A.3. Reliability and cosst of some path hs Path

a

Cosst

Reliability

M-Te-I

1

1329 9

0.805

M-Sh-I

2

1914 4

0.812

M-Te-Sh-II

3

2392 2

0.733

M-Sh-Te-II

4

2729 9

0.698

M-Te-k

1

934 4

0.777

M-Sh-k

2

2288

0.856

M-Te-Sh-k k

3

2766 6

0.818

M-Sh-Te-k k

4

2334 4

0.674

M-Te-Ta

1

1509 9

0.932

M-Sh-Ta

2

2728

0.733

M-Te-Sh-Taa

3

3206 6

0.701

M-Sh-Te-Taa

4

2909 9

0.808

I-Te-M

1

1329 9

0.805

I-Sh-M

2

1914 4

0.812

I-Te-Sh-M M

3

2729 9

0.698

I-Sh-Te-M M

4

2392 2

0.734

I-Te-k

1

497 7

0.717

I-Sh-k

2

1424 4

0.876

I-Te-Sh-k

3

2329 9

0.754

I-Sh-Te-k

4

1560 0

0.690

I-Te-Ta

1

1072 2

0.859

I-Sh-Ta

2

1954 4

0.751


9,080 10000 00

320

M. M. M Nasiri, N. Sham msi Gamchi & S. A. A Torabi

Cuckoo Optimization O Algorrithm for a Reliab ble …

I-Te-Sh-Taa

3

2769 9

0.646

I-Sh-Te-Taa

4

2135

0.827

K-Te-M

1

934 4

0.777

K-Sh-M

2

2288

0.856

K-Te-Sh-M M

3

2334 4

0.674

K-Sh-Te-M M

4

2766 6

0.818

K-Te-I

1

497 7

0.717

K-Sh-I

2

1424 4

0.876

K-Te-Sh-I

3

1560 0

0.690

K-Sh-Te-I

4

2329 9

0.754

K-Te-Ta

1

677 7

0.829

K-Sh-Ta

2

2328

0.791

K-Te-Sh-Taa

3

2374 4

0.623

K-Sh-Te-Taa

4

2509 9

0.872

Ta-Te-M

1

1509 9

0.932

Ta-Sh-M

2

2728

0.733

Ta-Te-Sh-M M

3

2909 9

0.808

Ta-Sh-Te-M M

4

3206 6

0.701

Ta-Te-I

1

1072 2

0.859

Ta-Sh-I

2

1954 4

0.751

Ta-Te-Sh-II

3

2135

0.827

Ta-Sh-Te-II

4

2769 9

0.646

Ta-Te-k

1

677 7

0.829

Ta-Sh-k

2

2328

0.791

Ta-Te-Sh-kk

3

2509 9

0.872

Ta-Sh-Te-kk

4

2374 4

0.623

Follow w This Article at The T Following Site G N, Torab bi S A. Cuckoo Optimization O Alg gorithm for a Nasiri M M, Shamsi Gamchi a the Clientts. IJIEPR. 2016;; 27 (4) :309Reliable Location-Alloocation of Hubs among RL: http://ijiepr.iiust.ac.ir/article-1 1-644-en.html 320 UR Internationall Journal of Industriall Engineering & Production Research, Deceember 2016, Vol. 27, N No. 4