Using Simulated Annealing For Layout Planning of Construction Sites

Transcription

1 Usig Simulated Aealig For Layout Plaig of Costructio Sites Mohamed El-Gafy, PhD, PE ad Tariq Abdelhamid, PhD Michiga State Uiversity East Lasig, MI Amie Ghaem PhD Califoria State Northridge Northridge, Ca Costructio site layout is a importat activity that deals with the positioig of temporary facilities that are utilized durig the executio phase of a costructio proect This paper presets a formulatio for the costructio site layout problem i terms of a combiatorial problem that is suitable for solutio usig simulated aealig algorithms (SA) SA is a evolutioary method motivated by a aalogy to aealig i solids to avoid the solutio from gettig trapped i a local miimum A case study is preseted to demostrate the efficiecy of the Simulated Aealig heuristic algorithm i solvig the costructio site layout problem ad illustrates its essetial features Key Words: Costructio Maagemet, Costructio Sites, Layout plaig, Simulated Aealig Itroductio Plaig for costructio site layout depeds o a umber of factors such as the adacecy of permaet facilities, distace betwee facilities, facility resources ad the locatio of the facilities (Has 1984) Over the past 20 years, researchers have developed may costructive heuristics for the costructio site layout problem Recetly, evolutioary optimizatio techiques such as geetic algorithms have bee used extesively (Tog ad Tam, 2003; Osma et al, 2003; Cheug et al, 2002) The commo approach shared by all evolutioary techiques is the avoidace of gradiet-based search, thus reducig the possibility of gettig stuck i local optima Li et al (1998) used a improved crossover ad mutatio to miimize the total travelig distace of site persoel Cheug et al (2002) used the swap method for crossover ad mutatio i their geetic algorithm model to search for the least cost durig pre-cast cocrete layout plaig Layout plaig idicates the locatio ad umbers of temporary ad permaet facilities, travel distaces, facility resources, material ad persoel site access, ad pathways for material delivery, ad safe egress from the costructio site This problem ca be represeted mathematically as facilities located at locatios These facilities will be located based upo a obective fuctio May forms of obective fuctio(s) have bee developed for the costructio site layout plaig problem The pseudo models of these obective fuctio(s) are give i Table (1) Each placemet of a facility compared to aother will icrease or decrease the obective fuctio value The total cost ca be defied as follows: Total Cost= miimize Subect to TCL L QKi, LQi, C k 1 i 1 1 QK M TCL QKi, QKi, QKi, D i (1) QKi, QK1,1 QK2,1 QKq,1 QK1, 2 QK2, 2 QKq, 2 QK1, q QK2, q QKq, q

2 Where the umber of facilities; C the cost per uit distace betwee facilities i ad QK D, the distace betwee the facilities i ad i TCL QK i, Q LQK i, QK i, the total cost of resource flow betwee facilities i ad the traveled distace per uit time betwee facilities i ad the frequecy of resource flow betwee facilities i ad Table1: Obective Fuctios used i the literature No Pseudo model of the obective fuctio 1 To miimize the cost of facility costructio ad the iteractive cost betwee facilities 2 To miimize the frequecy of trips made by costructio persoel 3 To miimize the total trasportatio costs of resources betwee facilities 4 To miimize the total trasportatio costs of resources betwee facilities ad the total relocatio costs 5 To miimize the total trasportatio costs of resources betwee facilities Referece Yeh, 1995 Li ad Love, 1998 Hegazy ad Elbeltagi, 1999 Zouei ad Tommelie, 1999 Tam et al, 2001& Cheug et al, 2002 It is assumed that the umber of predetermied places should be equal to or greater tha the umber of predetermied facilities If the umber of predetermied places is greater tha the umber of predetermied facilities, the a umber of dummy facilities will be added to make both umbers equal I this paper, simulated aealig (SA), which is a optimizatio techique based o the aealig process of physical systems i thermodyamic, is proposed to better address the costructio site layout problem SA has the advatages of simple structure, efficiet operatio ad less sesitivity to iitial coditio (Liag ad Xu 2009) The paper refers to the issues related to the developmet ad adaptatio of a SA algorithm for solvig the costructio site layout problem The success of the proposed solutio algorithm i solvig the costructio site layout problem is demostrated usig a case study Simulated Aealig Techique Simulated Aealig (SA), also kow as Mote Carlo Aealig, borrows from the gradual coolig process of metal aealig after havig bee heated to the meltig poit At high temperature, the atoms are embodied with great amouts of eergy, ad move arbitrarily i ay state space As the temperature drops, the eergy of the atoms decreases ad gets close to the miimum poit of the eergy i the whole state space Whe the coolig process is completed, the whole state space eergy is at its lowest poit The simulated aealig acts like a radom search at the begiig ad gradually turs ito a more traditioal local search algorithm at the ed, which will ot accept a worse solutio tha the curret oe The basic algorithm of simulated aealig was described by Russell (1995) as show i Figure 1

3 Curret = MAKE-NODE (INITIAL-STATE [Problem]) For t=1 to do T= Schedule [t] If T=0 the retur Curret Next = radomly selected successor of Curret ΛE = VALUE [Next] Value [Curret] If ΛE > 0 the Curret = Next Else Figure Curret 1: = Simulated Next oly aealig with probability algorithm exp (Russell, (- 1995) The algorithm customarily starts with the radom creatio of iitial costructio layouts to be used as the startig poit ad curret solutio for the optimizatio process The, the choice of a appropriate coolig schedule is selected; Coolig schedule formulatios used i this study were origially set forth by Ballig (1991) ad are give i the followig equatios These equatios formulate the coolig schedule parameters based o assumed acceptace probabilities ad thus allow them to be chose automatically irrespective of problem type Otherwise, a arbitrary choice of these parameters exhibits problem depedecy ad etails a extesive umerical experimetatio s 1000 Startig Temperature, t (2) s l( P ) s P is the startig acceptace probability Where, f 1 Fial Temperature, t (3) f l( P ) Where, Coolig Factor, Where, Fuctio SIMULATED-ANNEALING (problem, Schedule) returs a solutio state Iputs : problem, a problem schedule, a mappig from time to temperature Local variables: Curret, a ode Next, a ode T, a temperature cotrollig the probability of dowward steps f P is the assumed fial acceptace probability l( P l( P s f ) ) 1 ( N c is the umber of coolig cycles? N c 1) I the followig step, a ier loop is performed, where each time the curret layout is give a small perturbatio to create a cadidate layout as a alterative solutio to the problem cosidered The uderlyig priciple related to the ier loop is associated with a thermodyamics cocept, which states that a physical system attais its lowest eergy provided that it acquires the least possible eergy required at each temperature durig the successive coolig process I the fial step, the temperature is reduced to a slightly lower value ad the ier loop is activated agai with the ew temperature The process is repeated util the whole coolig cycle is iterated Fially, the algorithm is termiated if: a) the coolig temperature is less tha the fial temperature; b) the umber of the quechig times reaches the preset umber; or c) the target fuctio is ot chaged after cotiuous ad repetitive executios for a preset umber of coolig times (Wog ad Fug, 1993) The Hypothetical Site Case Study A hypothetical costructio site was created for the applicatio of Simulated Aealig i order to fid the optimal site layout, uder a set of give coditios Agai, the itet is to create a plaig (4)

4 coversatio amogst the proect team that is iformed by a systematic process i lieu of ad-hoc ad iformal methods A mid-size Uiversity Buildig was assumed The hypothetical proect is a traditioal 4-story reiforced cocrete school block; costructio work icludes site work ad utilities, substructure, superstructure, eclosures, ad iterior fiishes The cotract period is 14 moths To facilitate the example, the site was simplified as show i a Figure 2 Figure 2: Layout of the Hypothetical site Site Facilities ad site represetatio The umber ad the type of facilities deped o the size ad the ature of the costructio proect Some site facilities are essetial, such as trailer city, portable toilets (eg, Porta-Johs ), a laydow ad storage area for materials, a refuse storage area, etc I order to simplify the complexity of the costructio site, some facilities have bee eglected ad the umber of facilities is assumed as i Table 2 Withi the site boudary, the area for locatig site facilities is limited by may costraits, such as maitaiig access Apart from that, 10 available locatios were predetermied i the costructio site for allocatig the remaiig six facilities as listed above Four dummy facilities were added It was assumed that each facility could be placed ito ay locatio ad that the area of the locatio was large eough for each facility Table 2: Assumed Facilities o the case study costructio site Site Facilities 1 Site Office 4 Carpetry shop 2 Debris Storage Area 5 Portable Johs 3 Bedig/ Storage Yard 6 Storage Area As preseted before, the optimizatio obective is preseted as MiZ i, 1 f * d i Where f was assumed to be the frequecies of trips (i 1 day) made betwee facilities (see Table 3), ad Di is the travel distace betwee facility i ad facility (see Table 4) However, the travel distace betwee locatios was measured usig rectagular distaces that represet actual operatios ad resource movemets o the site i order to simplify the sceario Table 3: Travel Frequecies betwee Facilities Facility D 1 D 2 D 3 D

5 D D D D Table 4: Travel Distace betwee Locatios Distace to A package was writte specifically to solve the problem uder cosideratio usig SA algorithm It was writte i Matlab; a commercially available developer of techical computig software I this experimet, differet heuristic parameters were ivestigated Table 5 presets a partial optimum layout represetatio (solutio) sorted by the obective fuctio Table 5: Optimum layout represetatio Facility Obective Fuctio Ru #11 Locatio Ru #5 Locatio Ru #13 Locatio Ru #9 Locatio Ru #16 Locatio Discussio I 20 trials, the optimal solutios were the layouts 5, ad 11 respectively The fial optimal layouts for the hypothetical site are show i Figures 3a ad 4b These two optimal results were the preseted to three costructio magers (with a miimum 15 years of experiece) for validatio a) Ru # 5 b) Ru # 11 Figure 3: optimum layout represetatio

6 For both layouts, it was suggested that the site office be relocated ear the mai gate For ru #5, the distace betwee debris storage area- ad Steel Bedig ad storage area was close eough to block the access to the Steel Bedig ad storage area Ru #11 was more acceptable to the costructio maagers, except for the locatio of the site office The costructio maagers appreciated havig this site layout plaig tool but suggested icludig the fixed utilities such as the gate locatio, the material hoist ad crae ito cosideratio for future work Algorithm Verificatio To cofirm the proposed algorithm performace, Literature data for two case studies (Cheug et al 2002; Li ad Love 1998), similar to the illustrated case study, were used to bechmark the algorithm results with the results provided Cheug et al (2002) developed a Geetic Algorithm (GA) model for site precast yard layout arragemet; i particular arragig the pre-cast facilities withi the compoud The obective fuctio is to miimize the total cost per day for trasportig all resources ecessary to achieve the aticipated productio output for the pre-cast yard The GA model yielded a ear-optimum layout as preseted i Table 6 while the proposed model proposed a improved layout The Modified Obective Fuctio for the GA model was $ 147,906 The obective fuctio of the proposed model was $105, 362 which represets 2876% improvemet i the daily cost Table 6: The optimal layout solutio Facility Cheug et al (2002) Locatio Proposed Model Locatio Li ad Love (1998) preseted the costructio site-level facility layout problem as allocatig a set of predetermied facilities ito a set of predetermied places, while satisfyig layout costraits ad requiremets Geetic Algorithm (GA) was employed to solve this problem by miimizig the total travelig distace of site persoel betwee facilities The GA model yielded a ear-optimum layout as preseted i Table 7 while the proposed model proposed a slightly improved layout The Modified Obective Fuctio was $ 12,819 The obective fuctio of the proposed model was $12,427 which represets 353% improvemet i the daily cost Table 7: The optimal layout solutio Facility Li ad Love (1998) Locatio Proposed Model Locatio The compariso to the models i Li ad Love (1998) ad Cheug et al (2002) uderscore the advatages of usig simulated aealig models to site layout plaig, especially from a computatioal efficiecy stadpoit The preseted algorithm ca be adapted to solve various practical problems ivolvig spatiotemporal plaig issues Coclusios This research ivestigated a scheme for represetig the costructio site layout plaig problem to suit the simulated aealig operatios The problem formulatio provided i this paper ca be exteded to iclude may other costs ad factors without sigificat icrease i computatio requiremets The stregth of the SA system lies i the ability to accept uphill moves with a limited probability ad the o-depedece of the fial solutio o the iitial solutio Therefore, the SA system is less likely to restrict the search to a local optimum The paper demostrated the robustess of the SA approach i solvig layout problems as combiatorial optimizatio problems

7 Plaig for proper arragemet of a costructio site layout is of paramout importace eve though the fial realized arragemet o site may differ As presidet Eisehower is kow to have said Plaig is everythig, the pla is othig The plaig process may ucover costraits which were ukow to the team, as well as be i a better positio to hadle those that they are aware of The proect will have a better chace of beig executed effectively ad efficietly The SA algorithm preseted will aid i the plaig process, but as aother plaig tool should be cosidered as ecessary but ot sufficiet Refereces Back T (1996) Evolutioary Algorithms i Theory ad Practice New York, Oxford Uiversity Press Ballig, R (1991) Optimal Steel Frame Desig by Simulated Aealig, Joural of Structural Egieerig, 117 (6), pp Beage W, Dhigra A (1995) Sigle ad Multi-obective Structural Optimizatio i Discrete- Cotiuous Variables Usig Simulated Aealig Iteratioal Joural of Numer Meth Egieerig; (38), pp Cheug S, Tog T, ad Tam C (2002) Site Pre-cast Yard Layout Arragemet through Geetic Algorithms ; Automatio i Costructio, 11 (1), pp Has, P (1984) Costructio Maagemet ad PWD Accouts, 6th Ed, Has Publicatios, Ludhiaa, Idia Hegazy T, ad Elbeltagi E(1999) EvoSite: Evolutio-based Model for Site Layout Plaig, Joural of Computig i Civil Egieerig, 13(3), pp Li, H & Love, P (1998) Site-level Facilities Layout Usig Geetic Algorithms, Joural of Computig i Civil Egieerig, ASCE, 12 (4) pp Liag Y ad Xu L (2009) Global path plaig for mobile robot based geetic algorithm ad modified simulated aealig algorithm GEC '09: Proceedigs of the first ACM/SIGEVO Summit o Geetic ad Evolutioary Computatio Metropolis N, Rosebulth A, Rosebulth A, Teller A, Teller, H (1953) Equatio of State Calculatios by Fast Computig Machies, J of Chem Phys, 21 (6), pp Michalewicz Z (1996) Geetic Algorithm Data Sources= Evolutio Programs, New York, Spriger Osma H, Georgy M, ad Ibrahim M (2003) A Hybrid CAD-based Costructio Site Layout Plaig System Usig Geetic Algorithms, Automatio i Costructio, 12 (6), pp Schwefel H (1995) Evolutio ad Optimum Seekig, New York: Wiley Tam C, Tog T, ad Cha W (2001) Geetic Algorithm for Optimizig Supply Locatios Aroud Tower Crae, Joural of Costructio Egieerig ad Maagemet, 127 (4), pp Tog T; Tam C, (2003) GA-ANN Model for Optimizig the Locatios of Tower Crae ad Supply Poits for High-rise Public Housig Costructio Joural of Costructio Maagemet ad Ecoomics, 21(3), pp Yeh, I (1995) Costructio Site Layout Usig Aealed Neutral Network, Joural of Computig i Civil egieerig, (ASCE), 9 (3), pp Zouei P, ad Tommelei I (1999) Dyamic layout plaig usig a hybrid icremetal solutio method, Joural of Costructio Egieerig ad Maagemet, 125(6), pp