SCHEDULING OPTIMIZATION IN CONSTRUCTION PROJECT BASED ON ANT COLONY GENETIC ALGORITHM

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1 Joural of Theoretical ad Applied Iformatio Techology 8 th February 013. Vol. 48 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: SCHEDULING OPTIMIZATION IN CONSTRUCTION PROJECT BASED ON ANT COLONY GENETIC ALGORITHM 1 JINGXIAO ZHANG, 1 HUI LI, LIEYAN REN, 3 ZHEN SHI 1 School of Civil Egieerig, Chag a Uiversity, Xi a Shaaxi, , Chia School of Iformatio ad Cotrol Egieerig, Xi a Uiversity of architecture & techology, Xi a Shaaxi, , Chia 3 School of Geology Egieerig ad Geomatics, Chag a Uiversity, Xi a, Shaaxi,710054, Chia ABSTRACT This paper itroduces the basic theory ad procedure for worig out solutios of at coloy geetic algorithm, describes optimizatio, costraits ad objectives of costructio project schedulig, the establishes basic model for schedulig optimizatio of costructio project, ad put forward improved at coloy geetic algorithm for solvig the basic model. Performace of at coloy geetic algorithm is aalyzed ad evaluated from aspect of schedule - cost equilibrium i practical egieerig optimizatio. Fially, case studies are doe. Keywords: At Coloy Geetic Algorithm, Costructio Project, Time-Cost Optimizatio, Optimizatio Model; Case Aalysis 1. INTRODUCTION ACA is featured i high-efficiet exact solutio, positive feedbac ad parallelism, but relatively poor global search ability; it is easy to fall ito local optimum. While GA has the advatages of rapidity, radomess ad global covergece, but it is sesitive to parameters, so its rate of covergece is ustable or eve stagated sometimes. The overall situatio of ACA ad GA ca be expressed as the velocity - time curve show i Figure 1 which idicates that i the iitial search stage ( t ~ 0 t a ),the covergece speed to optimal solutio of GA is higher, but after t a, its efficiecy to see optimal solutio decreases sigificatly. Sice ACA has o pheromoe, at the begiig of the search ( t 0 ~ t a ), the speed to search for the optimal solutio is very slow, but whe the pheromoe is accumulated to a certai itesity (after t a ), the speed of covergece to the optimal solutio rapidly icreases. I order to get rid of disadvatages of ACA ad GA, the two ca be orgaically combied, to give full play to their respective advatages. The basic priciple of ACA ad GA fusio is that before reachig the best poit (a), GA helps to geerate the iitial pheromoe distributio, ad after that, ACA is used to obtai the optimal solutio[1]. Figure 1: Velocity - Time Curve Of At Coloy Algorithm Ad Geetic Algorithm [] Geetic ad At Coloy the Algorithm (GAAA) is the result of fused GA ad ACA, aimig at givig full play to their advatages ad abadoig their shortcomigs, to itegrate their merits as far as possible []. Fusio algorithm is a ew heuristic method i time efficiecy ad solvig efficiecy. Accuracy of exact solutios of fusio algorithm is better tha that of GA, ad its time efficiecy is higher tha that of ACA. The overall framewor of fusio algorithm is as show i Figure. Accordig to the basic desig, the high speed, radomess ad global covergece of GA are made full use of, so as to achieve iitial iformatio distributio of related issues. I the latter stage, ACA algorithm is adopted, with certai iitial pheromoe, so as to tae advatage of high 1540

2 Joural of Theoretical ad Applied Iformatio Techology 8 th February 013. Vol. 48 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: efficiecy, positive feedbac ad parallelism of ACA to obtai exact solutios[3].. THE OVERALL FRAMEWORK OF ANT COLONY FUSION GENETIC ALGORITHM The overall framewor of at coloy fusio geetic algorithm is as show i Figure Questios To idetify the objective fuctio ad fitess f ctio To iitialize parameters ad achieve pheromoe iitial distributio accordig to the optimized solutio ad put m ats i the odes To radomly geerate a set of real umber codig X,Y To idetify X ad Y accordig to the fitess fuctio Cross calculatio of X ad Y Recursive iterative Calculatio of the probability p of each at s movig to ext ode, movig each at to ext ode accordig to the probability. After M ats traversig the N odes, pheromoe of the best at circle will icrease τ = Q/ Z. Recursive iterative Reverse mutatio accordig to the fitess fuctio The pheromoe of all the paths is updated. τ( t+ 1) = ρτ ()+ t τ () t Geeratio of several groups of optimal solutio The output of the optimal solutio Figure : a. Radomly select a matig area from the paret strig, such as the two paret strigs ca be idetified as fuch1 ad fuch whose specific defiitios are as follows: fuch1= fuch= b. If the matig area of fuch1 is placed before fuch whose matig area is the added before fuch1, the: fuch1= fuch= c. Accordig to the order, the value of differet matig areas are deleted i tur, the fial two strigs are as follows: zich1= zich= Framewor Of At Coloy Fusio Geetic Algorithm DESCRIPTION OF OPTIMIZATION OF THE PROJECT SCHEDULE Optimizatio of the project schedule maily refers to optimizatio of time ad cost i the implemetatio stage of project costructio[4], icludig that of time ad schedule cost ad the mai ivolved costrait coditios to be satisfied cotais: a. The time period from ode i to j must be betwee the shortest time ad ormal time; b. Whe the time of critical procedure is shorteed, critical path shall ot be chaged; c. The direct cost of each procedure should be cotrolled betwee that required for ormal time duratio ad that for the shortest time duratio, ad the direct cost after the chage ad the time duratio of correspodig procedure should meet a two-order relatioship; d. The direct cost rate of each procedure = (direct costs for the shortest time duratio - that for

3 Joural of Theoretical ad Applied Iformatio Techology 8 th February 013. Vol. 48 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: ormal time duratio)/ (ormal time duratio - the shortest time duratio)[5]. 4. OPTIMIZATION MODEL OF CONSTRUCTION PROJECT SCHEDULE Accordig to the above descriptio about costructio project, the followig mathematical model of schedule-time optimizatio ca be established [6]: Defiitios of variables: 1 i - jis the ey wor x = (1) 0 i - jis ot the ey wor 0 1 C < C y = () 0 0 C C Mathematical model: D D ( ) i j i j i j = 1 = = 1 = = 1 = 1 MiC = C + C C + t C C y (3) MiFT = t x (4) s.t 0 t (5) t t t (6) N L L t t t D l C C C D C αt β N L N L C C t t L N N L N L C t C t t t l C 0 C C = L N t t = (7) (8) = + (9) α = [ ] / [( ) ( ) ] (10) β = [ ( ) ( )]/[( ) ( )] (11) (1) Note: (1) ad () are defiitios of variable; (3) is the objective fuctio to allow the miimum total project cost; (4) is the objective fuctio to allow the shortest project time duratio; (5) ad (6) are costraits for time duratio of each procedure; (7) is the costraits for shorteed time duratio of each ey procedure; (8), (9), (10) ad (11) are costraits for direct cost of procedure i j ; (1) is costrait for formula of idirect cost rate[7] D D 0 MiC = C + C C + t ( C C ) is the objective fuctio to allow the miimum total project cost; 1 C D is the total direct costs of costructio project, 1 D C C is the total idirect cost of costructio project, 1 0 t ( C C ) is the sum of compressed direct ad idirect costs of the costructio project. MiFT 1 = t x is the target fuctio to allow the shortest time duratio of costructio project; 1 tx is total time limit for critical path. 5. SOLVING STEPS OF OPTIMIZATION ALGORITHM FOR CONSTRUCTION PROJECT SCHEDULE Solutio to at coloy fusio geetic algorithm ad its correspodig schedule-time cotais the followig steps: (1) Iitialize α, β, m, ρ ad other parameters, ad divide the solutio space ito several sub space accordig to the dimesio for optimizatio (such as the shortest time duratio ad the lowest cost) ad costraits for time duratio of each procedure ad costraits for direct cost of each procedure. Calculate the total cost of the project; () Put m ats o the iitial poit which is the applied ito the curret solutio set tabu (s) ; (3) Trasfer each at (=1,, 3, m) to the ext ode j accordig to the state trasitio probability formula ad apply ode j ito tabu (s) ; (4) Calculate the time duratio Tm of the mth at, update the route of the logest time duratio; (5) Update pheromoe of each procedure (i, j), accordig to the formula (1); (6) Calculate τ ( t+ ) = ρτ t+ τ of each procedure (i, j), apply t t+, NC c+1 o each edge, set τ 0; (7) Chec whether the costraits are satisfied, if they are satisfied, idetify FT total time duratio of critical path, otherwise, tur to step (); (8) Update the amout of iformatio i the subspace, the paret will be got by iformatio, objective fuctio ad other comprehesive factors; 154

4 Joural of Theoretical ad Applied Iformatio Techology 8 th February 013. Vol. 48 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: (9) Select some excellet decisios from decisio set ad add them to paret, after crossover ad mutatio, elimiate ifeasible decisios; (10) Have recursive hierarchy for optimal ad updated decisio; (11) Chec whether the costraits are satisfied, if they are satisfied, idetify the optimal decisio ad algorithm covergece coditio, otherwise, tur to step (8). 6. PERFORMANCE ANALYSIS OF OPTIMIZATION ALGORITHM OF CONSTRUCTION PROJECT SCHEDULE Tae schedule-time equilibrium of schedule optimizatio of costructio project as a example, we will verify the superior performace of improved at coloy geetic algorithm. We ca see from Table 1, the results of the two variable costraits from coloy fusio geetic algorithm are better tha multi-objective geetic algorithm, ad the solutios are more widely spread. Table 1: Compariso Of The Two Algorithms I Stadard Deviatio (Or Distace) Ad Maximum Scatter Extet Algorithm Multi-objective geetic algorithm Improved algorithm Number of solutios Stadard Maximum deviatio (S) scatter extet The aalysis shows that the result of multiobjective geetic algorithm is betwee 0~ 0.9 ad that obtaied from the improved at coloy geetic algorithm is betwee 0~1, which meas the distributio of the latter is better[8].the aalysis shows the iteratio global covergece from the improved at coloy geetic algorithm is quic, a total of 77 times, ad 16 times i multi-objective geetic algorithm. 7. CASE STUDIES ABOUT PROJECT SCHEDULE OPTIMIZATION A costructio project covers m, with total costructio area of m. This project cosists of commercial buildigs 1# ad #, residetial buildigs 3# - 1#, oe-layer udergroud garage. Residetial buildig cosists of layers of floors whose floor height is.9m. The plaed time duratio for this project is 145 wees, ad the plaed ivestmet is 3 millio yua. 7.1 Schedule Optimizatio of At Coloy Fusio Geetic Algorithm of Costructio Project Schedule-time optimizatio of costructio project with improved at coloy fusio geetic algorithm ca be divided ito the followig steps: parameter settigs Firstly, set the ecessary parameters of at coloy fusio geetic algorithm; the maximum umber of iteratios of the at coloy operatio c-max=00, heuristic iformatio factor α =1, at umber m=11, expected heuristic factor β =4, pheromoe evaporatio coefficiet =0.5, the costat q0=0.8, t= 0, mutatio probability PM=0.1, crossover probability PC=0.7, ad C =0. millio / wee. Specific parameter settigs are as show i Table : Table : Parameter Settig α β ρ m q 0 c-max PM PC t examples of basic data The basic data cotais three parts: No. of each procedure i the project, time duratio ad direct cost. The pair of No. ad ame of correspodig procedure is as follows(ormal time duratio ad the shortest; ormal time duratio ad the shortest): A-foudatio excavatio ad slope support(11,10;0.8,1.), B-pile foudatios (16,14;3.6,3.), C-thermal layer ad waterproof layer(8,7;0.8,1), D- basemet structure (13,11;1.4,1.5), E-electrical pipelies, water supply ad draiage, embedded-reserved heatig vetilatio (75,70;0.5,0.6), F- exterior wall waterproof ad outdoor bacfill of basemet (14,13;1.1,1.4), G -the mai structure (7,5;4.8,5.4), H - frame erectio (4,,40;0.5,0.9), I - basemet masory ad bacfill (14,1;1,1.), J - the mai masory ad plasterig(38,35;,.4), K - tower structure(9,8;1.6,1.8), L - the removal of frame (46,43;0.5,0.7), M - roof project (9,8;,.5), N exterior wall decoratio ad iterior decoratio (17,15;,.5), O istallatio of widows ad doors (13,1;1,1.3), P water ad electricity supply, elevator istallatio ad debuggig (1,10;,.3), Q-outdoor project (10,8;1,1.), R - completio ad acceptace (5,4;0.6,0.8).Before optimizatio, the direct cost of all procedures for ormal time duratio is 6.8 millio yua, ad that of the shortest time duratio is 3.3 millio yua. 1543

5 Joural of Theoretical ad Applied Iformatio Techology 8 th February 013. Vol. 48 No JATIT & LLS. All rights reserved. ISSN: E-ISSN: schedule-time optimizatio Schedule-time optimizatio is based o at coloy fusio geetic algorithm. The mai process is to fid critical path ad o critical path by usig at coloy algorithm, ad wor out optioal solutio with geetic algorithm. The optimizatio priciple is that the direct cost rate is less tha the rate of idirect cost ad the total cost should be decreased; compress the procedures i sequece from the lowest rate of direct costs to the highest. Repeat the process util the time whe further compressed time duratio of ay procedure will mae the total project cost icrease results Apply the basic data ad iformatio related to the project from the iterface ito the simulated algorithm software, clic the "calculate" butto, the we ca wor out the solutios with the help of at coloy fusio geetic algorithm based o the data provided. The optioal solutios to Hope City project with improved at coloy geetic algorithm show that the total time duratio is 144 wees, shorter tha 145 wees which is defied by project plaig. With the optimizatio solutio, total cost of the project is reduced to millio yua from millio yua which is the result before optimizatio, which meas obvious optimizatio effect is achieved. 7. Results of costructio project schedule optimizatio The plaed period for this project is 145 wees, ad the plaed ivestmet is 3 millio yua. Before optimizatio, the plaed period is 151 wees ad the plaed total cost of the project is millio yua, however, with the help of improved at coloy geetic algorithm for solvig the optimal radomized solutios for 97 times, the optioal time duratio ad optimal total cost of each procedure of the project are achieved as is show i Figure 3. After optimizatio, the optimal time duratio optimal total cost are respectively: t={11, 16, 8, 11, 71, 14, 7, 4, 13, 36, 9, 43, 9, 17, 13, 11.5, 8, 5}, C={0.96, 3.84, 0.96, 1.38, 1.4, 1.3, 5.76, 0.6, 0.8,, 1.9, 0.,.4,.4, 1.,.03, 1, 0.7}; optimized total time duratio is 144 wees, shorter tha plaed period of 145 wees; the total cost is millio yua, amely 1.11 millio yua less tha plaed total ivestmet; compared with the results before optimizatio, the total costructio period is shorteed by 7 wees, the total cost reductio is reduced by 3.07 millio yua. Therefore, at coloy fusio geetic algorithm to wor out solutios for costructio project schedule-time optimizatio ca achieve good results. Figure 3: Percetage curve of iterative chage of the optimizatio procedures 8. PERFORMANCE ANALYSIS OF OPTIMIZATION ALGORITHM OF CONSTRUCTION PROJECT SCHEDULE The improved automatic at coloy geetic algorithm ca help to solve the problems about schedule-time equilibrium. The results show that, the improved at coloy geetic algorithm is suitable for solvig the costructio project schedule-time optimizatio, ad its performace i optimizatio is better to some degree. The optimized precisio ca meet developers demad; therefore the improved at coloy geetic algorithm ca quicly ad effectively help the project maager with schedule - cost optimizatio, providig better services for the real estate developers. ACKNOWLEDGEMENTS This article is speder by the Shaaxi Soft Sciece Fud(0llKRM0); Shaaxi social Sciece Fud(llE177);The Chag a Uiversity Basic Scietific Research Fuds for the Cetral Uiversities CHD011JC116(01109);Miistry of housig ad Urba-Rural Costructio Soft Sciece Fud(011-R1-6; 0ll-R3-19);Shaaxi Social Scieces 01 major theoretical ad practical issues research project (01C008); Xi'a Soft Sciece Fud HJ111 (1). Thas for professor Yi-fa Tag's idess ad help, ad assistat professor Hai-ya xie (uiversity of Arasas Little Roc, USA) s costructive suggestio. 1544

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