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Tishreen University Journal for Research and Scientific Studies - Engineering Sciences Series Vol. ( ) No. ( )
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Tishreen University Journal for Research and Scientific Studies - Engineering Sciences Series Vol. ( ) No. ( )
Fitting Genetic Algorithms Into Scheduling Construction Projects
Dr. Ali Al-Dabbab* Dr. Hamza Ali**
Nasib Za'rour***
(Received ٢٠٠٨ / ١ / ٦. Accepted ٢٠٠٨ / ٧ / ٢٩)
� ABSTRACT �
The genetic algorithms theory is considered one of the best and newest mathematical methods being used to find the optimal solution to problems that have a great number of solutions. The scheduling problem is one of the most important problems in engineering management that has a variety of solutions, where the request is to find the sequence of executing the tasks (activities) of a project, taking precedence and renewable resources constraints into account, without changing the duration of the tasks or splitting them or changing the renewable resources needed for the tasks in order to get the shortest schedule for the construction project. This paper is concerned with fitting genetic algorithms in order to be capable of solving the problem mentioned above, where the construction project scheduling problem components are expressed by random key types.
Keywords: Construction, Project Management, Scheduling, Genetic Algorithms, Random Key.
* Assistant Professor, Department of Management and Construction Engineering, Faculty of Civil
Engineering, Al-Baath University, Homs, Syria. ** Assistant Professor, Department of Management and Construction Engineering, Faculty of Civil
Engineering, Al-Baath University, Homs, Syria. *** Postgraduate Student, Assistant Professor, Department of Management and Construction
Engineering, Faculty of Civil Engineering, Al-Baath University, Homs, Syria.
Tishreen University Journal. Eng. Sciences Series
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Construction
project scheduling with resource constraintsToklu,
CPM
Resource allocation
(RCPSP)Kolisch,
deterministic
٢٣٤
Kolisch,
Toklu, J={ ,...,n,n }
n
KҚ = { ,...,K} jrj,k
k∈Қdj k
RkRk,tRkRk,tdj ,
rj,k , dj = rj,k = k∈Қ j
Sj fj.
n
K
lag
Tishreen University Journal. Eng. Sciences Series
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K=١ , R٤=١
dj / rj,١
٢٣٦
ij
FSi,jSSi,jFFi,jSFi,j
Lags
S
F = (f , f ,…,fn) ,…,n
S = (s , s ,…,sn)
Kolisch,
Genetic Algorithms (GAs)
Metaheuristic
Hartmann,
The fitness function
The crossover operator
The mutation operatorgenes
The selection operator
Hartmann,
The representation
i
j
SSi,j
SFi,j
FFi,j
FSi,j
time
Tishreen University Journal. Eng. Sciences Series
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The decoding procedure
GA
(initializing)
crossover
(mutation)
Kolisch,
Holland
Genetic algorithms (GAs)
Goldberg ( )
(bit)
Random Key Representation
ρ=(r ,r ,...,rn) rjj
٢٣٨
ρg
jrj = max{ri|i∈Dg} Dg
Dg
j
rj = max{ri|i∈Dg}
.
Kolisch,
Kolisch,
GA
Hartmann,
Hartmann,
GA.popsize
popsize
·popsize
Tishreen University Journal. Eng. Sciences Series
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(ties)Hartmann,
popsize
( -tournament selection)II
II(ties)
popsize
Hartmann,
Priority Value based Genetic
Algorithm
II =( pvI ,..., pvnI )j = ,...,
n pvjI∈[ ]
I=( )
I
pv I =
MFD
Hartmann,
٢٤٠
q ≤ q < n.qD
i = ,...,n
pviM, if i ∈{ ,...,q}
pviD =
pviF , if i ∈{q + ,...,n}
q =
M =( ) F =( )
D =( )
qq ≤ q < q ≤ n
i = ,...,n
pviM, if i ∈{ ,...,q }
pviD = pvi
F , if i ∈{q + ,...,q }
pviM, if i ∈{q + ,...,n}.
MF q = q =
D =( )
pi ∈{ }, i = ,...,n
i = ,...,n
pviM , if pi =
pviD =
pviF , otherwise
MF
D =( )
I
i = ,...,n
pviI
∈ [ ]pmutation
Hartmann,
Tishreen University Journal. Eng. Sciences Series
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II =( pvI ,..., pvnI )j = ,...,
n pvjI∈{ ,...,n}{ pvI ,..., pvn
I } = { ,...,n}
I=( )
I =( )
Position-based Crossover
(PBC)Syswerda,
(left-to-right scan)
MF
D
pi ∈{ }, i = ,...,n
i = ,...,npi = pviD
:= pvi
M
i = ,...,npi = pviD
:= pvk
F
kpvkF
F =( )M =( ), :D =( )
MFq ≤ q < n
DSD
i = ,...,qDpviD
:= pvi
M
i = q + ,...,nD
pviD
:= pvk
F
kpvkF
∉{pv D,…, pviD
− }
MF q=
D =( )
SFM,...,q
٢٤٢
qq≤ q < q ≤ n
Di = ,..., q
pviD
:= pvi
M
i = q + ,...,n
pviD
:= pvi
M
i = q + ,..., q
pviD
:= pvk
F
k pvkF
∉{pv D,…, pviD− }pvk
F
∉{pvqD
,…, pvn D }
MF q = q =
D =( )
q = n.
Partially Mapped Crossover
(PMX)
Gen,
q = q =
PMX
PMX
M
F
Tishreen University Journal. Eng. Sciences Series
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PMX
411
7936
78
89
45
36
511
36
79789
4114511
PMX
PMX
Swap MutationI
Gen, i = ,...,npviI
pvj
Ipmutation
j
٢٤٤
.
Forward–backward improvement
The peak crossover
operator
Debels,
Random Key (RK) xf Sf
xmSmRKxcSc
Resource Utilization
Ratio (RUR)tActive(t,S)
StRURDebels,
RUR(t, S) =
St,ctiveAj
K
k k
kj
R
r
K 1
,1
RUR
.[t (S) , t (S)]
Sl¼ * makespan(S) ¾ *
makespan(S)makespan(S)S
Total Resource Utilization (TRU)lt
-l t+
t=time
Stime,1
)RUR( TRU(t,l,S) =
l[t (S), t (S)]t (S)
t ∈ [t , t + makespan(S) − l]TRU(t, l, S) t
t (S)t (S)+l[t , t (S)][t (S), t + makespan(S)]
t (Sf)t (Sf)RK
case : If xmi < t (Sf) ⇒ xci := xmi − c
case : If t (Sf) ≤ xmi ≤ t (Sf) ⇒ xci := xfi
case : If xmi > t (Sf) ⇒ xci := xmi + c
Tishreen University Journal. Eng. Sciences Series
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Sf
Sm
c
RK
RK
(case )(case ).
RKRK
R =
Sft (Sf)t (Sf)
RURtl
TRU(t, , Sf) t =t (Sf)t (Sf)
SmRK xf
Sf xmSm
RKxc
, , , , , , , xmi ∈ [ , ]
xfixci
, , , , , , , xmi >
, , , , xmi <
xmixc c
٢٤٦
c
c =RK:xc
Act.
xf
xm
xc
Sf
Tishreen University Journal. Eng. Sciences Series
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Sm
xc
[-n, n] Debels,
[ ]
٢٤٨
- DEBELS, D; VANHOUCKE, M. A Decomposition-Based Heuristic for the Resource-
Constrained Project Scheduling Problem. Ghent University, Faculty of Economics
and Business Administration, Belgium, WPS No. , .
- GEN, M; CHENG, R. Genetic Algorithm and Engineering Optimization. John Wily and
Sons, New York, .
- HARTMANN, S. A Competitive Genetic Algorithm for the Resource-Constrained
Project Scheduling. Naval Research Logistics, , , .
-HARTMANN, S. Self-Adapting Genetic Algorithms With an Application to Project
Scheduling. Manuskripte aus den Instituten für Betriebswirtschaftslehre, University of
Kiel, Germany, No. , .
- KOLISCH, R; HARTMANN, S. Heuristic Algorithms for Solving the Resource-
Constrained Project Scheduling Problem: Classification and Computational
Analysis. Project Scheduling, ed. by Weglarz, J., Kluwer, Boston, , .
- SYSWERDA, G. Scheduling Optimization Using Genetic Algorithms. in Davis, L. Ed.:
Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, .
- TOKLU, Y. C. Application of Genetic Algorithms to Construction Scheduling With or
Without Resource Constraints. Canadian Journal of Civil Engineering, vol. , No. ,
, .
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