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٢٣١ Tishreen University Journal for Research and Scientific Studies - Engineering Sciences Series Vol. ( ) No. ( )

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Page 1: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

٢٣١

Tishreen University Journal for Research and Scientific Studies - Engineering Sciences Series Vol. ( ) No. ( )

��

Page 2: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

٢٣٢

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.

Page 3: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٣٣

Construction

project scheduling with resource constraintsToklu,

CPM

Resource allocation

(RCPSP)Kolisch,

deterministic

Page 4: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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

Page 5: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٣٥

K=١ , R٤=١

dj / rj,١

Page 6: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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

Page 7: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٣٧

The decoding procedure

GA

(initializing)

crossover

(mutation)

Kolisch,

Holland

Genetic algorithms (GAs)

Goldberg ( )

(bit)

Random Key Representation

ρ=(r ,r ,...,rn) rjj

Page 8: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

٢٣٨

ρg

jrj = max{ri|i∈Dg} Dg

Dg

j

rj = max{ri|i∈Dg}

.

Kolisch,

Kolisch,

GA

Hartmann,

Hartmann,

GA.popsize

popsize

·popsize

Page 9: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٣٩

(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,

Page 10: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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,

Page 11: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٤١

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

Page 12: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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

Page 13: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٤٣

PMX

411

7936

78

89

45

36

511

36

79789

4114511

PMX

PMX

Swap MutationI

Gen, i = ,...,npviI

pvj

Ipmutation

j

Page 14: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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

Page 15: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٤٥

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

Page 16: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

٢٤٦

c

c =RK:xc

Act.

xf

xm

xc

Sf

Page 17: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٤٧

Sm

xc

[-n, n] Debels,

[ ]

Page 18: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

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. ,

, .

Page 19: Tishreen University Journal for Research and Scientific ...tishreen.edu.sy/sites/default/files/Tishreen_Magazine/14_12.pdf · Handbook of Genetic Algorithms, Van Nostrand Reinhold,

Tishreen University Journal. Eng. Sciences Series

٢٤٩