ArticlePDF Available

Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm

Authors:

Abstract and Figures

The main purpose of this study is to investigate the performance of the proposed hybrid teaching-learning based optimization algorithm on the optimum design of reinforced concrete (RC) cantilever retaining walls. For this purpose, three different design examples are optimized with 100 independent runs considering continuous and discrete variables. In order to determine the algorithm performance, the optimization results were compared with the outcomes of the nine powerful meta-heuristic algorithms applied to this problem, previously: the big bang-big crunch (BB-BC), the biogeography based optimization (BBO), the flower pollination (FPA), the grey wolf optimization (GWO), the harmony search (HS), the particle swarm optimization (PSO), the teaching-learning based optimization (TLBO), the jaya (JA), and Rao-3 algorithms. Moreover, Rao-1 and Rao-2 algorithms are applied to this design problem for the first time. The objective function is defined as minimizing the total material and labor costs including concrete, steel, and formwork per unit length of the cantilever retaining walls subjected to the requirements of the American Concrete Institute (ACI 318-05). Furthermore, the effects of peak ground acceleration value on minimum total cost is investigated using various stem height, surcharge loads, and backfill slope angle. Finally, the most robust results were obtained by HTLBO with 50 populations. Consequently the optimization results show that, depending on the increase in PGA value, the optimum cost of RC cantilever retaining walls increases smoothly with the stem height but increases rapidly with the surcharge loads and backfill slope angle.
Content may be subject to copyright.
Geomechanics and Engineering Vol24 No3 (2021) 237-251
DOI: https://doi.org/10.12989/gae.2021.24.3.237
Copyright © 2021 Techno-Press, Ltd.
http://www.techno-press.org/?journal=gae&subpage=7 ISSN: 2005-307X (Print), 2092-6219 (Online)
1. Introduction
      
       
       


        
      
      
      

      
      


-      
  -

       

et al.       
et al.    et al. 
        
       
Corresponding author, Assistant Professor
E-mail: temur@istanbul.edu.tr

          

      
        
        
-
        
        
  -

       
       et al.
--
     
et al.
       
     - 
 

      
      
      
    et al.  
et al.         
 et al.  et al. 
     
     
  et al.    
  et al. 
Optimum design of cantilever retaining walls
under seismic loads using a hybrid TLBO algorithm
Rasim Temür
Department of Civil Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey
(Received June 11, 2020, Revised January 19, 2021, Accepted January 20, 2021)
Abstract. The main purpose of this study is to investigate the performance of the proposed hybrid teaching-learning based
optimization algorithm on the optimum design of reinforced concrete (RC) cantilever retaining walls. For this purpose, three
different design examples are optimized with 100 independent runs considering continuous and discrete variables. In order to
determine the algorithm performance, the optimization results were compared with the outcomes of the nine powerful meta-
heuristic algorithms applied to this problem, previously: the big bang-big crunch (BB-BC), the biogeography based optimization
(BBO), the flower pollination (FPA), the grey wolf optimization (GWO), the harmony search (HS), the particle swarm
optimization (PSO), the teaching-learning based optimization (TLBO), the jaya (JA), and Rao-3 algorithms. Moreover, Rao-1
and Rao-2 algorithms are applied to this design problem for the first time. The objective function is defined as minimizing the
total material and labor costs including concrete, steel, and formwork per unit length of the cantilever retaining walls subjected
to the requirements of the American Concrete Institute (ACI 318-05). Furthermore, the effects of peak ground acceleration value
on minimum total cost is investigated using various stem height, surcharge loads, and backfill slope angle. Finally, the most
robust results were obtained by HTLBO with 50 populations. Consequently the optimization results show that, depending on the
increase in PGA value, the optimum cost of RC cantilever retaining walls increases smoothly with the stem height but increases
rapidly with the surcharge loads and backfill slope angle.
Keywords: -
Rasim Temür
    et al.  
     
     
     
et al.    
 et al.    
et al.-
     et al.  
et al.

       
       
et al.
     

-   

  
       
 
      -  
       
      
       
       

        

      

       
        
 - -  -   
-

-
      -  



       
    -   
      
       
     
         
 -

      -     
      
  -   
      

 -     
-

et al.        
 et al.      
et al.--
-
          
       
        
    
             
²
          



      
  
  
        
         
 

238
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm
2. Design of reinforced concrete cantilever retaining
walls
        
 
 

   WW 
WR
WT
  PA PP PB  Pq     
 -
      α  
      q  
γϕ
c

       


      
       
        
        



2.1 Earth pressure conditions
       
      
       

 - -    
       
        


; γHkvKae
         

 
      
           
      et al.
kv
       


 ϕβ
δ
        α  
θ 


kh



PGAgd
     
     -  
       
      Pa  
 ΔPae  




-

        





D1Kpe


       
         
  Pp     
PpePp


 c         
0 25
1
2
0 74 25 4 1
.
h
PGA if d
g
k. PGA PGA . mm if d
g d g





ae ae ae
P P P  
239
Rasim Temür
        


2.2 Stability of retaining walls

      
       SFO 


MRMO
       
         
 SFS         
FF


   
       


VLF


  SFB      
qu
qmax

        
     qu    
      
          
      
qmaxqmin


Be 

V

2.3 Reinforced concrete design
       
-
       



 ϕ      As    
   fy   
      d     
       
 a      

       


fc
b
         
       




  β1       
       



ψtψeλ
      


3. Formulation of optimum design problem
3.1 Design variables


 -   
 
         -
      
R
OO
M
SF M
R
SS
F
SF F
22
tan 33
B F B
RP
Lc
F V P
 

 



max
u
Bq
SF q
6
1
min
max
Ve
qBB

 


2RO
MM
B
eV


2
n s y a
M A f d

 


0.17 '
nc
V f b d
 
1.4
0.25 c
min yy
f
ff
  
max 1 600
0.85 600
c
yy
f
ff


  


300 19
2.1
300 19
1.7
y t e bb
c
dy t e bb
c
fd mm for d mm
f
lfd mm for d mm
f
 
 
  

 


  

 


240
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm





-

x

x

x

x

x

x

x

x




R


R-

R

R-

R


R-

R


R-







-
*2




















    -  
   -  
      


          
       
      
      
      
 
3.2 Design constraints
       
       
      
      
      
       
-
   -
       
      
       -


  
  

3.3 Objective function
        


        
fcost


   Cc Cs  Cf      
VcWsAf

  
     

        


 gi
F

 

        

       
        

4. The proposed hybrid approach
          
-

      -
-  -      

 

          
cost c c s s f f
f C V C W C A  
4
34
1
1i
ig

 


cost
Ff 
241
Rasim Temür

      
  -     

4.1 Teaching-learning based optimization algorithm
-   

       

         Xnew 
        Xold 
  Xbest     Xmean  


 rnd      
      TF     
           

      


       
       
   et al.  

4.2 Flower pollination algorithm

  
        
      
       
     L
         
   rnd2   
ij
         

 
new old best F mean
X X rnd X T X  
 
 
 
 
 
 
old i j i j
new
old j i i j
X rnd X X if f X f X
XX rnd X X if f X f X
  
  
-
242
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm


4.3 Jaya algorithm
        -
      
     

        



Xworst
4.4 Rao algorithms
   -  
       

       
 - -  -     
-



Xr


  Xold  Xr  Xold    
Xold  XrXr

       
Xr  Xold  Xr     Xr  Xold
Xold
-

         

4.5 The proposed hybrid teaching-learning based
optimization algorithm
-   
        
      

-
      
 

        -


 -   -    - 
         
      
 
         
        

          

5. Design examples
        

-     
      

     
-  -      
       
-
       
et al.
     et al.  
      et al.  
-
       
          
        
      

         


   
  -
        

 m  -

       

        




X
H
H
X
H
H
X

H
X


X
H
H
X

H
X


X


 
1new old old best
X X L X X if rnd p  
 
21new old i j
X X rnd X X if rnd p  
 
12new old best old worst old
X X rnd X X rnd X X  
 
new old best worst
X X rnd X X  
 
 
12new old best worst old r r old
X X rnd X X rnd X or X X or X  
 
 
 
12new old best worst old r r old
X X rnd X X rnd X or X X or X  
243
Rasim Temür

Input parameters
Symbol
Unit
Values
Example-1
Example-2
Example-3

H




α



q





Df



Retained soil

ϕR




cR


γR




Sub-base soil

ϕB



cB




γB




Reinforcing steel

fy





γs





Cs




Concrete

c





γc





Cc




Reinforced concrete

cc



-




Cf





ρst
-



Factors of safety

SFO,design
-




SFS,design
-




SFB,design
-



-
Algorithm
PGA
Stem
Height
Total Cost ($) (Continuous)
Total Cost ($) (Discrete)
Min
Max
Mean
St. Dev.
Min
Max
Mean
St. Dev.
-


116.17



121.74






116.17



121.74






116.17



121.74






116.17



121.74
121.74
121.74
0.00



116.17



121.74










121.74
121.74
121.74
0.00



116.17



121.74



-


116.17



121.74
121.74
121.74
0.00
-


116.17

116.17
0.00
121.74



-


116.17

116.17
0.00
121.74






116.17



121.74



244
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm
5.1 Example-1: The retaining wall without shear key
under static loads
       
        
-
          

   

   HTLBO-p10 for 10 populations
        

      
       
         
       
  
        

-

          
       

Algorithm
PGA
Stem
Height
Total Cost ($) (Continuous)
Total Cost ($) (Discrete)
Min
Max
Mean
St. Dev.
Min
Max
Mean
St. Dev.
-


116.17



121.74



-


116.17

116.17

121.74



-


116.17

116.17

121.74
121.74
121.74
0.00
-


116.17

116.17
0.00
121.74
121.74
121.74
0.00
-


116.17
116.19
116.17
0.00
121.74
121.74
121.74
0.00

-
-
Variables
Type
Dimensions (m)
Reinforcements (size/spacing)
Total
X1
X2
X3
X4
X5
R1
R5
R9
Cost ($)




















245
Rasim Temür
    

  -   

         
 
5.2 Example-2: The retaining wall with shear key
under static loads
          
        
et al.
       
           

   
  

  
  -       
-
Algorithm
PGA
Stem
Height
Total Cost ($) (Continuous)
Total Cost ($) (Discrete)
Min
Max
Mean
St. Dev.
Min
Max
Mean
St. Dev.
-






325.09






316.76



325.09






316.76



325.09






316.76



325.09






316.76



325.09






316.76
319.18

0.43
325.09






316.76



325.09



-


317.36



325.09



-


316.76



325.09



-


316.76



325.09






316.76



325.09



-


316.76



325.09



-


316.76



325.09



-


316.76



325.09



-


316.76



325.09



-


316.76

317.04

325.09
328.03
325.19
0.50

-
-
Variables
Type
Dimensions (m)
Reinforcements (size/spacing)
Total
X1
X2
X3
X4
X5
X6
X7
X8
R1
R5
R9
R13
Cost ($)




























246
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm
-
      
       
   

       
       
         -

for population size = 50
          



5.3 Example-3: The retaining wall under seismic
loads

 
  
       

       
-
        


  
 XX  


        

     
       
-

      
with
50 populations       
      -
with 40 populations
      

         
          

    
       
-
Algorithm
PGA
Stem
Height
Total Cost ($) (Continuous)
Total Cost ($) (Discrete)
Min
Max
Mean
St. Dev.
Min
Max
Mean
St. Dev.
-






347.64






345.63










345.63



347.64






345.63



347.64






345.63



347.64






345.63



347.64






345.63



347.64



-


345.63



347.64
347.64
347.64
0.00
-


345.63



347.64



-


345.63



347.64






345.63



347.64
356.54
347.82
1.25
-


345.63



347.64



-


345.63



347.64



-


345.63
345.72
345.63

347.64



-


345.63
345.72
345.63

347.64
347.64
347.64
0.00
-


345.63
345.72
345.63
0.01
347.64
347.64
347.64
0.00

-
Variables
Type
Dimensions (m)
Reinforcements (size/spacing)
Total
X1
X2
X3
X4
X5
X6
X7
X8
R1
R5
R9
R13
Cost ($)












-













-

247
Rasim Temür
-
--



248
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm
 

     
 -
           
  -     
      
-
  -    
 

        

 
     ²  ² 
 


       
     
    
            
        
     g  
 


         

 
       
    
          
        
        

       


         

6. Conclusions
       
 

         
-     

       






249
Rasim Temür
 -

      
       
  -     

-

        

       
        

 
-  
      
        

        
        
   



       

   

       
   
         
         


         

References
 -  Building Code Requirements for Structural
Concrete and Commentary

       
-Comput Struct147-

       
       
-
Eng Optimiz49-

         
      
 Proceedings of the International Conference of
Numerical Analysis and Applied Mathematics


-J Struct Eng138-
-

       
   Comput Struct 79 -
--

      J Geotech
Geoenviron Eng135-
-
        
       Soft Comput
24----
  -
      Reinforced soil
Structures Volume I, Design and Construction Guidelines

       
 

        
Memoires de l’Academie Royal Pres Divers Savants 7 -

         

Expert Syst. Appl39-

        
       
Eng Struct103-

        
      
  Struct Multidiscip O 55 -
---
       
      
 Int J Numer Anal
Met Geomech41-


 Proceedings
of the 3rd International Symposium on Geotechnical Safety and
Risk (ISGSR)
        
       
     Proceedings of the
3rd International Symposium on Geotechnical Safety and Risk
(ISGSR)
  -
     
Geomech Eng20-

         
       
    Structures 23 -

        
        
Int J Civ Eng9-
        
        
Arab J Sci Eng38-
---
 

Eng Comput-
---
       
 Asian J
Civ Eng17-
  -   -  
     
250
Optimum design of cantilever retaining walls under seismic loads using a hybrid TLBO algorithm
    -  
Struct Eng Mech47-

        
Iran
J Sci Technol Trans Civ Eng38-

         
   -   Int J
Civ Eng10-
        
      
Pamukkale Univ J Eng Sci22-

        -
 
Civ Eng Environ Syst31
-
   Geotechnical Earthquake Engineering

        
      
Struct Multidiscip O61-
---
       
     Proceedings of the 3rd
International Conference on Soil Mechanics and Foundation
Engineering 

   Proceedings of the World
Engineering Congress


Int J Optimiz Civ Eng7-
   
       J. Japan Soc Civ Eng
10-

      
Structures25-

         
     
Procedia Earth Planet Sci5-

      -  
       
Adv Eng Softw39-

        
      
KSCE J Civ Eng17
----
       

 Proceedings of the Geotechnical Frontiers 2017

 
       
J GeoEng12-

      - 
      Int J Industr
Eng Comput11-

        -
-      
    Computer-Aided
Des43-
        
    
Eng Optimiz9-


J Geotech Eng122-
-
        

     KSCE J
Civ Eng20-
---
        
   -- 
      Int J
Comput Appl-

         
  -      -
   Proceedings of the 3rd
International Conference on Internet of Things and Connected
Technologies (ICIoTCT)
        
      
J Intell Fuzzy Syst34-
-
         
  --  
Appl Math Model77-


    
KSCE J Civ Eng18-
---
       -
       Struct
Eng Mech57-

   Flower Pollination Algorithm for Global
Optimization
-
-
Eng Struct30-


      
Sustainability12
CC
251
... However, the novel study was of Sarıbaş and Erbatur [19] which solidified the direction taken by researchers for problem formulation of RC cantilever retaining walls and is the most common reference study used by subsequent researchers. Since then multiple theses (Medhekar [20], Purohit [21], Naeem [22], Rahbari [23], and Schmied and Karlsson [24]), conference papers (Bhatti [25], Ahmadi-Nedushan and Varaee [26], Villalba et al. [27], Pei and Xia [28], Papazafeiropoulos et al. [29], Uray and Tan [30], Al Sebai et al. [31], Srivastavaa et al. [32], and Yücel et al. [33]), and journal articles (Ceranic et al. [34], Chau and Albermani [35], Babu and Basha [36], Yepes et al. [37], Khajehzadeh et al. [38], Ghazavi and Bonab [39], Kaveh and Abadi [40], Khajehzadeh et al. [41], Camp and Akin [42], Khajehzadeh and Eslami [43], Sable and Patil [44], Sable and Patil [45], Kaveh and Behnam [46], Kaveh et al. [47], Kaveh and Khayatazad [48], Khajehzadeh et al. [49], Sheikholeslami et al. [50], Talatahari and Sheikholeslami [51], Gandomi et al. [52], Kaveh and Mahdavi [53], Singla and Gupta [54], Bekdaş et al. [55], Kaveh and Farhoudi [56], Sheikholeslami et al. [57], Temür and Bekdas [58], Aydogdu [59], Kaveh and Laien [60], Gandomi et al. [61], Gandomi et al. [62], Kumar and Suribabu [63], Rahbari et al. [64], Ukritchon et al. [65], Kayhan and Demir [66], Mohammad and Ahmed [67], Kalateh-Ahani and Sarani [68], Moayyeri et al. [69],Öztürk and Türkeli [70], Uray et al. [71], Dagdeviren and Kaymak [72], Kaveh et al. [73], Kaveh et al. [74], Kayabekir et al. [75], Konstandakopoulou et al. [76], Mergos and Mantoglou [77], Kalemci et al. [78], Kayabekir et al. [79], Hoang and Cong [80], Millán-Paramo et al. [81], Kashani et al. [82], Uray et al. [83], Ravichandran et al. [84], Yücel et al. [85], Kaveh et al. [86], Sharma et al. [87], Mevada et al. [88], Uray and Çarbaş [89], Tousi et al. [90], Eroglu et al. [91], Uray et al. [92], Linh et al. [93], Dodigović et al. [94], Tutuş et al. [95], Uray et al. [96], Yücel et al. [97], Tutuş et al. [98], Temür [99], Shakeel et al. [100], Khajehzadeh et al. [101], Uray et al. [102], and Khajehzadeh et al. [103]) have been written on this topic. Despite ample work conducted that demonstrates the potential of optimization in this field, its acceptance in practical works is still little to none [100,104,105]. ...
... All these variables must be provided with their upper and lower bounds; otherwise an infeasible section may be obtained. A penalty function must be applied while using continuous variables without bounds to ensure the algorithm rejects the infeasible answer and moves on to a better solution as done by Sarıbaş and Erbatur [19], Medhekar [20], Srivastava [95], Temür [99], and Uray et al. [102] have tried to optimize steel areas while keeping in mind the practicality of available rebars and their spacing. is is achieved by generating a pool of predefined steel bars and indexing them in tabular form while programming. ...
... e harmony search (HS) is also able to perform local and randomization searches and replace bad solutions with those of good harmony due to its memory function. It has also been used by several studies to optimize retaining wall design and has proven its effectiveness and robustness; see, for example, the papers of Uray and Tan [30], Kaveh [99], and Uray et al. [102]. e HS has also been improved over the years by updating its memory considering rate, randomization, and local search capabilities. ...
Article
Full-text available
The booming growth of computational abilities in the 21st century has led to its assimilation and benefit in all horizons of engineering. For civil engineers, these advancements have led to groundbreaking technologies such as BIM, automation, and optimization. Unfortunately, even in an era of dwindling resources and dire need for sustainability, optimization has failed to attract implementation in practice. Despite an exponential growth as an area of research interest, the optimization of engineering structures such as reinforced concrete (RC) is still a complex task that requires multidisciplinary knowledge, hindering its practicability. Although past review papers have delved into this topic, they have only been able to cover the breadth of information available by covering broader aspects of optimization of structures. This study on the other hand aims to cover this topic in depth to uncover problem specific trends and issues, by focusing only on optimization of RC cantilever retaining walls. Although there is an abundance of research studies on this topic, there is an absence of any critical review to tie them up, and concurrently with its broader scope, it suffers the same lack of applicability in the field. The in-depth review presents a summarization of all the online publications including research articles, conference papers, and theses to the best of authors’ knowledge on the topic of RC cantilever retaining wall optimization. Geographical trends, regional developments, and prominent journals have been identified. The design codes, problem formulation, objectives, constraints, variables, and their optimization techniques are tabulated for ease of understanding. Unique areas of development investigated by the different researchers have been highlighted. Lastly, comprehensive recommendations for future works have been detailed with a focus on improving its applicability and assimilation into the construction industry.
... Since the spatial distribution studies and comparison of the average observed regional salinity with that calculated in the optimal network (covering all selected monitoring wells) showed that the calculated values were larger than the observed average, the network provided the optimal data of the groundwater quality in more polluted areas (Janatrostami and Salahi 2020). Temur (2021) used the hybrid TLBO algorithm for Optimum design of cantilever retaining walls under seismic loads. The robust results were obtained by HTLBO with 50 populations. ...
... The robust results were obtained by HTLBO with 50 populations. Consequently, the results showed that the hybrid TLBO algorithm optimized the implementation cost of RC cantilever retaining walls well (Temur 2021). Recently, various researchers have used combined optimization algorithms to overcome computational complexity. ...
Article
Full-text available
As the groundwater quantitative monitoring aimed to determine the factors affecting the aquifer behavior plays an important role in its regional management, studying the temporal and spatial groundwater level variations requires a comprehensive monitoring network. Effort has been made in this study to introduce a new linked simulation–optimization method, named MLPG-TLBO to quantitatively monitor the Birjand aquifer and determine the optimal points for piezometers. This model uses meshless local Petrov Galerkin (MLPF) method in the simulation part and teaching–learning-based optimization (TLBO) method in the optimization part. The objective function, in this study, is to minimize the difference between the groundwater level observed in piezometers and obtained computationally by the model. Since this coupled model is independent from the meshing, it eliminates the mesh-dependent shortcomings and, hence, yields more accurate results. It has been calibrated and validated in previous Birjand area studies and has led to acceptable results. By implementing the model in Birjand aquifer, the optimal positions of ten piezometers were determined mostly in areas where the density of the extraction wells was lower. Finally, the RMSE of both MLPG-TLBO and FDM was obtained to be 0.334 m and 1.483 m for 10 optimal piezometers. The RMSE value for MLPG-TLBO has shown a 0.423 m reduction compared to its previous value. This difference is quite meaningful as it shows good performance of this method in designing an optimal network for the aquifer.
... Li and Wu [20] proposed an improved slap swarm optimization for determining the crucial failure surface in slope stability evaluation. Temur [21] introduced a hybrid version of teaching learning-based optimization for the optimum design of cantilever retaining walls under seismic loads. Bardhan et al. [22] proposed a modified equilibrium optimizer for predicting soil compression index. ...
Article
Full-text available
This paper aims to introduce an adaptive metaheuristic algorithm based on tunicate swarm optimization (TSA) for effectively solving global optimization problems and the optimum design of a shallow spread foundation. The proposed adaptive tunicate swarm optimization (ATSA) has two main phases at each iteration: searching all around the search space based on a randomly selected tunicate and improving the search using the position of the best tunicate. This modification improves the algorithm’s exploration ability while also preventing premature convergence. The suggested algorithm’s performance is confirmed using a set of 23 mathematical test functions of well-known CEC 2017 and the outcomes are compared with TSA as well as some effective optimization algorithms. In addition, the new method automates the optimum design of shallow spread foundations while taking two objectives into account: cost and CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emissions. The analysis and design procedures are based on both geotechnical and structural limit states. A case study of a spread foundation has been solved using the proposed methodology, and a sensitivity analysis has been conducted to investigate the effect of soil parameters on the total cost and embedded CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emissions of the foundation. The simulation results demonstrate that, when compared to other competing algorithms, ATSA is superior and may produce better optimal solutions.
... There are numerous studies on the optimization of retaining structures under static loads [16][17][18][19][20]. However, the research into the optimum design of these structures under seismic loading is limited [21][22][23][24]. Due to the effectiveness of the proposed PSSCA, the applicability of this method for solving difficult optimization problems will be investigated via seismic optimization of retaining structures. ...
Article
Full-text available
This study introduces an effective hybrid optimization algorithm, namely Particle Swarm Sine Cosine Algorithm (PSSCA) for numerical function optimization and automating optimum design of retaining structures under seismic loads. The new algorithm employs the dynamic behavior of sine and cosine functions in the velocity updating operation of particle swarm optimization (PSO) to achieve faster convergence and better accuracy of final solution without getting trapped in local minima. The proposed algorithm is tested over a set of 16 benchmark functions and the results are compared with other well-known algorithms in the field of optimization. For seismic optimization of retaining structure, Mononobe-Okabe method is employed for dynamic loading condition and total construction cost of the structure is considered as the objective function. Finally, optimization of two retaining structures under static and seismic loading are considered from the literature. As results demonstrate, the PSSCA is superior and it could generate better optimal solutions compared with other competitive algorithms.
Article
Full-text available
Based on the salp swarm algorithm (SSA), this paper proposes an efficient metaheuristic algorithm for solving global optimization problems and optimizing two commonly encountered geotechnical engineering structures: reinforced concrete cantilever retaining walls and shallow spread foundations. Two new equations for the leader- and followers-position-updating procedures were introduced in the proposed adaptive salp swarm optimization (ASSA). This change improved the algorithm’s exploration capabilities while preventing it from converging prematurely. Benchmark test functions were used to confirm the proposed algorithm’s performance, and the results were compared to the SSA and other effective optimization algorithms. A Wilcoxon’s rank sum test was performed to evaluate the pairwise statistical performances of the algorithms, and it indicated the significant superiority of the ASSA. The new algorithm can also be used to optimize low-cost retaining walls and foundations. In the analysis and design procedures, both geotechnical and structural limit states were used. Two case studies of retaining walls and spread foundations were solved using the proposed methodology. According to the simulation results, ASSA outperforms alternative models and demonstrates the ability to produce better optimal solutions.
Article
Full-text available
This study developed an efficient evolutionary hybrid optimization technique based on chaotic sand cat optimization (CSCO) and pattern search (PS) for the evaluation of the minimum safety factor of earth slopes under static and earthquake loading conditions. To improve the sand cat optimization approach's exploration ability, while also avoiding premature convergence, the chaotic sequence was implemented. The proposed hybrid algorithm (CSCPS) benefits from the effective global search ability of the chaotic sand cat optimization, as well as the powerful local search capability of the pattern search method. The suggested CSCPS algorithm's efficiency was confirmed by using mathematical test functions, and its findings were compared with standard SCO, as well as some efficient optimization techniques. Then the CSCPS was applied for the calculation of the minimum safety factors of the earth slope exposed to both static and seismic loads, and the objective function was modeled based on the Morgenstern-Price limit equilibrium method, along with the pseudo-static approach. The CSCPS's efficacy for the evaluation of the minimum safety factor of slopes was investigated by considering two case studies from the literature. The numerical experiments demonstrate that the new algorithm could generate better optimal solutions via calculating lower values of safety factors by up to 10% compared with some other methods in the literature. Furthermore, the results show that, through an increase in the acceleration coefficient to 0.1 and 0.2, the factor of safety decreased by 19% and 32%, respectively.
Article
Full-text available
In this paper, a recently developed meta-heuristic algorithm, shuffled shepherd optimization algorithm (SSOA), is employed for optimal design of reinforced concrete cantilever retaining wall structures under static and seismic loading conditions. The concepts of set theory are employed to express the SSOA in a set theoretical term. The Rankine and Coulomb theories are utilized in order to estimate the lateral earth pressures under the static loading condition, whereas the Mononobe–Okabe method is employed for the seismic one. Optimization aims to minimize the cost of cantilever retaining wall while satisfying some constraints on stability and strength limits. The design is based on the requirements of ACI 318-05. In order to investigate the efficiency of the SSOA, one benchmark cantilever retaining wall problem is considered from the literature. Comparing the optimization results obtained by the SSOA with those of other meta-heuristics shows the efficient performance of the SSOA in both aspects of accuracy and convergence rate.
Article
Full-text available
The paper presents an estimation of the optimum cost of an isolated foundation following the safety and serviceability guidelines of Indian Standard (IS) 456:2000. Two adaptable optimization algorithms are developed for the first time to optimize the cost of any type of isolated footing design. Two optimization methods, i.e., constrained binary-coded genetic algorithm, with static penalty function approach and unified particle swarm optimization are developed in MATLAB compliant for optimal design of any isolated foundations. The objective function formulated is based on the total cost of footing. This includes the cost of concrete, the cost of steel and cost of formwork. The design variables which influence the total cost of footing are plan area and depth of footing and area of flexural reinforcement at moment critical sections. The footing design algorithm is developed according to the biaxial-isolated rectangular footing as per IS codes. The constraints, e.g., dimension of footing, restriction on bending, shear stresses and displacements, are considered in the footing design algorithm which acted as a subroutine to the developed optimization programs. Four different numerical examples have been solved to evaluate the versatility of the developed method. A comparison study has been done to observe the efficacy of both the optimization methods.
Article
Full-text available
The flower pollination algorithm (FPA) is an efficient metaheuristic optimization algorithm mimicking the pollination process of flowering species. In this study, FPA is applied, for the first time, to the optimum design of reinforced concrete (RC) cantilever retaining walls. It is found that FPA offers important savings with respect to conventional design approaches and that it outperforms genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm in this design problem. Furthermore, parameter tuning reveals that the best FPA performance is achieved for switch probability values ranging between 0.4 and 0.7, a population size of 20 individuals and a Lévy flight step size scale factor of 0.5. Finally, parametric optimum designs show that the optimum cost of RC retaining walls increases rapidly with the wall height and smoothly with the magnitude of surcharge loading.
Article
The paper represents an optimization algorithm for reinforced concrete retaining wall design. The proposed method, called Rao-3 optimization algorithm, is a recently developed algorithm. The total weight of the steel and concrete, which are used for constructing the retaining wall, were chosen as the objective function. Building Code Requirements for Structural Concrete (ACI 318-05) and Rankine’s theory for lateral earth pressure were considered for structural and geotechnical design, respectively. Number of the design variables are 12. Eight of those express the geometrical dimensions of the wall and four of those express the steel reinforcement of the wall. The safety against overturning, sliding and bearing capacity failure were regarded as the geotechnical constraints. The safety against bending and shear failure, minimum and maximum areas of reinforcement, development lengths of steel reinforcement were regarded as structural constraints. The performance of proposed algorithm was evaluated with two design examples.
Article
In this study, the optimum design of a reinforced concrete counterfort retaining wall for minimum cost is investigated by using TLBO and Jaya algorithms. There are 17 design variables in the problem of reinforced concrete counterfort retaining wall created in the study. These design variables are related to the wall geometry and steel reinforcement in various parts of the wall. There are a number of charts used in the technical literature to determine the cross-sectional effects of the stem and heel slabs of the wall. However, it is seen that these charts have been prepared at certain aspect ratios of the plates. In this case, Open Application Programming Interface of SAP2000 Software (called SAP2000-API) is used within the algorithm to realize a more realistic structural analysis. Thus, the desired structural analysis can be performed by applying external loads on the wall model prepared in SAP2000 Software through MATLAB Software where the algorithm is encoded. The desired cross-sectional effects are taken from this Software and used in the algorithm. The problem has a total of 46 constraints which consist of checks of sliding, overturning, and bearing capacity of the wall, reinforced concrete cross-section controls, and conditions related to size and reinforcement. The performance of the algorithms according to the findings from the optimum design performed on a numerical application is evaluated with standard statistical data and Wilcoxon test. According to Wilcoxon test, it is also observed that TLBO algorithm is more successful than Jaya algorithm for this problem.
Article
The purpose of this article to design a low-weight cantilever reinforced concrete retaining wall with shear key by using an optimization algorithm, which is programmed in MATLAB. Grey Wolf Optimization (GWO) is an optimization technique which is developed by mimicking hierarchy and hunting methods of grey wolves. The Retaining Wall was formulated as an optimization problem based on ACI 318–05 code and Rankine's theory for lateral earth pressure. The constrains based on safety factors and design factors were used to reach the best design. The geotechnical constraints were determined as the factor of safety against overturning, bending, bearing capacity failure and the structural constraints were determined as the moment and shear capacities of for elements of the wall. Two numerical examples for optimal design of retaining wall with/without shear key were considered to evaluate the efficiency of GWO algorithm compared to similar studies.
Article
Metaheuristic algorithms have probable to solve global optimization problems in various fields of engineering and industry. To find a global solution by exploring irregular or non-linear surfaces, classical optimization techniques are not able. To overcome the limitation of the classical approach, in the recent study, a large number of metaheuristic methods have been investigated to improve the solution quality concerning convergence and accuracy on the complex problems. Nowadays, a popular metaheuristic algorithm is introduced called teaching–learning-based optimization (TLBO). It is recently being used as an innovative, and robust method to solve the global optimization problem, inspired by the teaching–learning phenomenon. On the other hand, particle swarm optimization (PSO) algorithm is one of the most utilized algorithms in the current scenario, which has indicated acceptable efficiency. Genetic algorithm (GA) is a valuable component of metaheuristic which has been applied in various research applications. In this article, the performance of TLBO algorithm is estimated on 25 numerical test suites against other metaheuristic algorithms such as PSO and GA. The results of our experimental study show that TLBO outperforms the PSO and GA algorithm regarding convergence solution.
Article
This paper presents an effective metaheuristic algorithm called teaching learning-based optimization which is widely applied to solve the various real-world optimization problems. However, teaching learning-based optimization is rapidly trapped into local optima. To handle this kind of problem, we proposed an improved teaching learning-based optimization algorithm using adaptive exponential distribution inertia weight and altering the position-updating equation. In addition, the logistic map is applied to generate a uniformly distributed population to enhance the quality of the initial populations. The performance of the proposed method is evaluated on a suite of benchmark functions with different characteristics. The efficiency of the proposed technique is also evaluated on six gene expression datasets with the help of three classifiers. The experimental result demonstrates that the proposed method is comparatively useful in adapting the inertia weight in comparison to the existing inertia weight strategies with regards to the quality of solutions, convergence rate along with classification accuracy. In particular gene selection, the proposed method has achieved up to 98% classification accuracy for three out of six datasets with optimal gene subsets for all six datasets and maximum accuracy is achieved as 100% in small round blue-cell tumor dataset.