1. OPTIMIZATION OF PLANAR TRUSS STRUCTURE USING FIREFLY ALGORITHM
MANIKANDAN .A
MANIKANDAN .B
MOHAMED ANSARI.S
RAGAVAN.V
THIRUNAVUKARASU.S
Under the guidance of,
MS. N. MUTHU ABINAYA.,ME,
Assistant professor,
Department of Civil Engineering
Sethu Institute of Technology.

2. Content Introduction Optimization Objective of project
Scope of project
Review of literature
Structural optimization
18 – bar truss structure
Components of optimization
objective function
Constraints
Variables
Variables of choice
Material property
Allowable for 18-bar truss
Range of design variables
Results from firefly algorithm
optimum layout
conclusion

3. Introduction Traditional method – not satisfied.
Nature inspried metaheuristic algorithms
Firefly Algorithm (FA)
Ability of metaheuristic algorithms

4. Optimization
The act of obtaining the best result under the given circumstances.
Design, construction and maintenance of engineering system involve decision making both at the managerial and technological level.
Goals of such decision
To minimize the effort required or
To maximize the desired benefit.

5. Role of optimization in design
Decision making
Satisfactory decision under given circumstances
Minimum weight design

6. Objective of the project
Study the basic concept and functional behaviour
Develop computer program for the optimization algorithm
To obtain minimum weight of truss structure

7. Scope of the project
Understand the need and origin of the optimization methods.
Get a broader picture of the various applications of optimization methods used in engineering.
Formulate optimization problem as mathematical programming problem.

8. Review of literature

9. S. Gholizadeh et al (2011)
has described the shape optimization of truss structures tackled using an enhanced HS metaheuristic algorithm, in order to improve the computational performance of HS. The proposed meta-heuristic algorithm is termed as modified harmony search (MHS) algorithm. Both size and shape structural optimization problems were solved by the proposed algorithm and the results were compared to those of the other researchers. The numerical results indicate that using MHS not only better solutions can be found but also a significant reduction in computational effort may be achieved.

10. Xin - She Yang (2011) 
The author intended to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications. The author had compared the proposed firefly algorithm with other meta-heuristic algorithms such as particle swarm optimization (PSO). Simulations and results indicate that the proposed firefly algorithm was superior to existing meta-heuristic algorithms. Finally author discussed its implications for further research.

11. S. Kazemzadeh Azad et al (2011)
In this paper, optimum design of truss structures with both sizing and geometry design variables is carried out using the firefly algorithm. Additionally, to improve the efficiency of the algorithm, modifications in the movement stage of artificial fireflies are proposed and the general performance of the algorithm in 50 runs is reported . Numerical results indicate the efficiency of the proposed approach.

12. Structural optimization
Three categories
Sizing – cross – sectional areas
Configuration – nodal co-ordinates
Topology – nodal co-ordinates & connectivity

13. 18 – bar truss structure

14. Components of optimization
Objective function
constraint
variables
optimization

15. Objective function
The optimal design of truss optimization can be treated as
Minimize f(x)
So the objective function can be written as
f(x)=∑ƿAl

16. Total design variables - 12
sizing variables – (A1,A2,A3,A4) - 4
geometry variables – (X3,Y3,X5,Y5,X7,Y7,X9,Y9) - 8
Total design variables - 12

17. Cross sectional area & geometry variable
Variable of choice
Design variables
Discrete variables
Continuous variables
Cross sectional area & geometry variable
Variable of choice

18. Optimization algorithm
Constraints
Optimization algorithm
stress
Set the constraint

19. Material property S. No Property Value 1 Material Aluminium 2
Young’s modulus
Mpa 3
Density
Kg/m3

20. Allowable for 18-bar truss
S. No
Allowable
Value 1
Stress
N/mm2 2
Range of design variables
≤ A ≤
mm2

21. Range of design variables
S. No
Design variable
Lower limit
(mm2)
Upper limit 1
A (1,4,8,12,16)
7903.2
8871 2
A (2,6,10,14,18)
9838.7
12258 3
A (3,7,11,15)
2903.8
4032.3 4
A (5,9,13,17)
1290.3

22. Boundary limits for geometry variables
S. No
Design Variable
Lower limit
‘mm’
Upper limit 1 X3
19685
31115 2 X5
13335
24765 3 X7
6985
18415 4 X9
635
12065 5 Y3
-5715
6223 6 Y5 7 Y7 8 Y9

23. Firefly algorithm The algorithm is formulated by assuming,
All fireflies are unisexual
Attractiveness is proportional to their brightness.
If there are no firefly brighter than a given firefly, it will move randomly.

24. Mat lab implementation
Check for constraints
matlab program for 18 - bar truss.

26. Results from firefly algorithm
S.NO
SIZING VARIABLE
INITIAL SOLUTION (mm2)
FINAL SOLUTION (mm2) 1 A1
6451.5
8094 2 A2
11560 3 A3
3656 4 A4
2200

27. Geometry variables using firefly algorithm
S.NO
GEOMETRY VARIABLE
INITIAL SOLUTION
(mm)
FINAL SOLUTION 1 X3
25400 2 X5
19050 3 X7
12700 4 X9
6350
5808 5 Y3
4897 6 Y5
3852 7 Y7
2389.3 8 Y9
1045
WEIGHT(kg)
13394
2053

28. Optimum layout of 18 – bar truss using firefly algorithm

29. Conclusions
The effectiveness of the methods are demonstrated through a bar planar truss problem.
The numerical results demonstrate the superiority of the various
methods like firefly algorithm and particle swarm optimization.
The results obtained by considering both the size and shape variable.
Optimum solution obtained using firefly algorithm –
From the optimum solution it is found that the firefly algorithm is more efficient

30. THANK YOU