This document describes using a genetic algorithm to optimize the parameters of a vehicle suspension system. A quarter-car model with 5 parameters is developed in Matlab and Simulink. The objective is to minimize sprung mass acceleration. A genetic algorithm is run for 51 generations to optimize the parameters. The optimized parameters found are reported, and plots show the genetic algorithm converged on optimal solutions. The optimized suspension model response matches the goal of minimizing sprung mass acceleration compared to initial arbitrary parameter values.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
47
OPTIMIZATION OF VEHICLE SUSPENSION SYSTEM
USING GENETIC ALGORITHM
Ranjeet kumar S. Gupta1
, Vilas Sonawane2
, Dr. D. S. S. Sudhakar3
1
Asst. Prof., Mechanical Engg. Dept., D.J. Sanghvi College of Engineering, Mumbai, India,
2
SGGS Institute of Technology, Mechanical Dept., Nanded, India
3
HOD, Production Engg. Dept., Fr. Conceicao Rodrigues College of Engineering, Mumbai, India,
ABSTRACT
Modeling the suspension of an automobile is of interest for many automotive and vibration
engineers. Of importance for these engineers is the ride quality of the vehicle traversing over broken
roads and control of body motion. When traveling over rough terrain, the vehicle exhibits bounce (up
and down), pitch (rotation about the center of gravity along the vehicle's length) and roll (rotation
about the center of gravity along the vehicle's width) motions.
Optimization of vehicle ride and handling performance must meet many competing
requirements. For example, vibration in the frequency range that causes driver discomfort needs to
be minimized, which requires decreasing suspension stiffness. Yet the suspension deflection should
stay within travel constraints, so suspension stiffness needs to be increased. The traditional practice
of relying on test cars for suspension development is time consuming and costly.
In this paper, we will demonstrate a simulation-led design approach, which reduces reliance
on test vehicles and produces optimal results. The approach starts with the development of a fast and
accurate vehicle model in Matlab®
and Simulink®
combined for testing the parameters, and
concludes by automated optimization of suspension parameters using Genetic Algorithm, to meet
performance requirements specified. This would produce more applicable results of industrial and
commercial merit.
Keywords: Optimization, Vehicle Suspension, Genetic Algorithm, Matlab, Simulink
1. INTRODUCTION
There is a clear trend in industry towards more complex products spanning over several
engineering domains. Simultaneously, there is a pressure on developing products faster, at
competitive prices, and to a high quality standard. In order to meet these demands, manufacturing
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND
TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 6, Issue 2, February (2015), pp. 47-55
© IAEME: www.iaeme.com/IJMET.asp
Journal Impact Factor (2015): 8.8293 (Calculated by GISI)
www.jifactor.com
IJMET
© I A E M E

2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
48
companies have been forced to focus their efforts on the development process. In that respect, one
issue has been to ensure the efficiency of the development process, which has resulted in methods to
analyze and manage the design process. Another issue has been to develop tools and techniques that
support the design of complex products, which has produced a wealth of computerized engineering
tools. As the computational capabilities of the computers increase, the scope for simulation and
numerical optimization is enlarged. A great part of the design process will always be intuitive.
However, analytical techniques, simulation models and numerical optimization could be of great
value and can permit vast improvements in design.
The first issue is to ensure an efficient design process. In this paper, a design process
modeling approach is presented where simulation is employed in order to predict the performance of
the design process in terms of lead-time and cost. Design process modeling gives enhanced
understanding of the properties of the process, which is important as a thorough understanding of the
design process forms the basis for further process improvements. With the help of design process
models, different competing design processes can be compared and evaluated based on process lead-
time and costs.
The second issue focuses on how to improve the design of complex systems by employing
simulation and optimization techniques. As widely recognized, engineering design is an iterative
process where new design proposals are generated and evaluated. According to Roosenburg and
Eekels[9], the iterative part of the design process consists of synthesis, simulation, evaluation and
decision. For each provisional design, the expected properties are predicted using simulation models,
which are then compared to the requirements on the system. If the design does not meet the
requirements it is modified and evaluated again in the search for the best possible design. Based on
this description, it could be seen that design is essentially an optimization process. In order to raise
the level of automation, and thereby speed up parts of the process, the optimization could be
formalized and an optimization algorithm introduced.
The presence of several conflicting objectives is typical for engineering design problems. In
many cases where optimization techniques are utilized, the multiple objectives are aggregated into
one single objective function. Optimization is then conducted with one optimal design as the result.
The result is then strongly dependent on how the objectives are aggregated.
Here a multiobjective problem is solved aggregating it into a single objective genetic
algorithm applied to support the design of a passenger vehicle suspension system. The outcome from
this optimization is a set of Pareto optimal solutions that visualizes the tradeoffs between system
performance and design. The solution is quickly achieved using GA tool of Matlab®
In real-world situations, system parameters will always include variations to some extent, and
this fact is likely to influence the performance of the system. However, we want the system to be
robust and perform well under a wide range of operational conditions. Therefore we need to answer
not only the question What is best? but also What is sufficiently robust?
Genetic algorithms (GAs) and the closely related evolutionary algorithms are a class of non-
gradient methods which has grown in popularity ever since Rechenberg [7] and Holland [1] first
published their work on the subject in the early 70s. For a more comprehensive study of genetic
algorithms, see Goldbergs [1] splendid book on the subject.
Genetic algorithms are modeled after mechanisms of natural selection. Each optimization
parameter (xn)is encoded by a gene using an appropriate representation, such as a real number or a
string of bits. The corresponding genes for all parameters x1...xn form a chromosome capable of
describing an individual design solution. A set of chromosomes representing several individual
design solutions comprises a population where the fittest are selected to reproduce. Mating is
performed using crossover to combine genes from different parents to produce children. The children
are inserted into the population and the procedure starts over again, thus creating an artificial
Darwinian environment.

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
49
2. MATHEMATICAL MODEL
A vehicle suspension system is a complex vibration system having multiple degrees of
freedom [3]. The purpose of the suspension system is to isolate the vehicle body from the road
inputs. Various aspects of the dynamics associated with the vehicle put different requirements on the
components of the suspension system. Passenger ride comfort requires that the acceleration of the
sprung mass be relatively smaller whereas the lateral dynamic performance requires good road
holding which needs consistent normal force between the road and the tires. This all has to work
within the maximum allowed deflection of the suspension spring and limitations of the dynamic tire
deflection [6].
An automobile traveling along a level road at a constant speed v0 encounters a speed bump
shown in (1). The vehicles suspension system (front and rear springs and shock absorbers) is
modeled by linear springs and dampers, and the compliance of the tires is modeled by front and rear
springs. The vehicle cab motion is limited to heave in the y-direction and a small amount of pitch
ϴof the vehicles longitudinal axis [4]. The tires are assumed to remain in contact with the road
surface at all times.
The road profile is responsible for the systems input, the height of the road (with respect to
some reference) underneath the front and rear tires, respectively. The system has three translational
degrees of freedom, y, yf, yr which are the vertical displacements of the vehicle cab and both front
and rear axles from their equilibrium positions. The lone rotational degree of freedom is the pitch
angle ϴ.
The model equations are listed as follows:
M‫ݕ‬ሷ = Kfs[yf-(y + Lf ϴ)] + Bf [‫ݕ‬ሶf - (‫ݕ‬ሶ+ Lfߐሶ)] + krs[yr - (y - Lrϴ)
+ Br[‫ݕ‬ሶ௥- (‫ݕ‬ሶ - Lrߐሶ)](Eqn. 1)
M‫ݕ‬ሷ = - (Kfs + Krs)y - (Bf + Br)‫ݕ‬ሶ + Kfsyf + Bf ‫ݕ‬ሶf + Krsyr + Br‫ݕ‬ሶ௥ + (KrsLr - KfsLf) ϴ
+ (BrLr- Bf Lf)ߐሶ(Eqn. 2)
Figure 1: Moving vehicle and suspension system model.

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
50
Mf‫ݕ‬ሷ௙ = - Kfs[yf - (y + Lf ϴ)] - Bf [‫ݕ‬ሶf - (‫ݕ‬ሶ + ‫ܮ‬௙ߐሶ)] + Kft(uf - yf)
= - (Kfs + Kft)yf - Bf‫ݕ‬ሶf + Kfsy + Bf‫ݕ‬ሶ + KfsLf ϴ + Bf Lfߐሶ+ Kftuf(Eqn. 3)
Mr‫ݕ‬ሷ௥ = - Krs[yr - (y - Lrϴ)] - Br[‫ݕ‬ሶ௥ - (‫ݕ‬ሶ- Lrߐሶ)] + Krt(ur - yr)
= - (Krs + Krt)yr - Br‫ݕ‬ሶ௥ + Krsy + Br‫ݕ‬ሶ- KrsLr ϴ - BrLr ߐሶ+ Krtur(Eqn. 4)
lߐሷ = Kfs[yf - (y + Lf ϴ)] + Bf [‫ݕ‬ሶf - (‫ݕ‬ሶ + Lf ߐሶ )]Lf - Krs[yr - (y - Lrϴ)]
+ Br[‫ݕ‬ሶ௥ - (‫ݕ‬ሶ - Lr ߐሶ)]Lr(Eqn. 5)
On this basis the following Simulink®
Model is created.
Figure 2: Simulink®
Model.
3. OPTIMIZATION
Optimization objective is to minimize the sprung mass acceleration of the quarter car model.
So the required comfort is obtained from the system. For the above requirement we use the objective
function which is tness function for Genetic Algorithm (GA) op-timization process [10]. According
to James principal, the root mean square (RMS) of sprung mass acceleration can be expressed as:
ߙሷ௦ሺ݉௨, ݉௦, ‫ܭ‬௧, ‫,ܭ‬ ‫ܥ‬ሻ = ඨߨܴܸ[
௄೟஼
ଶ௠ೞ
ቀ
య
మ
ቁ
௄
ቀ
భ
మ
ቁ
+
ሺ௠ೠା௠ೞሻ௄మ
ଶ஼௠ೞ
మ ](Eqn. 5)
The optimization results are derived for a vehicle having front and rear as same con-
gurations, travelling at the speed of 30 m/s on the road with an irregularity coefficient of power
spectrum taking the value of 6.5x10-6
m3
.

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
51
4. RESULTS AND CONCLUSIONS
The total number of generations to study was not determined before testing began. Because
of the complex nature of the genetic algorithm and time limitations for the number of possible
generations run, it was decided to start the genetic algorithm and observe how the genetic algorithm
progressed before convergence criteria were set. In the end, the algorithm was terminated at the 51st
generation.
Provided the lower and upper bounds for the variables as per shown in the table followed:
Table 1: Bounds for the Optimization Problem.
Parameters
Bounds
Lower Upper
mu (Kg) 25 40
ms (Kg) 400 550
Kt (N/m) 420000 700000
K (N/m) 60000 90000
C (Ns/m) 1900 3100
After running the GA Optimisation, the optimised values of the variables are as follows:
mu = 25.903 Kg.
ms = 418.389 Kg.
Kt = 435,301.526 N/m.
K = 61,531 N/m.
C = 3004.699 Ns/m.
The plot of the optimization run is as shown:
Figure 3: Plot of Average between Individuals and the Best, Worst and Mean values for each
iteration.

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
52
Figure 4: Plot of Average Fitness of Individuals.
Due to the overall conformity of the generation and the fact that the total error bars on the
average parent variable values encompassed both the high parameter values and the average
parameter values it was determined that further testing with a higher n generations was not likely to
yield a stronger solution. While there is no guar-antee that the best solution found is indeed the
optimal con guration, it is, with several other similar parameters, a very strong solution. In this
regard, the time available was also a factor in the termination of the genetic algorithm. If more time
were available more generations could have been tested to increase the level of con dence that the
best solution had been found.
One can see clearly that maximum, minimum, and average parameters values all ap-proach
towards optimum in Figure with increasing generation number , indicating that the genetic algorithm
was functioning correctly.
Due to the overall conformity of the generation and the fact that the total error bars on the
average parent variable values encompassed both the high parameter values and the average
parameter values (see Fig. 3) it was determined that further testing with a higher n generations was
not likely to yield a stronger solution. While there is no guarantee that the best solution found is
indeed the optimal configuration, it is, with several other similar parameters, a very strong solution.
In this regard, the time available was also a factor in the termination of the genetic algorithm. If more
time were available more generations could have been tested to increase the level of confidence that
the best solution had been found.
One can see clearly that maximum, minimum, and average parameters values all approach
towards optimum in Figure with increasing generation number, indicating that the genetic algorithm
was functioning correctly.
Figure 5: Plot of Stopping Criteria.

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
53
Figure 6: Termination of Optimization.
The results that we are obtaining from GA optimization can be verified by checking the
response of our Simulink® Model. First we just take some arbitrary values from the ranges, and get
the response for these values. Then we'll compare the results which we are getting from our GA
optimized parameters.
The output of the model are namely the body deflection, front deflection, rear deflection and
the pitch. It is shown by the plot represented as in Fig. 5 and 6. The displacements is much reduced
as compared to a that generated by arbitrary parameter values. Also there is subsequent reduction in
the front and rear deflection of the vehicle; and the pitch (theta) is reduced as well.
Figure 5: Response of the Model for the General Parameter Values.

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
54
Figure 6: Response of the Model for the Optimized Parameter Values.
This proves that the parameter values that we are getting from GA optimization are actually
optimized for the vehicles response.
As GA is an discrete optimization technique, i.e. it comes out with a different set of results
for the same optimization problem in every subsequent run. And also the objective function value is
optimized to almost to the same extent. Hence for every run, with same set of parameters and
conditions the optimized parameter values will be substantially different. Still it can be taken as an
advantage that there are multiple set of solutions available through GA; unlike many other
optimization technique that tend to give only one solution.
5. CONCLUSION
The integration of the optimization algorithms with the vehicle model has been success-fully
achieved allowing for an automated optimization process. It has been learnt that GA is verily suitable
for such kind of iterative design problems. The number of parameters as applicable was
appropriately selected by the algorithm for the optimized RMS of sprung mass acceleration. And
also the parameters selected for optimization were infact ideal.
Usage of Matlab®
for the application of the optimization algorithm i.e. GA made it very easy;
else otherwise the massive amount of calculations to be carried for 'n' number of generations would
have been practically impossible. It also gave the advantage of quickly adapting to the changes as per
the algorithm to provide with the systems response.
6. REFERENCES
1. GOLDBERG D., 1989, Genetic Algorithms in Search and Machine Learning Reading,
Addison Wesley.
2. BALL M., FLEISCHER M., CHURCH D., A Product Design System Employing
Optimization-based Tradeoff analysis, in Proceedings of ASME DETC Design Theory and
Methodology Conference, Baltimore, USA, September 10-13, 2000.
3. ESCHENAUER H., KOSKI J., AND OSYCZKA A., "Multicriteria Design Optimization,"
Berlin: Springer-Verlag, 1990.

9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 47-55© IAEME
55
4. HORN J., "Multicriterion decision making", Handbook of Evolutionary Computation, T.
Bck, D. Fogel, and Z. Michalewicz, Eds., IOP Publishing Ltd. and Oxford University Press,
1997.
5. KEENEY R. AND RAIFFA H., "Decisions with multiple objectives – preferences and value
tradeoffs", John Wiley & Sons, New York, USA, 1976.
6. MANETSCH T. J., "Toward effcient global optimization in large dynamic systems - The
adaptive complex method", IEEE Transactions on Systems, Man &Cybernetics, vol. 20, pp.
257-261, 1990.
7. PAHL G. AND BEITZ W., Engineering Design A Systematic Approach, Springer-Verlag,
London, 1996.
8. PHADKE M. S., Quality Engineering Using Robust Design., Springer- Prentice Hall, 1989.
9. ROOZENBURG N. AND EEKELS J., Product Design: Fundamentals and Methods,
Springer- John Wiley & Sons Inc, 1995.
10. PROF. D. A. HULLENDER., Modeling and Simulation of Engineering Systems, Springer-
Course Notebook for Dynamic Systems Modeling.
11. Chaitanya Kuber, “Modelling Simulation And Control of an Active Suspension System”
International Journal of Mechanical Engineering & Technology (IJMET), Volume 5, Issue
11, 2014, pp. 66 - 75, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.
12. Alok Kumar Pandey and Dr R. P. Sharma, “Simulation of Eight Wheeled Rocker Bogie
Suspension System Using Matlab” International Journal of Mechanical Engineering &
Technology (IJMET), Volume 4, Issue 2, 2013, pp. 436 - 443, ISSN Print: 0976 – 6340,
ISSN Online: 0976 – 6359.
13. Flt Lt Dinesh Kumar Gupta, “Linear Programming In Matlab” International Journal of
Industrial Engineering Research and Development (IJIERD), Volume 4, Issue 1, 2013, pp. 19
- 24, ISSN Online: 0976 - 6979, ISSN Print: 0976 – 6987.