International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
Study of Optimal Mutation factor for Genetic
Algorithm (GA).
Waghoo Parvez1, Sonal Dhar2
1
Department of Mechanical Engg, Mumbai University, MHSSCOE, Mumbai – 400008
2
Department of Production Engg, Mumbai University, DJSCOE, Mumbai – 410206
ABSTRACT
Genetic Algorithm (GA) was invented by John Holland in around 1975. Genetic Algorithm has a number of operator’s viz.
Selection, Crossover, Mutation. Mutation is one of the basic operators of Genetic Algorithm. Several techniques of mutation
are proposed with their merits and de-merits in various books and technical papers. This paper presents study on random
mutation technique in order to find out the optimum probability of mutation. GA program is executed on a static environment
for path planning of a robot.
Keywords: Mutation, Genetic Algorithm, path planning.
1. INTRODUCTION
Path planning is a term used in robotics for the process of detailing a task into discrete motions. It is a process to
compute a collision-free path between the initial and final configuration for a rigid or articulated object (the "robot")
among obstacles. It is aimed at enabling robots with capabilities of automatically deciding and executing a sequence
motion in order to achieve a task without collision with other objects in a given environment. [1]
The Genetic algorithm is an adaptive heuristic search method based on population genetics. Genetic algorithm were
introduced by John Holland in the early 1970s [2].Genetic algorithm is a probabilistic search algorithm based on the
mechanics of natural selection and natural genetics. Genetic algorithm is started with a set of solutions called
population. A solution is represented by a chromosome. The population size is preserved throughout each generation.
At each generation, fitness of each chromosome is evaluated, and then chromosomes for the next generation are
probabilistically selected according to their fitness values [3].
A genetic algorithm is a search technique used in computing to find exact or approximate solutions to optimization and
search problems. Genetic algorithms are categorized as global search heuristics. Genetic algorithms are a particular
class of evolutionary algorithms (EA) that use techniques inspired by evolutionary biology such as inheritance,
mutation, selection, and crossover [4]. Genetic algorithms have been used to find optimal solutions to complex
problems in various domains such as biology, engineering, computer science, and social science.
Genetic algorithms fall under the heading of evolutionary algorithm. Evolutionary algorithms are used to solve
problems that do not already have a well defined efficient solution [5]. Genetic algorithm have been used to solve
optimization problems (scheduling, shortest path, etc), and in modeling systems where randomness is involved (e.g.,
the stock market).
The organization of the thesis is as follows
Section 2 consists of the work done by other authors on topic related to the work.
Section 3 consists of environment design and assumptions made in study.
Section 4 is the actual study which is done by running the program collecting the date and plotting of results.
Section 5 summarizes the result and discussion.
Section 6 gives the conclusion.
2. RELATED WORK
Recently number of researchers have studied the operators of GA and developed new techniques for the operators and
compared the techniques with one another. Greenwell [6] et.al studied the performance of various mutation techniques
of GA in order to maximize the fitness function. Fuat Erbatur et al [7] studied and analyzed various crossover
techniques based on optimal structural design and proposed two new developed crossover technique. Srinivas et al [8]
described an efficient approach for multimodal optimization using GA and recommended adaptive probabilities of
Volume 2, Issue 6, June 2013
Page 429
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
crossover and mutation. Thomas back [9] has discussed three fitness function counting one problem, standard binary
encoded integer and grey coded integer problem.
3. ENVIRONMENT & PROBLEM STATEMENT
3.1 Representation of Environment
Many path planning methods use a grid-based model to represent the environment space as shown in Fig. 1. It has been
determined that calculation of distance and representation of obstacle is easier with grid-based representation. The gridbased environment space is represented in two ways, by the way of an orderly numbered grid or by the way of (x, y)
coordinates plane. It has been found that the orderly numbered grid representation is widely used; therefore this
representation method is used in the present study. [10]
3.2 Fitness Function
The objective function plays a key role in the reproduction process in terms of obtaining feasible and high fitness
solution. Generally in the path planning problems the objective function is considered as the shortest path (1). Optimal
path may be the shortest and may lead to least time. Objective value is the sum of distances between each grid.
n-1
F = ∑ d (gi,gi+1)
(1)
j=1
d (gi,gi+1) = √ [(x1-x2)2 + (y1 – y2)2 ]
(2)
3.3 Problem Assumption [11]
1. The environment is modeled in 2-D space.
2. The environment and obstacles are of polygon shape.
3. The boundary of every obstacle is expanded by an amount that is equal to half of the greater size in the length &
width of the robot.
4. The environment is of 10 X 10 units.
5. It should always travel the centre of the grid.
6. It always starts from 0 and terminates at 99.
3.4 Operator Values
The program was executed on Sony Vaio Laptop with 2 GHz processor and 2G RAM.
Operators of GA:
Population size
= 120
Crossover Operator
= 0.3
Mutation Operator
= Varied from 0 ~ 0.8
No. of generations/iterations = 50
4. STUDY OF EFFECT OF MUTATION FACTOR
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Figure 1 Environment No. 1
Volume 2, Issue 6, June 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
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Figure 2 Environment No. 2
33 - Defines obstacle (in yellow colour)
Table 1: Fitness Values for the two environments
Environment No
Fig No
Fitness Value
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13.8995
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14.4853
Figure 3 Fitness Value vs Mutation Rate for Environment 1.
Figure 4 Fitness Value vs Mutation Rate for Environment 2.
Volume 2, Issue 6, June 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
5. RESULTS AND DISCUSSIONS
The program was run 10 times and the average result of 10 readings was taken to plot the graph. The results of
variation in the mutation factor of Genetic Algorithm can be seen in fig 3 & 4. The results indicate that as the mutation
factor lies in the range of 0 – 0.3 there is not much change in the fitness function but as the value increases beyond 0.3
the fitness function changes.
6. CONCLUSION
This experiment was carried out on a static environment for path planning. Similarly experiments can be performed on
various applications of GA and the results can be compared. Further new techniques can be generated to give more
optimum results than the present ones.
References
[1.] http://en.wikipedia.org/wiki/Motion_
[2.] Manoj Kumar, Mohammad Husian, Naveen Upreti, & Deepti Gupta (2010) “Genetic Algorithm: Review &
Application” International Journal of Information Technology and Knowledge Management July-December 2010,
Volume 2, No. 2, pp. 451-454.
[3.] Buniyamin N et al (2011) “Robot global path planning overview and a variation of ant colony system algorithm”
International Journal of Mathematics and computers in simulation Issue 1Volume 5 2011 9-16.
[4.] David E. Goldberg, Genetic Algorithms in search, optimization & Machine Learning“(Pearson Education Twelfth
Impression 2013).
[5.] Melanie Mitchell, an Introduction to Genetic Algorithms (Prentice Hall of India Edition 2005).
[6.] Greenwell, R. N., Angus, J. E., & Finck, M. (1995). Optimal mutation probability for genetic algorithms.
Mathematical and computer modelling, 21(8), 1-11.
[7.] Hasançebi, O., & Erbatur, F. (2000). Evaluation of crossover techniques in genetic algorithm based optimum
structural design. Computers & Structures,78(1), 435-448
[8.] Srinivas, M., & Patnaik, L. M. (1994). Adaptive probabilities of crossover and mutation in genetic algorithms.
Systems, Man and Cybernetics, IEEE Transactions on, 24(4), 656-667.
[9.] BVack, T. (1993). Optimal M utation Rates in Genetic Search.
[10.] Tuncer, A., & Yildirim, M. (2012). Dynamic path planning of mobile robots with improved genetic algorithm.
Computers & Electrical Engineering.
[11.] Waghoo Parvez & Sonal Dhar (2013)‘Path Planning of Robot in static environment using Genetic Algorithm
(GA) Technique’ Accepted for publication in International Journal of Advances in Engineering & Technology.
AUTHOR
Waghoo Parvez has completed his graduation in 2009 from University of Mumbai India with a Bachelor
Degree in Production Engineering.. He is currently working as a lecturer in MHSSCOE and pursuing his
Masters in Mechanical Engineering with specialisation in manufacturing systems engineering from
University of Mumbai. His research interest is in path planning, CAD, Algorithms, Manufacturing.
Sonal Dhar graduated from Sardar Patel University India with a Bachelor Degree in Mechanical
Engineering in 1994. She then pursued her Masters in Mechanical Engineering with specialization in
CAD/CAM & Robotics from Mumbai University in 2005.She is working as an Assistant Professor in
DJSCOE Mumbai. Her research interest is CAD/CAM, Automation, path planning, FMS.
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