Genetic Algorithm Based on Sorting Techniques

Parul Aggrawal; Faisal Naved; Mohd Haider

doi:10.12691/jcsa-3-2-4

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Genetic Algorithm Based on Sorting Techniques

Parul Aggrawal^1,, Faisal Naved¹, Mohd Haider¹

¹Department of Computer Science, Jamia Hamdard University, New Delhi-62, India

Abstract

1. Introduction

2. Related Work

3. Experimental Results

Abstract

Genetic Algorithm, an Artificial Intelligence approach is based on the theory of natural selection and evolution. Traditional methods of sorting data are too slow in finding an efficient solution when the input data is too large. In contrast, Genetic Algorithm generates fittest solutions to a problem by exploiting new regions in the search space. This paper targets the three most commonly used Bubble, Selection and Insertion sorting techniques and executes memory on an input ranging from 1,000 to 10,000 where the input is entered in increasing, decreasing and random order. It mainly uses the Genetic Algorithm approach to optimize the effect of the three algorithms by generating an output which is consistent in terms of time variations which is not otherwise. This has been achieved by exploiting the property of Genetic Algorithm by choosing best parameter for population size, encoding, selection criteria, operator choice and optimized fitness function.

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Keywords: genetic algorithm, sorting, selection, crossover, mutation

Journal of Computer Sciences and Applications, 2015 3 (2), pp 40-45.
DOI: 10.12691/jcsa-3-2-4

Received March 18, 2015; Revised April 03, 2015; Accepted April 16, 2015

Cite this article:

Aggrawal, Parul, Faisal Naved, and Mohd Haider. "Genetic Algorithm Based on Sorting Techniques." Journal of Computer Sciences and Applications 3.2 (2015): 40-45.

Aggrawal, P. , Naved, F. , & Haider, M. (2015). Genetic Algorithm Based on Sorting Techniques. Journal of Computer Sciences and Applications, 3(2), 40-45.

Aggrawal, Parul, Faisal Naved, and Mohd Haider. "Genetic Algorithm Based on Sorting Techniques." Journal of Computer Sciences and Applications 3, no. 2 (2015): 40-45.

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1. Introduction

Section 1 of this paper comprises of introduction to the basic sorting and Genetic Algorithm. Section 2 comprises of related work in which average elapsed time is calculated at different inputs for Bubble, Insertion and Selection Sort. Section 3 contains the Experimental Results in which Inconsistency in Bubble Sort, Insertion sort and Selection sort is shown when inputs are entered in increasing order, decreasing order and randomly. Section 4 is the proposed work containing the Algorithm. Section 5 is the Conclusion and future scope. Section 6 are the references in support to the research paper

Sorting is considered as the most fundamental problem while studying Algorithms. The basic principle behind sorting a sequence of n numbers is that its elements are placed randomly and needs to be reordered in ascending order..Search preprocessing is the most important application of sorting. When the values are in sorted order, a better approach is to use binary search. O (n2) time proportion will be taken by an inefficient algorithm where n is equal to the number of elements in an array, whereas, an efficient algorithm takes O (n. lgn) time proportion to sort sequence of numbers where n is the size of the array.For small inputs, we cannot see a big difference, but if we have a larger input (say Population of a city) we can see that an enormous amount of usability played off between the efficient and inefficient algorithms:

Population of a city: =6 million people

n=6 X 10⁶steps needed

n²=36 X 10¹²

=3600 X 10¹⁰

=3600 seconds (Assuming that 10¹⁰steps are executed in 1 sec)

n.lgn =10⁶X 20 X 36 => 1 sec

So, if we have to sort a population of 6 million people, only 1 sec is taken by efficient algorithm.

O (n log n) time is needed to sort large data because, sorting by 0 (n²) becomes impossible if we have a large data. There are lots of applications, besides simply looking for the maximum or minimum:-- For finding duplicates in a set: sort first, then duplicates will appear next to each other, and can be found by scanning through the sorted array. In finding similar values. In Histograms (counting frequencies): sort first, then do a single pass: repeated items will occur in bunches, and can be counted easily. Note that there are other ways to this. Intersection: given two arrays, what values do they have in common? Sort both of them, and march down both lists, advancing down the list with the smaller value each time. You will find the common values easily. Setting data up for later fast searching: if your data is sorted, you can use binary search to find values in O (log (n)) time.

Sorting is defined as follow:

Input: A sequence of n numbers < A₁, A₂, A₃……………. A_n>

Output: A permutation (reordering) < A_1’, A2, ’, A3, ’……………. A_n’> of input sequence such that A_1’ <= A_2’ <=……… <= A_n’.^[4]

There are several sorting algorithms. Some of them are Bubble sort, Selection Sort, Insertion Sort, Quick sort, Merge sort, Heap sort, Counting Sort, Radix sort, Bucket sort. The Time and Space Complexities of these sorting techniques are:

1.1. Genetic Algorithm

Genetic Algorithms ^[1] are the adaptive heuristic search algorithms which are based on the process of growth and development ^[2]. The basic concept of genetic algorithm follows the principle of survival of the fittest, which was given by Charles Darwin. In 1960’s ^[2], John Holland discovered the genetic algorithm. This is the process of moving the chromosome of one population to a new population with the help of some operators such as selection, crossover and mutation.

A population is comprised of a finite value of chromosomes, each chromosome contains a number of genes ^[3].

A gene is represented by a binary number or decimal number according to the problem or just the sake of simplicity, this gene value is sometimes called as an allele.

1.2. Some Genetic Algorithm Operators

SELECTION: - This operator is used to select chromosomes for reproduction. Fitter chromosome has a higher probability of selection.

CROSSOVER: - This operator moves the genes of two parent chromosomes to create two new child's chromosomes ^[6].

No. of crossover = (Crossover rate*number of a chromosome * number of genes in a chromosome) /100

MUTATION: - Genetic diversity from one population to another is performed by mutation operator. This alters the genes or chromosome of the population.

Steps of Genetic Algorithm: Generate an initial population randomly as you want either in binary or in decimal format. Then the fitness of each chromosome is calculated. Selection operator is applied on the population. Crossover operator is applied on the population. Mutation operator is applied on whole population. These processes are repeated until we get the fittest chromosome or until we get the output.

2. Related Work

In our approach, we have taken the three sorting algorithms namely bubble sort, insertion sort and selection sort in increasing order, decreasing order and randomly in order to check the elapsed time taken by each sorting technique. In this section we have shown the elapsed time taken by each sorting technique with the help of tables and charts. Table 1 and the corresponding chart (Figure 1) shows the average elapsed time taken by insertion sort when inputs are entered ranging from 1,000 to 10,000 first in increasing order then in decreasing order and then the inputs are taken randomly.

Table 1. Average Elapsed Time of Insertion sort at different inputs

Download as

[1]	D. Goldberg. Genetic Algorithms in Search, Optimization, and Machine
	In article

[2]	Learning. Addison-Wesley, Reading, MA, 1989. [2] David E.Goldberg,” Genetic Algorithms in search, optimization and machine learning 1^st, Addison-Wesley Longman Publishing Co., Inc. Boston ©1989
	In article

[3]	H. Bhasin and Neha Singla, “Cellular Genetic Test Data Generation”, ACM SIGSOFT Software Enginnering Notes, Vol. 38 (5), September 2013, Pages 1-9.
	In article

[4]	Introduction to Algorithm, Second Edition Thomas H.Cormen, Charles E.Leiserson, Ronald L.Rivest, Clifford Stein, Mc-Graw Hill Publications
	In article

[5]	H. Bhasin, “Cost Priority Cognizant Regression Testing”, ACM SIGSOFT Software Enginnering Notes, Vol. 39 (3), May 2014, Pages 1-7.
	In article	CrossRef

[6]	T. Back, D. B. Fogel, and Z. Michalewicz. Evolutionary Computation Vol. I & II. Institute of Physics Publishing, 2000.
	In article

Genetic Algorithm Based on Sorting Techniques

Science and Education Publishing

Genetic Algorithm Based on Sorting Techniques

Abstract

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Cite this article:

1. Introduction

2. Related Work

Table 1. Average Elapsed Time of Insertion sort at different inputs

Table 2. Average Elapsed Time of Bubble sort at different inputs

Table 3. Average Elapsed Time of Selection sort at different inputs

3. Experimental Results

Table 4. Inconsistency in Bubble Sort when inputs are entered in increasing order

Table 5. Inconsistency in Bubble Sort when inputs are entered in decreasing order

Table 6. Inconsistency in Bubble Sort when inputs are entered randomly

Table 7. Inconsistency in Insertion Sort when inputs are entered in increasing order

Table 8. Inconsistency in Insertion Sort when inputs are entered in decreasing order

Table 9. Inconsistency in Insertion Sort when inputs are entered randomly

Table 10. Inconsistency in Selection Sort when inputs are entered in increasing order

Table 11. Inconsistency in Selection Sort when inputs are entered in decreasing order

Table 12. Inconsistency in Selection Sort when inputs are entered randomly

4. Proposed Work

5. Algorithm

6. Conclusion

References

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