Evolutionary Testing Approach for Solving Path- Oriented Multivariate Problems

Short Paper
ACEEE Int. J. on Information Technology, Vol. 3, No. 1, March 2013

Evolutionary Testing Approach for Solving Path-
Oriented Multivariate Problems
P.Maragathavalli1 and S.Kanmani2
1
Pondicherry Engineering College /Department of Information Technology, Puducherry, India
E-mail:marapriya@pec.edu
2
Pondicherry Engineering College /Department of Information Technology, Puducherry, India
E-mail:kanmani@pec.edu

Abstract— A multivariate approach involves varying number mation of multiple fitness values named random weighted
of objectives to be satisfied simultaneously in testing process. genetic algorithm (RWGA); another approach is consider-
An evolutionary approach, genetic algorithm is taken for ing multiple objectives at a time and generating Pareto opti-
solving multivariate problems in software engineering. The mal solution set named diversity based or non-dominated
Multivariate Optimization Problem (M OP) has a set of
sorting genetic algorithm (NSGA) [4] [7] [8].
solutions, each of which satisfies the objectives at an acceptable
level. Another evolutionary algorithm named SBGA (stage-
based genetic algorithm) with two stages is attempted for II. EXISTING METHODS
solving problems with multiple objectives like cost Genetic algorithms are the most popular heuristic
minimization, time reduction and maximizing early fault
technique to solve Multi-Objective Optimization Problems
deduction capabilities. In this paper, a multivariate genetic
algorithm (MGA) in terms of stages for path-based programs
[2]. A Multi-Objective Optimization Problem has a number of
is presented to get the benefits of both multi-criteria objective functions, which are to be minimized or maximized.
optimization and genetic algorithm. The multiple variables MOOP can be expressed as, fitness function fm(x), where m =
considered for test data generation are maximum path coverage 1, 2, 3… M no. of objective functions & x = single candidate
with minimum execution time and test-suite minimization. solution. The methods [1] [4] used for multi-objective
The path coverage and the no. of test cases generated using optimization are ranking, diversity and combined approach,
SBGA are experimented with low, medium and high complexity NRGA [5].
object-oriented programs and compared with the existing GA
approaches. The data-flow testing of OOPs in terms of path
III. STAGE-BASED GENETIC ALGORITHM (SBGA)
coverage are resulted with almost 88%. Thus, the efficiency
of generated testcases has been improved in terms of path The design diagram of stage-based genetic algorithm by
coverage with minimum execution time as well as with the considering multiple objectives for stage-wise optimization
minimal test suite size. is shown in Fig. 1. In this paper, the multi-objective
optimization using SBGA is attempted by changing the GA
Index Terms— multivariate problems, stage-based genetic
al gori thm, p ath coverag e, executi on time, test-sui te
operations with various GA parameter values. Instead of
reduction, evolutionary testing. two-point crossover and mutation, uniform crossover and
SBGA i.e. non-dominated sorting genetic algorithm [2] [6]
I. INTRODUCTION which use two stages in generating test cases.The test case
selection for next generation uses ranking of fitness values.
Evolutionary algorithms which are more advanced heu- By seeing the dominance between test cases, the test case is
ristic search techniques have been successfully applied in being selected for next iteration. In one-stage, sequencing
the area of software testing. For a large search space and of methods will take place and in another-stage the values
getting optimal set of solutions GA is the best choice in soft- will be passed to methods.
ware testing. Commonly, these techniques are referred as
evolutionary testing. Evolutionary testing tries to improve A. Input Representation
the effectiveness and efficiency of the testing process by The input representation is in the form of control flow
transforming testing objectives into search problems, and graphs (CFGs) and the output will be the generated test cases.
applying evolutionary similarity mutation is taken as new GA CFG will give the dependencies between variables associated
operators. Approaches, like ideal and preference are used in with specific nodes. Control-flow graph of classes (CCFG)
computation in order to solve them. In this testing of soft- For representing test objects in object-oriented programs by
ware can be done with a single objective or with multiple using CFGs in which a directed graph G = (N, E) where nodes
objectives [1][3]. Instead of fixing only one criteria or quality represent methods and edges represent procedure calls. The
parameter for generating test cases, multiple objectives like class control-flow graph (CCFG) is a class-call graph [2] [6] in
minimizing the time & cost and no. of test cases simulta- which each node is replaced with the control-flow graph of
neously maximizing the coverage (i.e., the test requirements) the corresponding method and all methods of the class are
would be considered. The techniques used in GA for multi- connected together by edges.
criteria optimization are of two types: one approach is sum Control-flow graph of classes (CCFG)
© 2013 ACEEE 54
DOI: 01.IJIT.3.1. 1100

Short Paper

For representing test objects in object-oriented programs by
using CFGs in which a directed graph G = (N, E) where nodes
represent methods and edges represent procedure calls. The
class control-flow graph (CCFG) is a class-call graph [2] [6] in
which each node is replaced with the control-flow graph of
the corresponding method and all methods of the class are
connected together by edges.

Fig. 2. Stack program as an example
parents go to offspring. The mutation is done using similarity
Fig. 1. Stage-Based Genetic Algorithm – An Evolutionary Approach mutation in which a similar gene is replaced with a different
test case.
B. Test criteria and Chromosome Representation
TABLE I. GA OPERATORS
The test criteria for generating test cases consists of a
triple [d, u, a] where‘d’ def_node, ‘u’ use_node & ‘a’
associated variable. For example, consider the stack program
with single class in Fig. 2; the criteria will be of the form [7, 11,
top]. A test case consists of a sequence of methods
invocation appended by their parameter values [1][2]. The
‘chromosome’ for a given criteria [d, u, a] contains the
following:
Invocation of a constructor ‘c’
Fitness function ft(vi) = ½(cov_d / tot_d) + ½(cov_u / tot_u)
Method md that causes the execution of ‘d’
* I = no. of chromosomes in next generation / no. of
Method mu that causes the execution of ‘u’
chromosomes in current generation
Values to the parameters ‘v’
TABLE II. GA PARAMETERS
C. Test Data Generation
The parameters and operators considered for test data
generation in GA, their initial and range of values are tabulated
in tableI and the results are shown in table II. The crossover
used for getting the offsprings is uniform crossover which
uses a fixed mixing ratio between two parents. For example, if
the mixing ratio is 0.5, then half of the genes from both the

© 2013 ACEEE 55
DOI: 01.IJIT.3.1.1100

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IV. EXPERIMENT covers only 87%. For print-token2, SBGA covers 96% with
ET = 5140ms and GA 86% with 5990ms. The parameter
A. Test Data
Immigration rate, ‘I’ value should be minimum; since the ‘I’
Initially, simple java programs upto 200 lines of code are value is taken from the difference between the current
experimented with various coverage criterions. The results generation test cases (chromosomes) and the initial test
are satisfactory, and then five programs from Software cases, the value of new generation chromosomes should be
Infrastructure Repository with equal complexity are taken for minimum.
experiment; the lines of code are from the range (200-800). For example, when 10 test cases is reduced to 4, the value
The no of classes are in the range of (1, 2, 4 … 24) and the will be 0.4; reduced to 3, then 0.3; so, when I is less, small no
branches of upto 60 are taken for experimentation. No. of of test cases are resulted; I is high, optimal set contains more
generations is from 95 to 150 with the interval of 5; one era no. of test cases; i.e. I = 4/10 = 0.4 ; I = 3/10 = 0.3; I = 5/10
can have max. of 30 generations. The path coverage is = 0.5. The value 10 is only for an example; so, it need not be
predicted as a ratio between the conditions covered by the 10; 8/20 or some, 6/20 etc. On the whole, the no. of conditions
total no. of conditions in the tested program and presented satisfied by SBGA is more when compared to GA and is the
in %. results are tabulated in table III.
B. Result Analysis The execution time variation for both SBGA and GA is
shown in graph 1; Test data generation time for each program
Programs like array-partition, ordset, replace, and
varies from 2200 – 5990 ms. When no of classes and variables
schedule2 gives better coverage results in fast execution;
are more, the time is also be more; the conditions to be
because, the number of conditions to be checked for selecting
checked by test data increases, execution time will also be
test cases are less whereas in print-token2 and traffic collision
increased directly. Search time is a main criterion in GA for
avoidance system (TCAS) type of programs classes and
test data generation. So, that should be minimized. By using
conditions are more almost 60, so takes more time for execution.
SBGA, the overall testing time is reduced by minimizing the
In TCAS, each and every vehicle should be monitored to
total no of test cases generated. Reduction in test suite in
order to avoid collision; so, takes more time to run the system
terms of immigration rate ‘I’ is also shown in graph 1. Total no
with execution time of 4265ms in SBGA whereas GA takes
of chromosomes reduction is reflected in ‘I’; initially, the rate
4912ms. The path coverage results are 97% in SBGA, GA
TABLE III. RESULTS OBTAINED FOR SAMPLE JAVA PROGRAMS

© 2013 ACEEE 56
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Graph. 1. Execution time in ms and Immigration rate ‘I’ results in SBGA and GA

is fixed as 0.3-0.9. In real scenario, SBGA ranges from 0.3-0.5 [2] Ahmed S. Ghiduk, “Automatic Generation of Object-Oriented
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Evolutionary Algorithms, Multi-Objective Optimization
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© 2013 ACEEE 57
DOI: 01.IJIT.3.1. 1100

Evolutionary Testing Approach for Solving Path- Oriented Multivariate Problems

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Evolutionary Testing Approach for Solving Path- Oriented Multivariate Problems